BIBLIOGRAPHY ROSALYN S. BAYACSAN, JANICE B....
BIBLIOGRAPHY
ROSALYN S. BAYACSAN, JANICE B. DAMULO and LAILANIE WAKAT
2008. Regression Analysis on the Academic Performance of the Bachelor of Science in
Applied Statistics Students in Statistics. Benguet State University, La Trinidad, Benguet.
Adviser: Cristina B. Ocden
ABSTRACT
This study was conducted to determine the variables that have contributions on
the academic performance of Bachelor of Science in Applied Statistics students in
Statistics. The study also aimed to construct a regression model for the factors affecting
academic performance in Statistics 11 of Bachelor of Science in Applied Statistics
students.
The population was represented by 83 Bachelor of Science in Applied Statistics
students who responded to the questionnaire administered on February 2008, at Benguet
State University, La Trinidad, Benguet.
Statistical analysis revealed that the grades in Statistics 11 was not affected by the
student’s demographic profile such as gender, type of high school graduated, family
annual income, and parents’ highest educational attainment. A positive marked
correlation existed between Statistics 11 and Mathematics 11. There are also significant
but low correlations between Statistics 11 with English 11 and with the IQ scores.
However, regression analysis revealed that only the grades in Mathematics 11 had direct
contribution to the performance of respondents in Statistics 11. The regression model
obtained is:
Y = .540 + .484X1 + .218X2 + .199X3 - .01507X4 + .01776X5 + .05577X6
(.000)
(.203) (.121) (.210) (.250) (.592)
+.03613X7-.171X8-.02033X9-.192X10-.08363x11-.03211X12-.04404X13
(.831) (.268)
(.871) (.437) (.208) (.615)
(.576)
The coefficients are the degree of correlation and the values in parenthesis are the
p-values associated with the t-test. The only variable that is linearly related to grades in
Statistics 11 is the grade in Mathematics 11 since the p-value is less than .05.
ii
TABLE OF CONTENTS
Page
Bibliography…………………………………………………………………. i
Abstract………… …………………………………………………………… i
Table of Contents ……………………………………………………………. iii
INTRODUCTION
Background of the Study…………………………………………….. 1
Objectives of the Study………………………………………………. 2
Importance of the Study……………………………………………… 3
Scope and Delimitation………………………………………………. 4
REVIEW OF LITERATURE………………………………………………... 5
THEORETICAL FRAMEWORK……………………………………………. 8
METHODOLOGY
Locale and Time of the Study………………………………………... 13
Respondents of the Study…………………………………………….. 13
Instrumentation………………………………………………………. 13
Data Gathering Procedure……………………………………………. 14
Data Analysis…………………………………………………………. 14
RESULTS AND DISCUSSION……………………………………………… 15
SUMMARY, CONCLUSION AND RECOMMENDATION
Summary……………………………………………………………... 25
Conclusion…………………………………………………………..... 25
Recommendation…………………………………………………….. 26
iii
LITERATURE CITED……………………………………………………… 27
APPENDICES
A. Request Letter to the Dean of College of Arts and Sciences……. 28
B. Survey Questionnaire Application for Oral Defense ………….... 29
C. Variable Coding ………………………………………………… 31
D. The Raw Data of the Respondents ……………………………… 32
E. Regression Analysis Printouts ………………………………..… 36
iv
1
INTRODUCTION
Background of the Study
The ability to present a solution to a problem inside the human mind is
knowledge. In a very complex environment where several unknowns are present,
one will find a way of dealing with them easily by viewing abstract mathematical
structures and drawing conclusions from scientific and logical analyses.
Mathematics plays an important role, by sharpening the intellect and developing
critical thinking.
One branch of mathematics is Statistics. It is concerned with the
collection, organization, and analysis of numerical data. The study in Statistics
emerged during the 19th century, when researchers recognized the need to reduce
bulky and unmanageable amounts of information in their studies. The solution is
to present data in the form of numerical values to avoid the ambiguous verbal
description. For this reason, Statistics is very useful in business, economics,
sociology, biology, psychology, education, physics, chemistry, agriculture and
related fields.
Statistics courses have become an essential part of many programs in
higher education. The rationale for teaching Statistics at the college level is to
enable students to handle, use, and interpret research or statistical data in their
field of study. Furthermore, teaching Statistics aims to prepare students to deal
effectively with statistical aspects of the world outside the classroom. However,
Regression Analysis on the Academic Performance of the Bachelor of Science in
Applied Statistics Students in Statistics / Rosalyn S. Bayacsan; et al. 2008
2
despite the effort instructors of Statistics devote in simplifying the subject, many
students encounter difficulties in their Statistics subjects. This is the reason why
the researchers choose to study the academic performance of BSAS students in
Statistics. They believe that the performance of students in Statistics 11
significantly affects their ability to perform well in higher Statistical subjects.
Lastly, multiple regression analysis was used for the purpose of this study.
Multiple regression analysis is a method in the explanation of phenomena and
prediction of future events. A coefficient of correlation between variables X and
Y is a quantitative index of association between these two variables. In its squared
form, as a coefficient of determination, it indicates the amount of variance
(information) in the criterion variable Y that is accounted for by the variation in
the predictor variable X. A multivariate counterpart of the coefficient of
determination is the coefficient of multiple determination, ( 2
R ) . In multiple
regression analysis, the set of predictor variables
is used to explain
variability of the criterion variable .
Objectives of the study
Specifically the study aimed: 1) to determine the factors that have
contributions to the academic performance of Bachelor of Science in Applied
Statistics students in Statistics 11. 2) to construct a model for the factors affecting
academic performance of Bachelor of Science in Applied Statistics students in
Statistics 11.
Regression Analysis on the Academic Performance of the Bachelor of Science in
Applied Statistics Students in Statistics / Rosalyn S. Bayacsan; et al. 2008
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Importance of the Study
The results of this study could provide point of reference to parents,
teachers, and school administrators on factors affecting students’ performance in
college, particularly in Statistics where most students fail.
The identification of variables that may have a contribution on the
academic performance of students in Statistics 11 could be of great help to
teachers, they would have better insight on what to prepare, and how to motivate
students. Findings of the study would also help administrators to perform their
roles in enhancing the strengths and lessening the weaknesses of the students.
To the students, knowledge on the contributory factors to their academic
performance may result to a reflection on their study habits and attitudes towards
Statistics. Through this study, the students might come to realize that passing
Statistics 11 is not as difficult as they think, because it might just be a matter of
attitude and habits. The result could also help students to realize and reflect on
their weaknesses; thus they would be encouraged to find ways to uplift
themselves.
The findings could convince parents to cooperate with the school in
guiding their children in their studies. This would also motivate them to devote
their time, attention and guidance needed by the students; to inspire them to excel
and not to fail in their performance.
Regression Analysis on the Academic Performance of the Bachelor of Science in
Applied Statistics Students in Statistics / Rosalyn S. Bayacsan; et al. 2008
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Scope and Delimitation of the Study
The focus of the study was to apply the multiple linear regression
procedure in analyzing and determining the variables that maybe related to the
respondent’s academic performance in Statistics 11. The respondents of the study
were second, third, and fourth year students enrolled in Bachelor of Science in
Applied Statistics, during the second semester of the academic year 2007-2008, at
Benguet State University, La Trinidad, Benguet.
Regression Analysis on the Academic Performance of the Bachelor of Science in
Applied Statistics Students in Statistics / Rosalyn S. Bayacsan; et al. 2008
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REVIEW OF LITERATURE
The process of determining the significant factors affecting students’
performance were chosen carefully by the researchers with consideration to the
related researches and studies done concerning the issue of students’ academic
performance.
A study of Remmers in 1964 (as cited by Azarcon and Lamsis, 2002)
stated that the school plays an important role in the development of a child. Its
influence goes far beyond the influence of the classroom learning. Beyond the
immediate family, home and environment, the school provides the most important
influence in the child’s interactions with other children. The child is freed from
parental control and is at the same time forced to adjust himself to others as an
independent citizen in a child community. He finds himself confronted with
attitudes, personality patterns and conduct in his teachers that vary from teacher to
teacher and differ from characteristics found in his parents. Next to home, the
school plays the most vital role in molding the child’s adjustment patterns.
In the study of Azarcon and Lamsis (2003), they researched on the factors
affecting students’ achievement of Benguet State University. Analysis revealed
that from the 19 variables, seven significant factors were extracted by applying
factor analysis. These are high school performance; inherited potential; home –
school situation; distance of school from home; preference of craft; influence of
intellect to organization preference and influence of the people in contact with
Regression Analysis on the Academic Performance of the Bachelor of Science in
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them. From these factors, regression analysis revealed that there is only one
significant factor affecting the student achievement in the university and that is
the inherited potential of the students.
Mathematical ability and background are frequently discussed in relation
to achievement in Statistics. Although it is often argued that understanding and
applying Statistics in empirical research does not require advanced mathematics, a
significant and positive relationship exists between mathematical ability and
performance has been consistently reported (Galagedera 1998; Galagedera,
Woodward, and Degamboda 2000; Lalonde and Gardner 1993; Nasser 1998,
1999; Wooten 1998). Galagedera (1998) found that first-year business
mathematics and Statistics students who were successful in mathematics at the
university entry-level examination were more likely to have performed better in
elementary Statistics than poor performers at matriculation level.
Studies concerning the effect of gender on performance in Statistics
courses delivered, mixed results. Schram’s (1996) meta-analysis of gender
differences (in applied Statistics) concludes that male-female performance is
sensitive to the type of Statistics course, the department offering the course, and
how course grades are determined. In general, women outperform men in
Statistics courses offered by business departments; however, the bulk of Schram’s
analysis was based on Statistics taught in education and psychology courses.
Johnson and Kuennen (2006) show that female students outperform male students
Regression Analysis on the Academic Performance of the Bachelor of Science in
Applied Statistics Students in Statistics / Rosalyn S. Bayacsan; et al. 2008
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in an introductory business Statistics course, while Harraway (2002) found no
gender difference in performance in an introductory bioStatistics course in New
Zealand. Buck (1985) hypothesized that gender affects students’ performance in
Statistics in several ways: (1) male students may tend to monopolize the inclass
attention of professors, (2) female students are more sensitive to role-model
effects, (3) professors have gender-specific performance expectations, and (4)
gender meaningfully affects academic confidence or math skills. However, in an
examination of psychology Statistics students (at both the introductory and
advanced undergraduate level), Buck found no significant differences in
performance across genders.
Scarr and Wimberg, 1978 (as cited by Laluan (1987), reported the
influence of family background on academic achievement. They discussed the
long-term effects of family background influences on adult, intellectual,
occupational and economic outcomes. Parental education, family income, family
size and parents’ IQ tend to be more correlated, and family size is unrelated to
child’s IQ.
Regression Analysis on the Academic Performance of the Bachelor of Science in
Applied Statistics Students in Statistics / Rosalyn S. Bayacsan; et al. 2008
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THEORETICAL FRAMEWORK
Regression Analysis
Regression analysis is a technique used for the modeling and analysis of
numerical data consisting of values of a dependent variable (response variable)
and of independent variables (explanatory variables). The model is a function of
the independent variables and one or more parameters. The parameters are
adjusted so as to give a best fit of the data. Most commonly, the best fit is
obtained by using the least squares method, but other criteria have also been used.
The dependent variable is assumed to be a random variable, due to the presence of
observational errors. The independent variable is assumed to be error-free.
Regression can be used for prediction (including forecasting of time-series
data), inference, hypothesis testing, and modeling of causal relationships. These
uses of regression rely heavily on the underlying assumptions being satisfied.
Regression analysis has been criticized as being misused in many cases where the
appropriate assumptions cannot be verified to hold. One factor contributing to the
misuse of regression is that, it would take considerable skill to critique a model
than to fit a model.
Regression Analysis on the Academic Performance of the Bachelor of Science in
Applied Statistics Students in Statistics / Rosalyn S. Bayacsan; et al. 2008
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Multiple Linear Regression Analysis
The general purpose of multiple regression is to analyze the relationship
between several independent or predictor variable and a dependent or criterion
variable. The multiple linear regression model can be written as:
Y = β + β X + β X + ... + β X + ε
0
1
1
2
2
k
k
Where:
Y = the response variable that you want to predict
X1, X2,…Xk = the explanatory variables
β = the regression constant
0
β , β ,..., β = the regression coefficients or partial correlation
1
2
k
coefficients
ε = the random error term
The
intercept
β of the regression model is the y-intercept of the
0
regression hyperplane which gives the value of Y at X1 = X2 = …=Xk = 0. In case
0 is in the scope of all the independent variables, the regression constant reflects
the dependent variable when the independent variables are equal to zero.
Otherwise β does not have a particular meaning.
0
The regression coefficient, say β indicates the change (increase if β is
1
1
positive, decrease if β is negative) in the dependent variable corresponding to a
1
Regression Analysis on the Academic Performance of the Bachelor of Science in
Applied Statistics Students in Statistics / Rosalyn S. Bayacsan; et al. 2008
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unit increase in X1 when all the other independent variables, X1,…, Xk are held
constant or fixed to some value.
Regression Analysis on the Academic Performance of the Bachelor of Science in
Applied Statistics Students in Statistics / Rosalyn S. Bayacsan; et al. 2008
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Definition of Terms
Academic
Performance. Refers to the student’ school achievements as
reflected from their grades.
Correlation. Refers to the degree of correspondence either positively or
negatively between variables.
Dependent Variable. Refers to the variable that is determined or explained
by one or more explanatory variables.
English 11. Refers to the subject with descriptive title Arts and
Communication 1 taken by the Bachelor of Science in Applied Statistics students.
Independent
Variable. Refers to a variable used to predict values of the
dependent variable in regression analysis.
Information
Technology
11. Refers to the subject with the descriptive title
Basic Computer Education taken by the Bachelor of Science in Applied Statistics
students.
Mathematics
11. Refers to the subject with the descriptive title College
Algebra taken by the Bachelor of Science in Applied Statistics students.
Multiple Regression. Refers to a method of taking into account
simultaneously the relationship between all the variables when two or more
independent variables are used in making estimates of the dependent variable.
Regression
Analysis. Refers to a set of statistical technique used to assess
the relationship between dependent and several independent variables.
Regression Analysis on the Academic Performance of the Bachelor of Science in
Applied Statistics Students in Statistics / Rosalyn S. Bayacsan; et al. 2008
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Statistics
11. Refers to the subject with the descriptive title Principles and
Methods of Statistics taken by the Bachelor of Science in Applied Statistics
students.
Variable. Refers to a characteristic of interest, which is measurable and
observable in every aspect in study.
Regression Analysis on the Academic Performance of the Bachelor of Science in
Applied Statistics Students in Statistics / Rosalyn S. Bayacsan; et al. 2008
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METHODOLOGY
Locale and Time of the Study
The study was conducted in the College of Arts and Sciences at Benguet
State University, La Trinidad, Benguet in November 2007 to March 2008.
Respondents of the Study
The respondents of the study were second, third, and fourth year students
enrolled in Bachelor of Science in Applied Statistics from the College of Arts and
Sciences at Benguet State University during the school year 2007 – 2008. Twenty
two were second years, thirty-two were third years, and twenty-nine were fourth
years with an overall total of eighty-three respondents.
Instrumentation
This study utilized a questionnaire as the main data – collection tool. It
consisted of the respondent’s demographic profile, which includes the following:
gender, type of high school graduated from, father’s highest educational
attainment, mother’s highest educational attainment, average family annual
income, and the grades in Statistics 11, Mathematics 11, English 11, IQ, and high
school average.
Regression Analysis on the Academic Performance of the Bachelor of Science in
Applied Statistics Students in Statistics / Rosalyn S. Bayacsan; et al. 2008
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Data Gathering Procedure
The permission of the Dean of the College of Arts and Sciences of
Benguet State University was first sought for the floating of questionnaires. The
questionnaires were distributed to the respondents with directions and instructions
for the respondents to follow.
Data Analysis
The data collected were analyzed using Statistical Packages for Social
Sciences. Multiple linear regression analysis technique was employed on the data
using grades in Statistics 11 as the dependent variable and the respondent’s
demographic profile such as gender, type of high school graduated, parents’
highest educational attainment, grades in Mathematics 11, English 11,
Information Technology 11, IQ, and high school average were treated as the
independent variables.
Regression Analysis on the Academic Performance of the Bachelor of Science in
Applied Statistics Students in Statistics / Rosalyn S. Bayacsan; et al. 2008
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RESULTS AND DISCUSSION
Profile of the Respondents
The descriptive Statistics was used in the study for the purpose of giving
an initial perspective on which variable contributes to the academic performance
of students in Statistics 11.
Table 1 presents the distribution of respondents according to their
demographic profile with their corresponding frequency and percentages. The
table indicates a total of 62.7 percent female and 37.3 percent male. 21.0 percent
graduated from a barangay high school, 13.3 percent from a city high school, 19.3
percent from a state college or university, 42.2 percent from a national high
school and 4.8 percent from a private high school.
In terms of parents’ highest educational attainment, 19.3 percent have
fathers who attended elementary, 39.8 percent in high school and some with
vocational courses and 41 percent in college. In the highest educational attainment
of mother, 18.1 percent have attended elementary, 32.5 percent have attended
high school and some with vocational courses and 49.4 percent have attended
college.
Under the respondents’ family annual income, 43.4 percent reported to
receive an income of below 60,000 pesos, 49.4 percent derive an income of 60,
000 to 100, 000 pesos, and 7.2 percent are lucky to gain an income of above
100,000 pesos.
Regression Analysis on the Academic Performance of the Bachelor of Science in
Applied Statistics Students in Statistics / Rosalyn S. Bayacsan; et al. 2008
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Table 1. Distribution of respondents according to their demographic profile
Variables Frequency
Percentage
Gender
Female 52
62.7
Male
31
37.3
Type of High
Barangay
17
20.5
School
City
11
13.3
Graduated
State College or
16
19.3
University
National
35
42.2
Private
4
4.8
Fathers’ Highest
Elementary
16
19.3
Educational
High School or
33
39.8
Attainment
Vocational
College
34
41
Mothers’ Highest
Elementary
15
18.1
Educational
High School or
27
32.5
Attainment
Vocational
College
41
49.4
Average Family
Below 60,000
36
43.4
Income
60,000-100,000
41
49.4
100,001-Above
6
7.2
Table 2 presents the distribution of respondents according to their grades
in Statistics 11. In this study grades ranging from 1 to 1.75 were referred to as
high grades. The table indicates that from the 50 female respondents, 9 have high
grades in Statistics 11 while from the 31 male respondents 4 obtained high grades.
Under the type of school graduated, respondents who graduated from a state
Regression Analysis on the Academic Performance of the Bachelor of Science in
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Table 2. Distribution of respondents according to their grades in Statistics 11
Grades in Statistics 11
Total
Mean
Variables
Independent
Percentages
1.5 1.75 2 2.25 2.50 2.75 3
A. Gender
Female 2
7 5
5
10
10
13 52
62.7
2.46
Male 1
3 4
4
1
8
10 31
37.3
2.52
B. Type of high school graduated
Barangay 0
2 2
2
3
4
4 17
20.5
2.5
City 1
2 0
1
0
4
3 11
13.3
2.48
National
1 2 2
1
3
4
3 16
19.3
2.42
State College/
University 1
3 4
5
5
6
11 35
42.2
2.51
Private 0
1 1
0
0
0
2
4
4.8
2.44
C. Fathers’ Highest Educational Attainment
Elementary 0
2 0
3
1
7
3 16
19.3
2.56
High School/
Vocational 1
5 5
2
2
5
13 33
39.8
2.5
College 2
3 4
4
8
6
7 34
41
2.43
D. Mothers’ Highest Educational Attainment
Elementary 0
3 0
1
2
4
5 15
18.1
2.57
High School/
Vocational 2
4 2
3
2
6
8 27
32.5
2.45
College 1
3 7
5
7
8
10 41
49.4
2.48
E. Annual Income
Below 60,000
1
4 5
4
5
5
12 36 43.4 2.49
60,000-100,000 2 6 4
4
6
11
8 41
49.4
2.43
100,001-Above 0 0 0
1
0
2
3
6 7.2
2.79
college or university and barangay high school obtained the lowest average of 2.5
and the rest have average of 2.42 to 2.48. Students whose fathers attended college
have higher average of 2.43 compared to those fathers who attended high school
and elementary with an average of 2.5 and 2.56 respectively. In the mothers’
Regression Analysis on the Academic Performance of the Bachelor of Science in
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highest educational attainment, respondents with mothers who have attended high
school or vocational have an average of 2.45, higher than those respondents
whose mothers have attended college and elementary. Under family income,
students with an average family annual income of 60,000 to 100,000 have higher
average of 2.43 than those who have an income of below 60,000 and above
100,001.
Correlation and Test of Significance Between
Grades in Statistics 11 and the Respondent's
Personal Profile
The grades in Statistics 11 were correlated with the non-intellective factors
such as personal profile of the respondents which includes gender and type of
high school graduated namely: Barangay, City, National, State college/ University
and Private to find out if these areas would serve as indicators of success or
failure in Statistics 11.
Table 3 presents the Pearson correlation ( r ) and the test of significance
using the 1-tailed test statistics (p). Results revealed no significant correlation
between grade in Statistics 11 and personal profile such as gender and type of
high school graduated. This implies that male and female perform equally in
Statistics 11 and in the type of high school graduated, although those from
national schools obtained higher average of 2.42 as compared to the other type of
schools, the test showed no significant correlation between the type of high school
graduated and grade in Statistics 11. This means that students who came from
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Table 3. Correlation and test of significance between Statistics 11 grades and the
personal profile of respondents
Dependent
Independent variable
variable
Statistics 11
Gender
Type of High School Graduated
Grade
Barangay City
National State
college/
Private
University
r (Pearson
.068 .018 .002
-.067 .050
-.028
Correlation)
p-value .269ns
.436ns
.494ns .274ns
.327ns
.402ns
barangay, city, national, state college or university, and private schools have equal
performance in Statistics 11.
Correlation and Test of Significance Between
Grades in Statistics 11 and the Parents’
Status of Respondents
The grades in Statistics 11 were also correlated with the parents’ status
such as fathers’ highest educational attainment, mothers’ highest educational
attainment, and annual family income.
Table 4 presents the Pearson correlation ( r ) and the test of significance
using the 1-tailed test statistics (p). It shows that there is no significant correlation
between grade in Statistics 11 and parents’ status. That is, the college students are
of the same level of performance in Statistics 11, regardless of parents’ level of
education and family income.
Regression Analysis on the Academic Performance of the Bachelor of Science in
Applied Statistics Students in Statistics / Rosalyn S. Bayacsan; et al. 2008
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Table 4. Correlation and test of significance between Statistics 11 grade and the
parents’ status
Dependent
Independent Variable
Variable
Statistics 11 Grade Fathers’ Highest Mothers’ Highest Family Annual
Educational
Educational
Income
Attainment
Attainment
r
-.116 -.061 -.073
p .257ns
.292ns
.148ns
Correlation Between Grades in Statistics 11
and the Intellective factors
The grades in Statistics 11 were also correlated with the intellective
factors such as college grades in Mathematics 11, English 11, IT 11, IQ, and high
school average.
Table 5 presents the Pearson correlation ( r ) and the test of significance
using the 1-tailed test statistics, between college grades in Mathematics 11,
English 11, IT 11, IQ, and high school average with Statistics 11. Analysis
showed that a marked or substantial relationship exists between Statistics 11 and
Mathematics 11. There are also significant but low correlations between Statistics
11 with English 11 and with the IQ scores. It is then inferred that students with
Regression Analysis on the Academic Performance of the Bachelor of Science in
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Table 5. Correlation and test of significance between Statistics 11 grade and the
respondent’s Intellective factors
Dependent
Independent Variables
Variables
Statistics 11
Math11
English 11
IT 11
IQ
High school average
Grade
r (Pearson
.448 .236 .174
-.239
.009
Correlation)
p - value
.000**
.016*
.058ns
.015*
.467ns
high grades in Mathematics 11, English 11 and high scores in IQ were likely to
have high grades in Statistics 11. It was found out that there is a negligible
correlation between Statistics 11 grade and IT 11 and between Statistics 11 grade
and high school average. This means that grade in IT 11 and high school average
whether high or low do not affect the student’s grades in Statistics 11.
Analysis of Variance
The analysis of variance tests the overall significance of the regression
model. It presents the value of the F-statistic and its significance. Table 6 shows
that the significance of the F value is below .05, so the model is significant
implying that there is a linear relationship between the grades in Statistics 11 and
the entire set of independent variables since F = 2.888 and p = .002. The value
6.300 represents the amount of variation in Statistics 11 grade explained by the
independent variables. The value 11.576 represents the unexplained variation in
Statistics 11 grade. And the value 17.876
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Table 6. ANOVA
Model
Sum of Squares
df
Mean Square
F
Sig.
1 Regression
6.300
13
.485
2.888 .002
Residual
11.576
69
.168
Total
17.876
82
represents the total variation in the grades in Statistics 11, which is simply the
sum of the explained and the unexplained parts.
Parameter Estimates
In the study, the variables considered that have contributions on the
academic performance of Bachelor of Science in Applied Statistics students in
Statistics 11 were gender, type of high school graduated (Barangay, city, national,
state college/university and private), father’s highest educational attainment
(elementary, high school/vocational, and college), mother’s highest educational
attainment (elementary, high school/vocational, and college), family annual
income, grades in Mathematics 11, English 11, IT 11, IQ, and general high school
average. For the students in the data set, grade in Statistics 11 can be represented
by the regression equation:
Y = β + β X + β X + β X + β X + β X + .... + β X + ε
0
1
1
2
2
3
3
4
4
5
5
n
n
ij
where the errors are independent normal variables with mean 0 and standard
deviation σ , unknown. Y is the dependent variable, and the X’s are the
Regression Analysis on the Academic Performance of the Bachelor of Science in
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independent variables. The β ' s represents unknown parameters that were
estimated from the data through the process called model fitting. Y = grade in
Statistics 11; X1 = Mathematics 11, X2 = English 11, X3 = IT 11, X4 =IQ, X5 =
High school average, X6 = Gender, X7 = Barangay, X8 = City, X9 = National,
X10 = State college/ University, X11 = Private X12 = Father’s highest
educational attainment, X13= Mother’s highest educational attainment, X14 =
Family annual income. The regression equation obtained is:
Y = .540 + .484X1 + .218X2 + .199X3 - .01507X4 + .01776X5 + .05577X6
(.000)
(.203) (.121) (.210) (.250) (.592)
+.03613X7-.171X8-.02033X9-.192X10-.08363x11-.03211X12-.04404X13
(.831) (.268)
(.871) (.437) (.208) (.615)
(.576)
The coefficients are the degree of correlation and the values in parenthesis
are the p-values associated with the t-test. The hypothesis being tested in each
case is whether each of the independent variables is linearly related to the
dependent variable. The only variable that is linearly related to grades in Statistics
11 is the grade in Mathematics 11 since the p-value is less than .05. On the other
hand, the factors that have no significant effect on the grades in Statistics 11 but
are accounted for in the model were gender, type of high school graduated
(Barangay, city, national, state college/university and private), father’s highest
educational attainment, mother’s highest educational attainment, income, high
school average, English 11, IT 11, IQ, and high school average.
Regression Analysis on the Academic Performance of the Bachelor of Science in
Applied Statistics Students in Statistics / Rosalyn S. Bayacsan; et al. 2008
24
The value 0.540 represents the estimated mean Statistics 11 grade of the
respondents when all the independent variables are set to 0. The value .484
represents the estimated increase in Statistics 11 grade when Mathematics 11 is
increased by 1 unit while holding the value of the other variables constant.
However, in the grading system of the university where 1 is the highest grade,
while 5 is the lowest, and 3 is the passing grade, increase in the value of
coefficients while other variables are held constant would mean a decrease in
Statistics 11 grade.
Coefficient of Multiple Determination
Table 7 shows the contribution of the independent variables treated as one,
to the variation of grades in Statistics. The table shows that 36.4 percent of the
variation are explained by the regressor variables. The remaining 63.6 percent of
the variation of grades in Statistics 11 can be attributed to factors not included in
the study.
Table 7. Coefficient of Multiple Determination
Model
R
R Square
Adjusted R Square
Std. Error of the Estimate
1
.594 .352
.230
.410
Regression Analysis on the Academic Performance of the Bachelor of Science in
Applied Statistics Students in Statistics / Rosalyn S. Bayacsan; et al. 2008
25
SUMMARY, CONCLUSIONS AND RECOMMENDATIONS
Summary and Conclusion
This study was conducted to identify the factors affecting academic
performance of BSAS students in Statistics and to construct a model for the
academic performance of Bachelor of Science in Applied Statistics in Statistics
11.
The variables collected are information about their personal profile that
includes gender and type of high school graduated, parents’ highest educational
attainment and family annual income, their grades in Statistics 11, Mathematics
11, English 11, Information Technology 11, IQ scores, and general high school
average annual income. A total of 83 Bachelor of Science in Applied Statistics
students were selected as respondents to this study.
Multiple linear regression technique was employed in analyzing variables
that have a significant contribution to the obtained grades of the respondents in
Statistics. The data were analyzed using SPSS and the computer output were
printed and analyzed.
Statistical analysis revealed that the grades in Statistics 11 was not
affected by students’ demographic profile such as gender, type of school
graduated, and family annual income, and parents’ highest educational attainment.
A positive marked correlation existed between Statistics 11 and Mathematics 11,
There are also significant but low correlations between Statistics 11 with English
Regression Analysis on the Academic Performance of the Bachelor of Science in
Applied Statistics Students in Statistics / Rosalyn S. Bayacsan; et al. 2008
26
11 and with the IQ scores. However, regression analysis revealed that only the
grades in Mathematics 11 had direct contribution to the respondents’ performance
in Statistics 11.
Recommendations
The results of this study could be of great help to the students. It may be
essential in the counseling and testing activities of the students. It maybe of help
in fostering awareness among students about factors that might affect their
academic performance especially in Statistics 11. To the teachers, the knowledge
of the students’ background will guide them in structuring their strategies to suit
the needs of their students.
A similar study could be conducted relating Statistics 11 with other
variables not included in the study such as students’ study habits, motivation and
attitude. If possible more subjects should be added and more respondents be
included. Other Statistics subjects could also be studied.
Mathematics 11 should be given focus or attention since it has significant
relationship to grades in Statistics 11.
Regression Analysis on the Academic Performance of the Bachelor of Science in
Applied Statistics Students in Statistics / Rosalyn S. Bayacsan; et al. 2008
27
LITERATURE CITED
AZARCON, D. Jr. and LAMSIS, J. A. (2003). Factor Analysis and Regression
Analysis on the Student Achievement of BSU. Undergraduate Thesis.
Benguet State University, La Trinidad, Benguet.
BUGNAY, J.T. 2001. An Analysis of the Different Factors Affecting the Delay of
Graduation Among BSU Students. Undergraduate Thesis. Benguet State
University, La Trinidad, Benguet.
GAL, I and GINSBURG, L. The Role of Beliefs and Attitudes in Learning
Statistics: Towards an Assessment Framework. Journal of Statistics
Education v.2, n.2 (1994)
LULUAN, D. 1987. Factors Affecting Students’ Performance in Mathematics,
Statistics, and Physics. Undergraduate Thesis. Benguet State University,
La Trinidad, Benguet.
NASSER, F. M. 2004. Structural Model of the Effects of Cognitive and Affective
Factors on the Achievement of Arabic-Speaking Pre-service Teachers in
Introductory Statistics. Journal of Statistics Education. Volume 12,
Number 1. www. Amstat. org/publications/jse/V12n1/Nasser.html
NETER, J. et. al. Applied Linear Regression Models. R.R. Donneley and Sons
Company. Second Edition. Pp. 453-457
WALPOLE, R. E. et. al. 1998. Probability and Statistics for Engineers and
Scientists. Prentice-Hall, Inc. 6th Edition. Pp. 353-358.
Regression Analysis on the Academic Performance of the Bachelor of Science in
Applied Statistics Students in Statistics / Rosalyn S. Bayacsan; et al. 2008
28
Appendix A. Letter of Communication
Benguet State University
College of Arts and Sciences
Math-Physics-Statistics Department
La Trinidad, Benguet
Letter of Permission
Madam Aurea Marie Sandoval
CAS Dean
Benguet State University
Madam:
The undersigned are conducting a research for their thesis entitled
“Regression Analysis on the Academic Performance of Bachelor of Science in
Applied Statistics in Statistics” as a requirement for the degree Bachelor of
Science in Applied Statistics for the subject Stat 200.
In this connection, may we ask your kind consideration to allow us to
gather information through a survey questionnaire among the College of Arts and
Sciences students of Benguet State University.
Your favorable action to this request is highly acknowledged.
Thank you very much and God bless.
Sincerely Yours,
Rosalyn Bayacsan
Janice Damulo
Lailanie Wakat
Noted:
Cristina B. Ocden
Adviser
Maria Azucena B. Lubrica Approved: Aurea Marie Sandoval
MPS Chairman CAS Dean
Regression Analysis on the Academic Performance of the Bachelor of Science in
Applied Statistics Students in Statistics / Rosalyn S. Bayacsan; et al. 2008
29
Appendix B. SAMPLE SURVEY QUESTIONNAIRE
Benguet State University
College of Arts and Sciences
Math-Physics-Statistics Department
La Trinidad, Benguet
Dear Fellow Students,
The undersigned are conducting a study entitled “Regression Analysis on
the Academic performance of Bachelor of Science in Applied Statistics students
in Statistics.” In this connection, may we request your kind assistance by
answering this questionnaire.
Your accurate and complete answers will help the success of this study.
Rest assured that answers would be treated confidentially.
Heartfelt thanks for your anticipated cooperation.
Yours
truly,
Rosalyn S. Bayacsan
Janice B. Damulo
Lailanie L. Wakat
Noted:
Cristina B. Ocden
Adviser
DIRECTION: Please check or write on the blank that corresponds to your
answers.
1. Name (Optional): _____________________________________________
2. Sex: ____Male
____Female
Regression Analysis on the Academic Performance of the Bachelor of Science in
Applied Statistics Students in Statistics / Rosalyn S. Bayacsan; et al. 2008
30
3. Type of High School Graduated
____Barangay High School
____State College/ University High School
____City High School
____Vocational/ Technical High School
____National High
School
____Private High School
4. Parents’ Highest Educational Attainment
Father
____________________________________________
Mother
___________________________________________
5. Average Family Annual Income
____Below 60, 000
____60,000 – 100,000
____100,000 - Above
6. Grades, Please specify
____IQ
____General High School Average
____Statistics
11
____Mathematics
11
____English
11
____Information Technology 11
Regression Analysis on the Academic Performance of the Bachelor of Science in
Applied Statistics Students in Statistics / Rosalyn S. Bayacsan; et al. 2008
31
Appendix C. Variable Coding
Variables Code
Dependent
Statistics
11
Y
Independent
Mathematics
11
X1
English
11 X2
IT
11
X3
IQ
X4
High
School
Average
X5
Gender
Code
Male
1
X6
Female
0
Code
Type of High
Barangay City National
State Private
School
College/
Graduated
University
Barangay 1
0
0
0
0
X7
City 0 1
0
0 0 X8
National 0
0 1
0
0
X9
State
0 0
0
1
X10
College/
University
Private 0
0 0 0
1 X11
Fathers’ Highest Educational
Code
Attainment
Elementary
1
High
School/
Vocational
X12
2
College
3
Fathers’ Highest
Code
Educational Attainment
Elementary
1
High
School/
Vocational
X13
2
College
3
Annual Income
Code
Below
60,000
1
60,000 – 100,000
2
X14
100,000 - Above
3
Regression Analysis on the Academic Performance of the Bachelor of Science in
Applied Statistics Students in Statistics / Rosalyn S. Bayacsan; et al. 2008
32
Appendix D. Raw Data
Fathers
Mothers’ Highest Educ
’
Hig
h
Respondents
est Educa
Annual Income
University
Stat 11
Math 11
English 11
HS. Ave.
National
IT 11
Gender
Barangay
Private
IQ
City
t
a
ional Atta
tiona
l Atta
in
in
ment
ment
1
1.7
2.2
2.5 1.5 5
5 87 87 0 0 0 0 1 0 3 3 1
2
1.7
1.7
1.5 1.8 5
5 89 89 1 0 1 0 0 0 3 2 2
3
1.7
2.2
3 2.3 5
5 80 83 1 0 0 0 0 1 2 3 1
4
2 1.5 2 3 85 88 1 0 0 0 0 1 3 3 2
5
2.5
2.5 2 2.5 82 85 0 0 0 0 1 0 3 3 2
6
2.2
2.7
1.8 1.5 5
5 84 88 0 0 0 0 1 0 3 2 2
7
2.2
1.8 1.3 2 5 85 85 0 0 0 0 1 0 2 2 2
8
1.7
1.7
1.5 1.3 5
5 88 86 0 0 0 1 0 0 3 2 2
9
1.5 2 2 2.5 87 87 0 0 0 0 1 0 2 3 1
10
3 2.8 2 3 80 85 0 0 0 0 1 0 2 3 1
11 1.8 2.3 2 2 86 84 0 0 0 1 0 0 2 3 1
12 2.3 2 2 2 83 85 1 0 0 0 1 0 2 2 2
13 2.5 2 2.5 2.5 82 85 0 1 0 0 0 0 3 3 2
14
2.2
2.2
1.8 1.5 5
5 83 87 1 0 0 1 0 0 1 2 1
15
2 2 2.5 2.5 81 82 0 1 0 0 0 0 2 3 2
16
2.2
1.8 1.8 2 5 85 85 0 1 0 0 0 0 1 1 1
17
2 1.5
2.5 2.5 85 87 0 0 0 0 1 0 3 3 1
Regression Analysis on the Academic Performance of the Bachelor of Science in
Applied Statistics Students in Statistics / Rosalyn S. Bayacsan; et al. 2008
33
18 2.3 2 2 3 84 84 0 0 0 0 1 0 3 3 1
19
2.7
3 2.3 3 5 79 84 1 0 0 1 0 0 2 3 1
20
2.2
2.3 2 2.5 5 80 86 1 0 1 0 0 0 2 2 3
21
2.2
1.7
3 2.3 5
5 81 85 0 1 0 0 0 0 3 1 2
22
2.2
3 1.3 2 5 79 87 1 0 1 0 0 0 2 3 1
23
2.2
2.8 2.8 5 2.5 82 87 0 1 0 0 0 0 2 1 2
24
1.7
2.8 2.3 2 5 85 89 0 0 1 0 0 0 2 2 1
25
3 2.5 2 2 80 88 0 0 0 0 1 0 2 2 3
26
1.7
2.7
3 2 5
5 83 84 0 1 0 0 0 0 2 1 1
27 2.5 2.5 2 2 86 87 0 0 0 0 1 0 2 3 2
28
3 3 2 2.5 85 90 0 0 0 1 0 0 1 1 2
29 2.8 3 2 2 87 87 0 0 0 0 1 0 1 1 2
30
2.2
2.8 3 2.5 5 82 89 0 0 0 1 0 0 3 3 2
31
1.7
2.8 2.5 2 5 86 92 0 0 0 0 1 0 3 3 1
32
2.2
2.7
3 3 5
5 78 85 0 0 0 0 1 0 2 2 2
33 2.8 2.5 2 2 85 90 1 1 0 0 0 0 2 2 2
34
1.7
1.7
2.3 2 5
5 88 93 1 0 0 0 1 0 1 3 2
35
1.7
1.7
2.5 2 5
5 83 92 0 1 0 0 0 0 3 3 1
36
2.2
2.8 2.5 5 2.5 82 85 0 1 0 0 0 0 1 3 2
37
2.2
2.7
2.8 3 5
5 85 87 1 0 0 1 0 0 3 3 2
38
2.2
3 3 5 2 85 89 0 0 0 0 1 0 2 3 1
39
1.7
1.7
2.3 2.3 5
5 85 93 0 0 0 0 1 0 1 1 2
40
2.2
2.8 2.8 5 2 79 85 0 0 0 0 1 0 3 1 3
41
1.7
1.7
2.3 2 5
5 89 93 0 0 0 1 0 0 3 3 1
42
1.7
1.7
2.5 2 5
5 87 92 0 0 0 0 1 0 3 1 1
43 2.3 2.8 2.5 2 85 85 0 0 0 0 1 0 3 3 1
44
2.2
2.8 2.5 5 2 86 88 1 0 0 0 1 0 1 3 2
45
3 2.8
2.7
2.5 82 85 1 0 0 1 0 0 2 1 1
Regression Analysis on the Academic Performance of the Bachelor of Science in
Applied Statistics Students in Statistics / Rosalyn S. Bayacsan; et al. 2008
34
5
46 2.8 2.8 2 2 85 89 1 1 0 0 0 0 1 3 1
47
1.7
3 2.3 5 2.5 85 90 0 0 1 0 0 0 3 3 1
48
2.2
3 3 5 2 87 85 0 0 0 0 1 0 3 2 1
49
1.7
1.7
3 3 5
5 83 88 0 0 0 0 1 0 1 2 2
50
2.2
2.8 2.3 5 2 81 89 0 0 1 0 0 0 2 1 2
51
3 3 2.5 2.5 83 88 1 0 0 0 1 0 2 2 1
52
1.7
2.8 2.8 5 2 85 85 0 0 0 1 0 0 2 3 3
53
3 2.5
2.5 2.5 52 86 0 0 1 0 0 0 3 3 3
54
1.7
2.8 1.5 2 5 78 87 1 0 0 0 1 0 1 2 1
55
2.2
1.7
2.5 2.8 5
5 80 88 1 0 0 0 1 0 3 2 2
56
2.2
2 2.5 5 2 81 85 0 0 0 1 0 0 2 3 2
57
2.7
2.8 2.8 5 2 83 83 1 0 0 1 0 0 1 2 2
58
2.2
3 2.3 2.5 5 83 82 1 0 0 0 1 0 2 3 1
59
2.7
3 2 1.5 5 82 84 1 0 0 0 0 1 2 2 2
60
1.7
3 2 5 3 81 89 0 0 0 0 1 0 2 2 2
61
1.7
2 2.8 5 2.5 85 88 0 1 0 0 0 0 2 2 2
62
2.2
3 2.3 5 3 79 90 1 1 0 0 0 0 3 3 2
63
2.2
1.8 2 2 5 78 95 0 1 0 0 0 0 3 1 2
64 1.8 1.8 2.5 2.5 79 86 1 0 1 0 0 0 2 1 1
65
2.7
3 1.8 2.5 5 85 85 0 0 0 0 1 0 3 1 1
66 2.8 1.8 2.5 2 86 83 1 0 1 0 0 0 1 3 1
67
2.2
1.7
2.5 3 5
5 82 85 0 0 0 1 0 0 3 3 1
68
1.7
2.5 2.8 2 5 85 85 0 0 0 1 0 0 3 3 2
69
1.7
1.8 2.5 5 2 83 82 1 0 1 0 0 0 3 3 2
70
1.7
2.3 2.5 5 2 82 82 0 1 0 0 0 0 3 3 2
71
1.7
2 2.8 1.5 5 85 80 1 0 0 0 1 0 2 3 1
Regression Analysis on the Academic Performance of the Bachelor of Science in
Applied Statistics Students in Statistics / Rosalyn S. Bayacsan; et al. 2008
35
72
2.7
2 2.8 2 5 86 81 0 0 0 1 0 0 3 3 1
73
2.2
2.8 2.3 5 3 84 82 1 0 1 0 0 0 3 2 2
74
1.7
2.3 1.8 1.5 5 81 83 1 1 0 0 0 0 1 2 1
75
2.2
2.5 2.3 5 2 80 83 0 1 0 0 0 0 1 2 2
76
2.2
3 1.8 2 5 84 85 1 1 0 0 0 0 1 2 2
77 1.8 1.8 2 2.5 83 82 0 0 0 0 1 0 2 3 2
78 2.8 2.3 2.5 2 86 80 0 0 0 0 1 0 3 2 2
79
1.7
2.7
3 2.8 5
5 85 81 1 0 0 0 1 0 3 3 3
80
1.7
1.7
2 2.5 5
5 82 85 1 0 0 0 1 0 3 2 1
81
1.7
2 2.3 5 2 81 86 1 0 0 0 1 0 2 3 1
82
1.7
1.7
1.8 1.5 5
5 85 88 0 0 0 0 0 1 2 2 2
83
2.5
2.3 2 2 83 89 0 0 0 1 0 0 2 1 1
Appendix E. Regression Analysis Printouts
Correlations
Regression Analysis on the Academic Performance of the Bachelor of Science in
Applied Statistics Students in Statistics / Rosalyn S. Bayacsan; et al. 2008
36
Fathers' Hig
Mothers' Highest Educ
High School Average
Mathe
h
Annual Income
Statis
est Educa
English 11
University
Gender
Barangay
National
Private
m
IT 11
City
tics 11
IQ
atic
a
s 11
t
ional Atta
tiona
l Atta
in
in
ment
ment
Statistics 11 1.00 .448 .236 .174 -.239 .009 .068 .018 .002 -.067 .050 -.028 -.116 -.061 .073
0
Mathematic .448 1.00 .152 -.050 -.069 -.077 -.090 -.050 -.172 .218 .079 -.218 .016 .056 .152
s 11
0
English 11 .236 .152 1.00 .256 -.279 -.183 .058 -.061 .098 .192 -.066 -.240 .028 -.031 .012
0
IT 11
.174 -.050 .256 1.00 -.198 -.214 .028 .039 .007 -.060 -.043 .125 .157 .083 .055
Pear
0
so
IQ
-.239 -.069 -.279 -.198 1.00 .097 -.032 -.088 -.245 .114 .149 .001 -.040 .008 -.274
n Cor
0
High School .009 -.077 -.183 -.214 .097 1.00 -.154 .027 -.004 -.028 .019 -.040 -.007 -.197 -.031
r
e
Average
0
l
a
tio
Gender .068
-.090
.058 .028 -.032 -.154 1.00 -.083 .212 -.062 -.105 .175 -.225 .108 -.073
n
0
Barangay .018
-.050
-.061 .039 -.088 .027 -.083 1.00 -.198 -.248 -.433 -.114 -.148 -.131 .056
0
City .002
-.172
.098 .007 -.245 -.004 .212 -.198 1.00 -.191 -.334 -.088 .077 -.021 .057
0
University -.067 .218 .192 -.060 .114 -.028 -.062 -.248 -.191 1.00 -.417 -.110 .022 .080 -.061
0
National .050
.079
-.066 -.043 .149 .019 -.105 -.433 -.334 -.417 1.00 -.192 .046 .033 -.054
0
Private -.028 -.218 -.240 .125 .001 -.040 .175 -.114 -.088 -.110 -.192 1.00 .010 .055 .041
0
Fathers' -.116 .016 .028 .157 -.040 -.007 -.225 -.148 .077 .022 .046 .010 1.00 .199 .040
Highest
0
Educational
Attainment
Mothers' -.061 .056 -.031 .083 .008 -.197 .108 -.131 -.021 .080 .033 .055 .199 1.00 -.093
Highest
0
Educational
Regression Analysis on the Academic Performance of the Bachelor of Science in
Applied Statistics Students in Statistics / Rosalyn S. Bayacsan; et al. 2008
37
Attainment
Annual .073 .152 .012 .055 -.274 -.031 -.073 .056 .057 -.061 -.054 .041 .040 -.093 1.00
Income
0
Statistics 11 . .000 .016 .058 .015 .467 .269 .436 .494 .274 .327 .402 .148 .292 .257
Mathematic .000 . .085 .327 .269 .243 .210 .326 .060 .024 .240 .024 .442 .307 .085
Sig
s 11
.
(1
English 11 .016 .085 . .010 .005 .049 .300 .293 .189 .041 .275 .014 .401 .389 .457
-Tailed)
IT 11
.058 .327 .010
. .037 .026 .402 .363 .474 .295 .348 .129 .078 .229 .310
IQ
.015 .269 .005 .037
. .191 .386 .214 .013 .152 .090 .498 .359 .470 .006
High School .467 .243 .049 .026 .191
. .082 .403 .487 .403 .432 .361 .474 .037 .390
Average
Gender .269 .210 .300 .402 .386 .082
. .227 .027 .290 .174 .057 .021 .166 .256
Barangay .436 .326 .293 .363 .214 .403 .227
. .036 .012 .000 .152 .091 .119 .308
City
.494 .060 .189 .474 .013 .487 .027 .036
. .042 .001 .215 .245 .426 .306
University .274 .024 .041 .295 .152 .403 .290 .012 .042
. .000 .161
.423 .236 .293
National .327 .240 .275 .348 .090 .432 .174 .000 .001 .000
. .041 .339 .383 .315
Private .402 .024 .014 .129 .498 .361 .057 .152 .215 .161 .041
. .464
.310 .357
Fathers' .148 .442 .401 .078 .359 .474 .021 .091 .245 .423 .339 .464 . .035 .361
Highest
Educational
Attainment
Mothers' .292 .307 .389 .229 .470 .037 .166 .119 .426 .236 .383 .310 .035 . .201
Highest
Educational
Attainment
Annual .257 .085 .457 .310 .006 .390 .256 .308 .306 .293 .315 .357 .361 .201
.
Income
N
83 83 83 83 83 83 83 83 83 83 83 83 83 83 83
Regression Analysis on the Academic Performance of the Bachelor of Science in
Applied Statistics Students in Statistics / Rosalyn S. Bayacsan; et al. 2008
38
Variables Entered/Removed
Model
Variables Entered Variables Removed
Method
1 Annual
Income, . Enter
English 11, Fathers'
Highest Educational
Attainment,
National, High
School Average,
Mathematics 11,
Gender, Mothers'
Highest Educational
Attainment, IT 11,
IQ, Private, City,
University
a Tolerance = .000 limits reached.
b Dependent Variable: Statistics 11
Model Summary
Model
R
R Square
Adjusted R Std. Error of the
Square
Estimate
1 .594 .352 .230 .410
a Predictors: (Constant), Annual Income, English 11, Fathers' Highest
Educational Attainment, National, High School Average, Mathematics 11,
Gender, Mothers' Highest Educational Attainment, IT 11, IQ, Private, City,
University
ANOVA
Model Sum
of
df Mean F Sig.
Squares
Square
1 Regression
6.300 13 .485 2.888 .002
Residual
11.576 69 .168
Total
17.876
82
a Predictors: (Constant), Annual Income, English 11, Fathers' Highest
Educational Attainment, National, High School Average, Mathematics 11,
Gender, Mothers' Highest Educational Attainment, IT 11, IQ, Private, City,
University
b Dependent Variable: Statistics 11
Regression Analysis on the Academic Performance of the Bachelor of Science in
Applied Statistics Students in Statistics / Rosalyn S. Bayacsan; et al. 2008
39
Coefficients
Unstandardized
Standardized
t Sig.
Coefficients
Coefficients
Model
B Std.
Error
Beta
1 (Constant) .540 1.896
.285 .777
Mathematics
.484 .102 .507
4.762
.000
11
English
11 .218 .170 .146 1.287 .203
IT
11 .199 .127
.168
1.568
.121
IQ
-1.507E-02
.012
-.141
-1.266
.210
High
School
1.776E-02 .015 .120 1.159 .250
Average
Gender
5.577E-02
.104 .058 .539
.592
City
3.613E-02
.169
.026
.214
.831
University -.171 .153 -.145 -1.117
.268
National
2.033E-02
.125 .022 .163
.871
Private .192 .245 .088 .783
.437
Fathers'
-8.363E-02 .066 -.134 -1.271 .208
Highest
Educational
Attainment
Mothers'
-3.211E-02 .063 -.053 -.506 .615
Highest
Educational
Attainment
Annual
-4.404E-02 .078 -.058 -.561 .576
Income
a Dependent Variable: Statistics 11
Excluded Variables
Beta
In
t
Sig.
Partial
Collinearity
Correlation Statistics
Model
Tolerance
1
Barangay
. . . .
.000
a Predictors in the Model: (Constant), Annual Income, English 11, Fathers'
Highest Educational Attainment, National, High School Average, Mathematics
11, Gender, Mothers' Highest Educational Attainment, IT 11, IQ, Private, City,
University
b Dependent Variable: Statistics 11
Regression Analysis on the Academic Performance of the Bachelor of Science in
Applied Statistics Students in Statistics / Rosalyn S. Bayacsan; et al. 2008
ROSALYN S. BAYACSAN, JANICE B. DAMULO and LAILANIE WAKAT
2008. Regression Analysis on the Academic Performance of the Bachelor of Science in
Applied Statistics Students in Statistics. Benguet State University, La Trinidad, Benguet.
Adviser: Cristina B. Ocden
ABSTRACT
This study was conducted to determine the variables that have contributions on
the academic performance of Bachelor of Science in Applied Statistics students in
Statistics. The study also aimed to construct a regression model for the factors affecting
academic performance in Statistics 11 of Bachelor of Science in Applied Statistics
students.
The population was represented by 83 Bachelor of Science in Applied Statistics
students who responded to the questionnaire administered on February 2008, at Benguet
State University, La Trinidad, Benguet.
Statistical analysis revealed that the grades in Statistics 11 was not affected by the
student’s demographic profile such as gender, type of high school graduated, family
annual income, and parents’ highest educational attainment. A positive marked
correlation existed between Statistics 11 and Mathematics 11. There are also significant
but low correlations between Statistics 11 with English 11 and with the IQ scores.
However, regression analysis revealed that only the grades in Mathematics 11 had direct
contribution to the performance of respondents in Statistics 11. The regression model
obtained is:
Y = .540 + .484X1 + .218X2 + .199X3 - .01507X4 + .01776X5 + .05577X6
(.000)
(.203) (.121) (.210) (.250) (.592)
+.03613X7-.171X8-.02033X9-.192X10-.08363x11-.03211X12-.04404X13
(.831) (.268)
(.871) (.437) (.208) (.615)
(.576)
The coefficients are the degree of correlation and the values in parenthesis are the
p-values associated with the t-test. The only variable that is linearly related to grades in
Statistics 11 is the grade in Mathematics 11 since the p-value is less than .05.
ii
TABLE OF CONTENTS
Page
Bibliography…………………………………………………………………. i
Abstract………… …………………………………………………………… i
Table of Contents ……………………………………………………………. iii
INTRODUCTION
Background of the Study…………………………………………….. 1
Objectives of the Study………………………………………………. 2
Importance of the Study……………………………………………… 3
Scope and Delimitation………………………………………………. 4
REVIEW OF LITERATURE………………………………………………... 5
THEORETICAL FRAMEWORK……………………………………………. 8
METHODOLOGY
Locale and Time of the Study………………………………………... 13
Respondents of the Study…………………………………………….. 13
Instrumentation………………………………………………………. 13
Data Gathering Procedure……………………………………………. 14
Data Analysis…………………………………………………………. 14
RESULTS AND DISCUSSION……………………………………………… 15
SUMMARY, CONCLUSION AND RECOMMENDATION
Summary……………………………………………………………... 25
Conclusion…………………………………………………………..... 25
Recommendation…………………………………………………….. 26
iii
LITERATURE CITED……………………………………………………… 27
APPENDICES
A. Request Letter to the Dean of College of Arts and Sciences……. 28
B. Survey Questionnaire Application for Oral Defense ………….... 29
C. Variable Coding ………………………………………………… 31
D. The Raw Data of the Respondents ……………………………… 32
E. Regression Analysis Printouts ………………………………..… 36
iv
1
INTRODUCTION
Background of the Study
The ability to present a solution to a problem inside the human mind is
knowledge. In a very complex environment where several unknowns are present,
one will find a way of dealing with them easily by viewing abstract mathematical
structures and drawing conclusions from scientific and logical analyses.
Mathematics plays an important role, by sharpening the intellect and developing
critical thinking.
One branch of mathematics is Statistics. It is concerned with the
collection, organization, and analysis of numerical data. The study in Statistics
emerged during the 19th century, when researchers recognized the need to reduce
bulky and unmanageable amounts of information in their studies. The solution is
to present data in the form of numerical values to avoid the ambiguous verbal
description. For this reason, Statistics is very useful in business, economics,
sociology, biology, psychology, education, physics, chemistry, agriculture and
related fields.
Statistics courses have become an essential part of many programs in
higher education. The rationale for teaching Statistics at the college level is to
enable students to handle, use, and interpret research or statistical data in their
field of study. Furthermore, teaching Statistics aims to prepare students to deal
effectively with statistical aspects of the world outside the classroom. However,
Regression Analysis on the Academic Performance of the Bachelor of Science in
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2
despite the effort instructors of Statistics devote in simplifying the subject, many
students encounter difficulties in their Statistics subjects. This is the reason why
the researchers choose to study the academic performance of BSAS students in
Statistics. They believe that the performance of students in Statistics 11
significantly affects their ability to perform well in higher Statistical subjects.
Lastly, multiple regression analysis was used for the purpose of this study.
Multiple regression analysis is a method in the explanation of phenomena and
prediction of future events. A coefficient of correlation between variables X and
Y is a quantitative index of association between these two variables. In its squared
form, as a coefficient of determination, it indicates the amount of variance
(information) in the criterion variable Y that is accounted for by the variation in
the predictor variable X. A multivariate counterpart of the coefficient of
determination is the coefficient of multiple determination, ( 2
R ) . In multiple
regression analysis, the set of predictor variables
is used to explain
variability of the criterion variable .
Objectives of the study
Specifically the study aimed: 1) to determine the factors that have
contributions to the academic performance of Bachelor of Science in Applied
Statistics students in Statistics 11. 2) to construct a model for the factors affecting
academic performance of Bachelor of Science in Applied Statistics students in
Statistics 11.
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Importance of the Study
The results of this study could provide point of reference to parents,
teachers, and school administrators on factors affecting students’ performance in
college, particularly in Statistics where most students fail.
The identification of variables that may have a contribution on the
academic performance of students in Statistics 11 could be of great help to
teachers, they would have better insight on what to prepare, and how to motivate
students. Findings of the study would also help administrators to perform their
roles in enhancing the strengths and lessening the weaknesses of the students.
To the students, knowledge on the contributory factors to their academic
performance may result to a reflection on their study habits and attitudes towards
Statistics. Through this study, the students might come to realize that passing
Statistics 11 is not as difficult as they think, because it might just be a matter of
attitude and habits. The result could also help students to realize and reflect on
their weaknesses; thus they would be encouraged to find ways to uplift
themselves.
The findings could convince parents to cooperate with the school in
guiding their children in their studies. This would also motivate them to devote
their time, attention and guidance needed by the students; to inspire them to excel
and not to fail in their performance.
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Scope and Delimitation of the Study
The focus of the study was to apply the multiple linear regression
procedure in analyzing and determining the variables that maybe related to the
respondent’s academic performance in Statistics 11. The respondents of the study
were second, third, and fourth year students enrolled in Bachelor of Science in
Applied Statistics, during the second semester of the academic year 2007-2008, at
Benguet State University, La Trinidad, Benguet.
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REVIEW OF LITERATURE
The process of determining the significant factors affecting students’
performance were chosen carefully by the researchers with consideration to the
related researches and studies done concerning the issue of students’ academic
performance.
A study of Remmers in 1964 (as cited by Azarcon and Lamsis, 2002)
stated that the school plays an important role in the development of a child. Its
influence goes far beyond the influence of the classroom learning. Beyond the
immediate family, home and environment, the school provides the most important
influence in the child’s interactions with other children. The child is freed from
parental control and is at the same time forced to adjust himself to others as an
independent citizen in a child community. He finds himself confronted with
attitudes, personality patterns and conduct in his teachers that vary from teacher to
teacher and differ from characteristics found in his parents. Next to home, the
school plays the most vital role in molding the child’s adjustment patterns.
In the study of Azarcon and Lamsis (2003), they researched on the factors
affecting students’ achievement of Benguet State University. Analysis revealed
that from the 19 variables, seven significant factors were extracted by applying
factor analysis. These are high school performance; inherited potential; home –
school situation; distance of school from home; preference of craft; influence of
intellect to organization preference and influence of the people in contact with
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them. From these factors, regression analysis revealed that there is only one
significant factor affecting the student achievement in the university and that is
the inherited potential of the students.
Mathematical ability and background are frequently discussed in relation
to achievement in Statistics. Although it is often argued that understanding and
applying Statistics in empirical research does not require advanced mathematics, a
significant and positive relationship exists between mathematical ability and
performance has been consistently reported (Galagedera 1998; Galagedera,
Woodward, and Degamboda 2000; Lalonde and Gardner 1993; Nasser 1998,
1999; Wooten 1998). Galagedera (1998) found that first-year business
mathematics and Statistics students who were successful in mathematics at the
university entry-level examination were more likely to have performed better in
elementary Statistics than poor performers at matriculation level.
Studies concerning the effect of gender on performance in Statistics
courses delivered, mixed results. Schram’s (1996) meta-analysis of gender
differences (in applied Statistics) concludes that male-female performance is
sensitive to the type of Statistics course, the department offering the course, and
how course grades are determined. In general, women outperform men in
Statistics courses offered by business departments; however, the bulk of Schram’s
analysis was based on Statistics taught in education and psychology courses.
Johnson and Kuennen (2006) show that female students outperform male students
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in an introductory business Statistics course, while Harraway (2002) found no
gender difference in performance in an introductory bioStatistics course in New
Zealand. Buck (1985) hypothesized that gender affects students’ performance in
Statistics in several ways: (1) male students may tend to monopolize the inclass
attention of professors, (2) female students are more sensitive to role-model
effects, (3) professors have gender-specific performance expectations, and (4)
gender meaningfully affects academic confidence or math skills. However, in an
examination of psychology Statistics students (at both the introductory and
advanced undergraduate level), Buck found no significant differences in
performance across genders.
Scarr and Wimberg, 1978 (as cited by Laluan (1987), reported the
influence of family background on academic achievement. They discussed the
long-term effects of family background influences on adult, intellectual,
occupational and economic outcomes. Parental education, family income, family
size and parents’ IQ tend to be more correlated, and family size is unrelated to
child’s IQ.
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THEORETICAL FRAMEWORK
Regression Analysis
Regression analysis is a technique used for the modeling and analysis of
numerical data consisting of values of a dependent variable (response variable)
and of independent variables (explanatory variables). The model is a function of
the independent variables and one or more parameters. The parameters are
adjusted so as to give a best fit of the data. Most commonly, the best fit is
obtained by using the least squares method, but other criteria have also been used.
The dependent variable is assumed to be a random variable, due to the presence of
observational errors. The independent variable is assumed to be error-free.
Regression can be used for prediction (including forecasting of time-series
data), inference, hypothesis testing, and modeling of causal relationships. These
uses of regression rely heavily on the underlying assumptions being satisfied.
Regression analysis has been criticized as being misused in many cases where the
appropriate assumptions cannot be verified to hold. One factor contributing to the
misuse of regression is that, it would take considerable skill to critique a model
than to fit a model.
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Multiple Linear Regression Analysis
The general purpose of multiple regression is to analyze the relationship
between several independent or predictor variable and a dependent or criterion
variable. The multiple linear regression model can be written as:
Y = β + β X + β X + ... + β X + ε
0
1
1
2
2
k
k
Where:
Y = the response variable that you want to predict
X1, X2,…Xk = the explanatory variables
β = the regression constant
0
β , β ,..., β = the regression coefficients or partial correlation
1
2
k
coefficients
ε = the random error term
The
intercept
β of the regression model is the y-intercept of the
0
regression hyperplane which gives the value of Y at X1 = X2 = …=Xk = 0. In case
0 is in the scope of all the independent variables, the regression constant reflects
the dependent variable when the independent variables are equal to zero.
Otherwise β does not have a particular meaning.
0
The regression coefficient, say β indicates the change (increase if β is
1
1
positive, decrease if β is negative) in the dependent variable corresponding to a
1
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unit increase in X1 when all the other independent variables, X1,…, Xk are held
constant or fixed to some value.
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Definition of Terms
Academic
Performance. Refers to the student’ school achievements as
reflected from their grades.
Correlation. Refers to the degree of correspondence either positively or
negatively between variables.
Dependent Variable. Refers to the variable that is determined or explained
by one or more explanatory variables.
English 11. Refers to the subject with descriptive title Arts and
Communication 1 taken by the Bachelor of Science in Applied Statistics students.
Independent
Variable. Refers to a variable used to predict values of the
dependent variable in regression analysis.
Information
Technology
11. Refers to the subject with the descriptive title
Basic Computer Education taken by the Bachelor of Science in Applied Statistics
students.
Mathematics
11. Refers to the subject with the descriptive title College
Algebra taken by the Bachelor of Science in Applied Statistics students.
Multiple Regression. Refers to a method of taking into account
simultaneously the relationship between all the variables when two or more
independent variables are used in making estimates of the dependent variable.
Regression
Analysis. Refers to a set of statistical technique used to assess
the relationship between dependent and several independent variables.
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Statistics
11. Refers to the subject with the descriptive title Principles and
Methods of Statistics taken by the Bachelor of Science in Applied Statistics
students.
Variable. Refers to a characteristic of interest, which is measurable and
observable in every aspect in study.
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METHODOLOGY
Locale and Time of the Study
The study was conducted in the College of Arts and Sciences at Benguet
State University, La Trinidad, Benguet in November 2007 to March 2008.
Respondents of the Study
The respondents of the study were second, third, and fourth year students
enrolled in Bachelor of Science in Applied Statistics from the College of Arts and
Sciences at Benguet State University during the school year 2007 – 2008. Twenty
two were second years, thirty-two were third years, and twenty-nine were fourth
years with an overall total of eighty-three respondents.
Instrumentation
This study utilized a questionnaire as the main data – collection tool. It
consisted of the respondent’s demographic profile, which includes the following:
gender, type of high school graduated from, father’s highest educational
attainment, mother’s highest educational attainment, average family annual
income, and the grades in Statistics 11, Mathematics 11, English 11, IQ, and high
school average.
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Data Gathering Procedure
The permission of the Dean of the College of Arts and Sciences of
Benguet State University was first sought for the floating of questionnaires. The
questionnaires were distributed to the respondents with directions and instructions
for the respondents to follow.
Data Analysis
The data collected were analyzed using Statistical Packages for Social
Sciences. Multiple linear regression analysis technique was employed on the data
using grades in Statistics 11 as the dependent variable and the respondent’s
demographic profile such as gender, type of high school graduated, parents’
highest educational attainment, grades in Mathematics 11, English 11,
Information Technology 11, IQ, and high school average were treated as the
independent variables.
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RESULTS AND DISCUSSION
Profile of the Respondents
The descriptive Statistics was used in the study for the purpose of giving
an initial perspective on which variable contributes to the academic performance
of students in Statistics 11.
Table 1 presents the distribution of respondents according to their
demographic profile with their corresponding frequency and percentages. The
table indicates a total of 62.7 percent female and 37.3 percent male. 21.0 percent
graduated from a barangay high school, 13.3 percent from a city high school, 19.3
percent from a state college or university, 42.2 percent from a national high
school and 4.8 percent from a private high school.
In terms of parents’ highest educational attainment, 19.3 percent have
fathers who attended elementary, 39.8 percent in high school and some with
vocational courses and 41 percent in college. In the highest educational attainment
of mother, 18.1 percent have attended elementary, 32.5 percent have attended
high school and some with vocational courses and 49.4 percent have attended
college.
Under the respondents’ family annual income, 43.4 percent reported to
receive an income of below 60,000 pesos, 49.4 percent derive an income of 60,
000 to 100, 000 pesos, and 7.2 percent are lucky to gain an income of above
100,000 pesos.
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Table 1. Distribution of respondents according to their demographic profile
Variables Frequency
Percentage
Gender
Female 52
62.7
Male
31
37.3
Type of High
Barangay
17
20.5
School
City
11
13.3
Graduated
State College or
16
19.3
University
National
35
42.2
Private
4
4.8
Fathers’ Highest
Elementary
16
19.3
Educational
High School or
33
39.8
Attainment
Vocational
College
34
41
Mothers’ Highest
Elementary
15
18.1
Educational
High School or
27
32.5
Attainment
Vocational
College
41
49.4
Average Family
Below 60,000
36
43.4
Income
60,000-100,000
41
49.4
100,001-Above
6
7.2
Table 2 presents the distribution of respondents according to their grades
in Statistics 11. In this study grades ranging from 1 to 1.75 were referred to as
high grades. The table indicates that from the 50 female respondents, 9 have high
grades in Statistics 11 while from the 31 male respondents 4 obtained high grades.
Under the type of school graduated, respondents who graduated from a state
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Table 2. Distribution of respondents according to their grades in Statistics 11
Grades in Statistics 11
Total
Mean
Variables
Independent
Percentages
1.5 1.75 2 2.25 2.50 2.75 3
A. Gender
Female 2
7 5
5
10
10
13 52
62.7
2.46
Male 1
3 4
4
1
8
10 31
37.3
2.52
B. Type of high school graduated
Barangay 0
2 2
2
3
4
4 17
20.5
2.5
City 1
2 0
1
0
4
3 11
13.3
2.48
National
1 2 2
1
3
4
3 16
19.3
2.42
State College/
University 1
3 4
5
5
6
11 35
42.2
2.51
Private 0
1 1
0
0
0
2
4
4.8
2.44
C. Fathers’ Highest Educational Attainment
Elementary 0
2 0
3
1
7
3 16
19.3
2.56
High School/
Vocational 1
5 5
2
2
5
13 33
39.8
2.5
College 2
3 4
4
8
6
7 34
41
2.43
D. Mothers’ Highest Educational Attainment
Elementary 0
3 0
1
2
4
5 15
18.1
2.57
High School/
Vocational 2
4 2
3
2
6
8 27
32.5
2.45
College 1
3 7
5
7
8
10 41
49.4
2.48
E. Annual Income
Below 60,000
1
4 5
4
5
5
12 36 43.4 2.49
60,000-100,000 2 6 4
4
6
11
8 41
49.4
2.43
100,001-Above 0 0 0
1
0
2
3
6 7.2
2.79
college or university and barangay high school obtained the lowest average of 2.5
and the rest have average of 2.42 to 2.48. Students whose fathers attended college
have higher average of 2.43 compared to those fathers who attended high school
and elementary with an average of 2.5 and 2.56 respectively. In the mothers’
Regression Analysis on the Academic Performance of the Bachelor of Science in
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highest educational attainment, respondents with mothers who have attended high
school or vocational have an average of 2.45, higher than those respondents
whose mothers have attended college and elementary. Under family income,
students with an average family annual income of 60,000 to 100,000 have higher
average of 2.43 than those who have an income of below 60,000 and above
100,001.
Correlation and Test of Significance Between
Grades in Statistics 11 and the Respondent's
Personal Profile
The grades in Statistics 11 were correlated with the non-intellective factors
such as personal profile of the respondents which includes gender and type of
high school graduated namely: Barangay, City, National, State college/ University
and Private to find out if these areas would serve as indicators of success or
failure in Statistics 11.
Table 3 presents the Pearson correlation ( r ) and the test of significance
using the 1-tailed test statistics (p). Results revealed no significant correlation
between grade in Statistics 11 and personal profile such as gender and type of
high school graduated. This implies that male and female perform equally in
Statistics 11 and in the type of high school graduated, although those from
national schools obtained higher average of 2.42 as compared to the other type of
schools, the test showed no significant correlation between the type of high school
graduated and grade in Statistics 11. This means that students who came from
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Table 3. Correlation and test of significance between Statistics 11 grades and the
personal profile of respondents
Dependent
Independent variable
variable
Statistics 11
Gender
Type of High School Graduated
Grade
Barangay City
National State
college/
Private
University
r (Pearson
.068 .018 .002
-.067 .050
-.028
Correlation)
p-value .269ns
.436ns
.494ns .274ns
.327ns
.402ns
barangay, city, national, state college or university, and private schools have equal
performance in Statistics 11.
Correlation and Test of Significance Between
Grades in Statistics 11 and the Parents’
Status of Respondents
The grades in Statistics 11 were also correlated with the parents’ status
such as fathers’ highest educational attainment, mothers’ highest educational
attainment, and annual family income.
Table 4 presents the Pearson correlation ( r ) and the test of significance
using the 1-tailed test statistics (p). It shows that there is no significant correlation
between grade in Statistics 11 and parents’ status. That is, the college students are
of the same level of performance in Statistics 11, regardless of parents’ level of
education and family income.
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Table 4. Correlation and test of significance between Statistics 11 grade and the
parents’ status
Dependent
Independent Variable
Variable
Statistics 11 Grade Fathers’ Highest Mothers’ Highest Family Annual
Educational
Educational
Income
Attainment
Attainment
r
-.116 -.061 -.073
p .257ns
.292ns
.148ns
Correlation Between Grades in Statistics 11
and the Intellective factors
The grades in Statistics 11 were also correlated with the intellective
factors such as college grades in Mathematics 11, English 11, IT 11, IQ, and high
school average.
Table 5 presents the Pearson correlation ( r ) and the test of significance
using the 1-tailed test statistics, between college grades in Mathematics 11,
English 11, IT 11, IQ, and high school average with Statistics 11. Analysis
showed that a marked or substantial relationship exists between Statistics 11 and
Mathematics 11. There are also significant but low correlations between Statistics
11 with English 11 and with the IQ scores. It is then inferred that students with
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Table 5. Correlation and test of significance between Statistics 11 grade and the
respondent’s Intellective factors
Dependent
Independent Variables
Variables
Statistics 11
Math11
English 11
IT 11
IQ
High school average
Grade
r (Pearson
.448 .236 .174
-.239
.009
Correlation)
p - value
.000**
.016*
.058ns
.015*
.467ns
high grades in Mathematics 11, English 11 and high scores in IQ were likely to
have high grades in Statistics 11. It was found out that there is a negligible
correlation between Statistics 11 grade and IT 11 and between Statistics 11 grade
and high school average. This means that grade in IT 11 and high school average
whether high or low do not affect the student’s grades in Statistics 11.
Analysis of Variance
The analysis of variance tests the overall significance of the regression
model. It presents the value of the F-statistic and its significance. Table 6 shows
that the significance of the F value is below .05, so the model is significant
implying that there is a linear relationship between the grades in Statistics 11 and
the entire set of independent variables since F = 2.888 and p = .002. The value
6.300 represents the amount of variation in Statistics 11 grade explained by the
independent variables. The value 11.576 represents the unexplained variation in
Statistics 11 grade. And the value 17.876
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Table 6. ANOVA
Model
Sum of Squares
df
Mean Square
F
Sig.
1 Regression
6.300
13
.485
2.888 .002
Residual
11.576
69
.168
Total
17.876
82
represents the total variation in the grades in Statistics 11, which is simply the
sum of the explained and the unexplained parts.
Parameter Estimates
In the study, the variables considered that have contributions on the
academic performance of Bachelor of Science in Applied Statistics students in
Statistics 11 were gender, type of high school graduated (Barangay, city, national,
state college/university and private), father’s highest educational attainment
(elementary, high school/vocational, and college), mother’s highest educational
attainment (elementary, high school/vocational, and college), family annual
income, grades in Mathematics 11, English 11, IT 11, IQ, and general high school
average. For the students in the data set, grade in Statistics 11 can be represented
by the regression equation:
Y = β + β X + β X + β X + β X + β X + .... + β X + ε
0
1
1
2
2
3
3
4
4
5
5
n
n
ij
where the errors are independent normal variables with mean 0 and standard
deviation σ , unknown. Y is the dependent variable, and the X’s are the
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independent variables. The β ' s represents unknown parameters that were
estimated from the data through the process called model fitting. Y = grade in
Statistics 11; X1 = Mathematics 11, X2 = English 11, X3 = IT 11, X4 =IQ, X5 =
High school average, X6 = Gender, X7 = Barangay, X8 = City, X9 = National,
X10 = State college/ University, X11 = Private X12 = Father’s highest
educational attainment, X13= Mother’s highest educational attainment, X14 =
Family annual income. The regression equation obtained is:
Y = .540 + .484X1 + .218X2 + .199X3 - .01507X4 + .01776X5 + .05577X6
(.000)
(.203) (.121) (.210) (.250) (.592)
+.03613X7-.171X8-.02033X9-.192X10-.08363x11-.03211X12-.04404X13
(.831) (.268)
(.871) (.437) (.208) (.615)
(.576)
The coefficients are the degree of correlation and the values in parenthesis
are the p-values associated with the t-test. The hypothesis being tested in each
case is whether each of the independent variables is linearly related to the
dependent variable. The only variable that is linearly related to grades in Statistics
11 is the grade in Mathematics 11 since the p-value is less than .05. On the other
hand, the factors that have no significant effect on the grades in Statistics 11 but
are accounted for in the model were gender, type of high school graduated
(Barangay, city, national, state college/university and private), father’s highest
educational attainment, mother’s highest educational attainment, income, high
school average, English 11, IT 11, IQ, and high school average.
Regression Analysis on the Academic Performance of the Bachelor of Science in
Applied Statistics Students in Statistics / Rosalyn S. Bayacsan; et al. 2008
24
The value 0.540 represents the estimated mean Statistics 11 grade of the
respondents when all the independent variables are set to 0. The value .484
represents the estimated increase in Statistics 11 grade when Mathematics 11 is
increased by 1 unit while holding the value of the other variables constant.
However, in the grading system of the university where 1 is the highest grade,
while 5 is the lowest, and 3 is the passing grade, increase in the value of
coefficients while other variables are held constant would mean a decrease in
Statistics 11 grade.
Coefficient of Multiple Determination
Table 7 shows the contribution of the independent variables treated as one,
to the variation of grades in Statistics. The table shows that 36.4 percent of the
variation are explained by the regressor variables. The remaining 63.6 percent of
the variation of grades in Statistics 11 can be attributed to factors not included in
the study.
Table 7. Coefficient of Multiple Determination
Model
R
R Square
Adjusted R Square
Std. Error of the Estimate
1
.594 .352
.230
.410
Regression Analysis on the Academic Performance of the Bachelor of Science in
Applied Statistics Students in Statistics / Rosalyn S. Bayacsan; et al. 2008
25
SUMMARY, CONCLUSIONS AND RECOMMENDATIONS
Summary and Conclusion
This study was conducted to identify the factors affecting academic
performance of BSAS students in Statistics and to construct a model for the
academic performance of Bachelor of Science in Applied Statistics in Statistics
11.
The variables collected are information about their personal profile that
includes gender and type of high school graduated, parents’ highest educational
attainment and family annual income, their grades in Statistics 11, Mathematics
11, English 11, Information Technology 11, IQ scores, and general high school
average annual income. A total of 83 Bachelor of Science in Applied Statistics
students were selected as respondents to this study.
Multiple linear regression technique was employed in analyzing variables
that have a significant contribution to the obtained grades of the respondents in
Statistics. The data were analyzed using SPSS and the computer output were
printed and analyzed.
Statistical analysis revealed that the grades in Statistics 11 was not
affected by students’ demographic profile such as gender, type of school
graduated, and family annual income, and parents’ highest educational attainment.
A positive marked correlation existed between Statistics 11 and Mathematics 11,
There are also significant but low correlations between Statistics 11 with English
Regression Analysis on the Academic Performance of the Bachelor of Science in
Applied Statistics Students in Statistics / Rosalyn S. Bayacsan; et al. 2008
26
11 and with the IQ scores. However, regression analysis revealed that only the
grades in Mathematics 11 had direct contribution to the respondents’ performance
in Statistics 11.
Recommendations
The results of this study could be of great help to the students. It may be
essential in the counseling and testing activities of the students. It maybe of help
in fostering awareness among students about factors that might affect their
academic performance especially in Statistics 11. To the teachers, the knowledge
of the students’ background will guide them in structuring their strategies to suit
the needs of their students.
A similar study could be conducted relating Statistics 11 with other
variables not included in the study such as students’ study habits, motivation and
attitude. If possible more subjects should be added and more respondents be
included. Other Statistics subjects could also be studied.
Mathematics 11 should be given focus or attention since it has significant
relationship to grades in Statistics 11.
Regression Analysis on the Academic Performance of the Bachelor of Science in
Applied Statistics Students in Statistics / Rosalyn S. Bayacsan; et al. 2008
27
LITERATURE CITED
AZARCON, D. Jr. and LAMSIS, J. A. (2003). Factor Analysis and Regression
Analysis on the Student Achievement of BSU. Undergraduate Thesis.
Benguet State University, La Trinidad, Benguet.
BUGNAY, J.T. 2001. An Analysis of the Different Factors Affecting the Delay of
Graduation Among BSU Students. Undergraduate Thesis. Benguet State
University, La Trinidad, Benguet.
GAL, I and GINSBURG, L. The Role of Beliefs and Attitudes in Learning
Statistics: Towards an Assessment Framework. Journal of Statistics
Education v.2, n.2 (1994)
LULUAN, D. 1987. Factors Affecting Students’ Performance in Mathematics,
Statistics, and Physics. Undergraduate Thesis. Benguet State University,
La Trinidad, Benguet.
NASSER, F. M. 2004. Structural Model of the Effects of Cognitive and Affective
Factors on the Achievement of Arabic-Speaking Pre-service Teachers in
Introductory Statistics. Journal of Statistics Education. Volume 12,
Number 1. www. Amstat. org/publications/jse/V12n1/Nasser.html
NETER, J. et. al. Applied Linear Regression Models. R.R. Donneley and Sons
Company. Second Edition. Pp. 453-457
WALPOLE, R. E. et. al. 1998. Probability and Statistics for Engineers and
Scientists. Prentice-Hall, Inc. 6th Edition. Pp. 353-358.
Regression Analysis on the Academic Performance of the Bachelor of Science in
Applied Statistics Students in Statistics / Rosalyn S. Bayacsan; et al. 2008
28
Appendix A. Letter of Communication
Benguet State University
College of Arts and Sciences
Math-Physics-Statistics Department
La Trinidad, Benguet
Letter of Permission
Madam Aurea Marie Sandoval
CAS Dean
Benguet State University
Madam:
The undersigned are conducting a research for their thesis entitled
“Regression Analysis on the Academic Performance of Bachelor of Science in
Applied Statistics in Statistics” as a requirement for the degree Bachelor of
Science in Applied Statistics for the subject Stat 200.
In this connection, may we ask your kind consideration to allow us to
gather information through a survey questionnaire among the College of Arts and
Sciences students of Benguet State University.
Your favorable action to this request is highly acknowledged.
Thank you very much and God bless.
Sincerely Yours,
Rosalyn Bayacsan
Janice Damulo
Lailanie Wakat
Noted:
Cristina B. Ocden
Adviser
Maria Azucena B. Lubrica Approved: Aurea Marie Sandoval
MPS Chairman CAS Dean
Regression Analysis on the Academic Performance of the Bachelor of Science in
Applied Statistics Students in Statistics / Rosalyn S. Bayacsan; et al. 2008
29
Appendix B. SAMPLE SURVEY QUESTIONNAIRE
Benguet State University
College of Arts and Sciences
Math-Physics-Statistics Department
La Trinidad, Benguet
Dear Fellow Students,
The undersigned are conducting a study entitled “Regression Analysis on
the Academic performance of Bachelor of Science in Applied Statistics students
in Statistics.” In this connection, may we request your kind assistance by
answering this questionnaire.
Your accurate and complete answers will help the success of this study.
Rest assured that answers would be treated confidentially.
Heartfelt thanks for your anticipated cooperation.
Yours
truly,
Rosalyn S. Bayacsan
Janice B. Damulo
Lailanie L. Wakat
Noted:
Cristina B. Ocden
Adviser
DIRECTION: Please check or write on the blank that corresponds to your
answers.
1. Name (Optional): _____________________________________________
2. Sex: ____Male
____Female
Regression Analysis on the Academic Performance of the Bachelor of Science in
Applied Statistics Students in Statistics / Rosalyn S. Bayacsan; et al. 2008
30
3. Type of High School Graduated
____Barangay High School
____State College/ University High School
____City High School
____Vocational/ Technical High School
____National High
School
____Private High School
4. Parents’ Highest Educational Attainment
Father
____________________________________________
Mother
___________________________________________
5. Average Family Annual Income
____Below 60, 000
____60,000 – 100,000
____100,000 - Above
6. Grades, Please specify
____IQ
____General High School Average
____Statistics
11
____Mathematics
11
____English
11
____Information Technology 11
Regression Analysis on the Academic Performance of the Bachelor of Science in
Applied Statistics Students in Statistics / Rosalyn S. Bayacsan; et al. 2008
31
Appendix C. Variable Coding
Variables Code
Dependent
Statistics
11
Y
Independent
Mathematics
11
X1
English
11 X2
IT
11
X3
IQ
X4
High
School
Average
X5
Gender
Code
Male
1
X6
Female
0
Code
Type of High
Barangay City National
State Private
School
College/
Graduated
University
Barangay 1
0
0
0
0
X7
City 0 1
0
0 0 X8
National 0
0 1
0
0
X9
State
0 0
0
1
X10
College/
University
Private 0
0 0 0
1 X11
Fathers’ Highest Educational
Code
Attainment
Elementary
1
High
School/
Vocational
X12
2
College
3
Fathers’ Highest
Code
Educational Attainment
Elementary
1
High
School/
Vocational
X13
2
College
3
Annual Income
Code
Below
60,000
1
60,000 – 100,000
2
X14
100,000 - Above
3
Regression Analysis on the Academic Performance of the Bachelor of Science in
Applied Statistics Students in Statistics / Rosalyn S. Bayacsan; et al. 2008
32
Appendix D. Raw Data
Fathers
Mothers’ Highest Educ
’
Hig
h
Respondents
est Educa
Annual Income
University
Stat 11
Math 11
English 11
HS. Ave.
National
IT 11
Gender
Barangay
Private
IQ
City
t
a
ional Atta
tiona
l Atta
in
in
ment
ment
1
1.7
2.2
2.5 1.5 5
5 87 87 0 0 0 0 1 0 3 3 1
2
1.7
1.7
1.5 1.8 5
5 89 89 1 0 1 0 0 0 3 2 2
3
1.7
2.2
3 2.3 5
5 80 83 1 0 0 0 0 1 2 3 1
4
2 1.5 2 3 85 88 1 0 0 0 0 1 3 3 2
5
2.5
2.5 2 2.5 82 85 0 0 0 0 1 0 3 3 2
6
2.2
2.7
1.8 1.5 5
5 84 88 0 0 0 0 1 0 3 2 2
7
2.2
1.8 1.3 2 5 85 85 0 0 0 0 1 0 2 2 2
8
1.7
1.7
1.5 1.3 5
5 88 86 0 0 0 1 0 0 3 2 2
9
1.5 2 2 2.5 87 87 0 0 0 0 1 0 2 3 1
10
3 2.8 2 3 80 85 0 0 0 0 1 0 2 3 1
11 1.8 2.3 2 2 86 84 0 0 0 1 0 0 2 3 1
12 2.3 2 2 2 83 85 1 0 0 0 1 0 2 2 2
13 2.5 2 2.5 2.5 82 85 0 1 0 0 0 0 3 3 2
14
2.2
2.2
1.8 1.5 5
5 83 87 1 0 0 1 0 0 1 2 1
15
2 2 2.5 2.5 81 82 0 1 0 0 0 0 2 3 2
16
2.2
1.8 1.8 2 5 85 85 0 1 0 0 0 0 1 1 1
17
2 1.5
2.5 2.5 85 87 0 0 0 0 1 0 3 3 1
Regression Analysis on the Academic Performance of the Bachelor of Science in
Applied Statistics Students in Statistics / Rosalyn S. Bayacsan; et al. 2008
33
18 2.3 2 2 3 84 84 0 0 0 0 1 0 3 3 1
19
2.7
3 2.3 3 5 79 84 1 0 0 1 0 0 2 3 1
20
2.2
2.3 2 2.5 5 80 86 1 0 1 0 0 0 2 2 3
21
2.2
1.7
3 2.3 5
5 81 85 0 1 0 0 0 0 3 1 2
22
2.2
3 1.3 2 5 79 87 1 0 1 0 0 0 2 3 1
23
2.2
2.8 2.8 5 2.5 82 87 0 1 0 0 0 0 2 1 2
24
1.7
2.8 2.3 2 5 85 89 0 0 1 0 0 0 2 2 1
25
3 2.5 2 2 80 88 0 0 0 0 1 0 2 2 3
26
1.7
2.7
3 2 5
5 83 84 0 1 0 0 0 0 2 1 1
27 2.5 2.5 2 2 86 87 0 0 0 0 1 0 2 3 2
28
3 3 2 2.5 85 90 0 0 0 1 0 0 1 1 2
29 2.8 3 2 2 87 87 0 0 0 0 1 0 1 1 2
30
2.2
2.8 3 2.5 5 82 89 0 0 0 1 0 0 3 3 2
31
1.7
2.8 2.5 2 5 86 92 0 0 0 0 1 0 3 3 1
32
2.2
2.7
3 3 5
5 78 85 0 0 0 0 1 0 2 2 2
33 2.8 2.5 2 2 85 90 1 1 0 0 0 0 2 2 2
34
1.7
1.7
2.3 2 5
5 88 93 1 0 0 0 1 0 1 3 2
35
1.7
1.7
2.5 2 5
5 83 92 0 1 0 0 0 0 3 3 1
36
2.2
2.8 2.5 5 2.5 82 85 0 1 0 0 0 0 1 3 2
37
2.2
2.7
2.8 3 5
5 85 87 1 0 0 1 0 0 3 3 2
38
2.2
3 3 5 2 85 89 0 0 0 0 1 0 2 3 1
39
1.7
1.7
2.3 2.3 5
5 85 93 0 0 0 0 1 0 1 1 2
40
2.2
2.8 2.8 5 2 79 85 0 0 0 0 1 0 3 1 3
41
1.7
1.7
2.3 2 5
5 89 93 0 0 0 1 0 0 3 3 1
42
1.7
1.7
2.5 2 5
5 87 92 0 0 0 0 1 0 3 1 1
43 2.3 2.8 2.5 2 85 85 0 0 0 0 1 0 3 3 1
44
2.2
2.8 2.5 5 2 86 88 1 0 0 0 1 0 1 3 2
45
3 2.8
2.7
2.5 82 85 1 0 0 1 0 0 2 1 1
Regression Analysis on the Academic Performance of the Bachelor of Science in
Applied Statistics Students in Statistics / Rosalyn S. Bayacsan; et al. 2008
34
5
46 2.8 2.8 2 2 85 89 1 1 0 0 0 0 1 3 1
47
1.7
3 2.3 5 2.5 85 90 0 0 1 0 0 0 3 3 1
48
2.2
3 3 5 2 87 85 0 0 0 0 1 0 3 2 1
49
1.7
1.7
3 3 5
5 83 88 0 0 0 0 1 0 1 2 2
50
2.2
2.8 2.3 5 2 81 89 0 0 1 0 0 0 2 1 2
51
3 3 2.5 2.5 83 88 1 0 0 0 1 0 2 2 1
52
1.7
2.8 2.8 5 2 85 85 0 0 0 1 0 0 2 3 3
53
3 2.5
2.5 2.5 52 86 0 0 1 0 0 0 3 3 3
54
1.7
2.8 1.5 2 5 78 87 1 0 0 0 1 0 1 2 1
55
2.2
1.7
2.5 2.8 5
5 80 88 1 0 0 0 1 0 3 2 2
56
2.2
2 2.5 5 2 81 85 0 0 0 1 0 0 2 3 2
57
2.7
2.8 2.8 5 2 83 83 1 0 0 1 0 0 1 2 2
58
2.2
3 2.3 2.5 5 83 82 1 0 0 0 1 0 2 3 1
59
2.7
3 2 1.5 5 82 84 1 0 0 0 0 1 2 2 2
60
1.7
3 2 5 3 81 89 0 0 0 0 1 0 2 2 2
61
1.7
2 2.8 5 2.5 85 88 0 1 0 0 0 0 2 2 2
62
2.2
3 2.3 5 3 79 90 1 1 0 0 0 0 3 3 2
63
2.2
1.8 2 2 5 78 95 0 1 0 0 0 0 3 1 2
64 1.8 1.8 2.5 2.5 79 86 1 0 1 0 0 0 2 1 1
65
2.7
3 1.8 2.5 5 85 85 0 0 0 0 1 0 3 1 1
66 2.8 1.8 2.5 2 86 83 1 0 1 0 0 0 1 3 1
67
2.2
1.7
2.5 3 5
5 82 85 0 0 0 1 0 0 3 3 1
68
1.7
2.5 2.8 2 5 85 85 0 0 0 1 0 0 3 3 2
69
1.7
1.8 2.5 5 2 83 82 1 0 1 0 0 0 3 3 2
70
1.7
2.3 2.5 5 2 82 82 0 1 0 0 0 0 3 3 2
71
1.7
2 2.8 1.5 5 85 80 1 0 0 0 1 0 2 3 1
Regression Analysis on the Academic Performance of the Bachelor of Science in
Applied Statistics Students in Statistics / Rosalyn S. Bayacsan; et al. 2008
35
72
2.7
2 2.8 2 5 86 81 0 0 0 1 0 0 3 3 1
73
2.2
2.8 2.3 5 3 84 82 1 0 1 0 0 0 3 2 2
74
1.7
2.3 1.8 1.5 5 81 83 1 1 0 0 0 0 1 2 1
75
2.2
2.5 2.3 5 2 80 83 0 1 0 0 0 0 1 2 2
76
2.2
3 1.8 2 5 84 85 1 1 0 0 0 0 1 2 2
77 1.8 1.8 2 2.5 83 82 0 0 0 0 1 0 2 3 2
78 2.8 2.3 2.5 2 86 80 0 0 0 0 1 0 3 2 2
79
1.7
2.7
3 2.8 5
5 85 81 1 0 0 0 1 0 3 3 3
80
1.7
1.7
2 2.5 5
5 82 85 1 0 0 0 1 0 3 2 1
81
1.7
2 2.3 5 2 81 86 1 0 0 0 1 0 2 3 1
82
1.7
1.7
1.8 1.5 5
5 85 88 0 0 0 0 0 1 2 2 2
83
2.5
2.3 2 2 83 89 0 0 0 1 0 0 2 1 1
Appendix E. Regression Analysis Printouts
Correlations
Regression Analysis on the Academic Performance of the Bachelor of Science in
Applied Statistics Students in Statistics / Rosalyn S. Bayacsan; et al. 2008
36
Fathers' Hig
Mothers' Highest Educ
High School Average
Mathe
h
Annual Income
Statis
est Educa
English 11
University
Gender
Barangay
National
Private
m
IT 11
City
tics 11
IQ
atic
a
s 11
t
ional Atta
tiona
l Atta
in
in
ment
ment
Statistics 11 1.00 .448 .236 .174 -.239 .009 .068 .018 .002 -.067 .050 -.028 -.116 -.061 .073
0
Mathematic .448 1.00 .152 -.050 -.069 -.077 -.090 -.050 -.172 .218 .079 -.218 .016 .056 .152
s 11
0
English 11 .236 .152 1.00 .256 -.279 -.183 .058 -.061 .098 .192 -.066 -.240 .028 -.031 .012
0
IT 11
.174 -.050 .256 1.00 -.198 -.214 .028 .039 .007 -.060 -.043 .125 .157 .083 .055
Pear
0
so
IQ
-.239 -.069 -.279 -.198 1.00 .097 -.032 -.088 -.245 .114 .149 .001 -.040 .008 -.274
n Cor
0
High School .009 -.077 -.183 -.214 .097 1.00 -.154 .027 -.004 -.028 .019 -.040 -.007 -.197 -.031
r
e
Average
0
l
a
tio
Gender .068
-.090
.058 .028 -.032 -.154 1.00 -.083 .212 -.062 -.105 .175 -.225 .108 -.073
n
0
Barangay .018
-.050
-.061 .039 -.088 .027 -.083 1.00 -.198 -.248 -.433 -.114 -.148 -.131 .056
0
City .002
-.172
.098 .007 -.245 -.004 .212 -.198 1.00 -.191 -.334 -.088 .077 -.021 .057
0
University -.067 .218 .192 -.060 .114 -.028 -.062 -.248 -.191 1.00 -.417 -.110 .022 .080 -.061
0
National .050
.079
-.066 -.043 .149 .019 -.105 -.433 -.334 -.417 1.00 -.192 .046 .033 -.054
0
Private -.028 -.218 -.240 .125 .001 -.040 .175 -.114 -.088 -.110 -.192 1.00 .010 .055 .041
0
Fathers' -.116 .016 .028 .157 -.040 -.007 -.225 -.148 .077 .022 .046 .010 1.00 .199 .040
Highest
0
Educational
Attainment
Mothers' -.061 .056 -.031 .083 .008 -.197 .108 -.131 -.021 .080 .033 .055 .199 1.00 -.093
Highest
0
Educational
Regression Analysis on the Academic Performance of the Bachelor of Science in
Applied Statistics Students in Statistics / Rosalyn S. Bayacsan; et al. 2008
37
Attainment
Annual .073 .152 .012 .055 -.274 -.031 -.073 .056 .057 -.061 -.054 .041 .040 -.093 1.00
Income
0
Statistics 11 . .000 .016 .058 .015 .467 .269 .436 .494 .274 .327 .402 .148 .292 .257
Mathematic .000 . .085 .327 .269 .243 .210 .326 .060 .024 .240 .024 .442 .307 .085
Sig
s 11
.
(1
English 11 .016 .085 . .010 .005 .049 .300 .293 .189 .041 .275 .014 .401 .389 .457
-Tailed)
IT 11
.058 .327 .010
. .037 .026 .402 .363 .474 .295 .348 .129 .078 .229 .310
IQ
.015 .269 .005 .037
. .191 .386 .214 .013 .152 .090 .498 .359 .470 .006
High School .467 .243 .049 .026 .191
. .082 .403 .487 .403 .432 .361 .474 .037 .390
Average
Gender .269 .210 .300 .402 .386 .082
. .227 .027 .290 .174 .057 .021 .166 .256
Barangay .436 .326 .293 .363 .214 .403 .227
. .036 .012 .000 .152 .091 .119 .308
City
.494 .060 .189 .474 .013 .487 .027 .036
. .042 .001 .215 .245 .426 .306
University .274 .024 .041 .295 .152 .403 .290 .012 .042
. .000 .161
.423 .236 .293
National .327 .240 .275 .348 .090 .432 .174 .000 .001 .000
. .041 .339 .383 .315
Private .402 .024 .014 .129 .498 .361 .057 .152 .215 .161 .041
. .464
.310 .357
Fathers' .148 .442 .401 .078 .359 .474 .021 .091 .245 .423 .339 .464 . .035 .361
Highest
Educational
Attainment
Mothers' .292 .307 .389 .229 .470 .037 .166 .119 .426 .236 .383 .310 .035 . .201
Highest
Educational
Attainment
Annual .257 .085 .457 .310 .006 .390 .256 .308 .306 .293 .315 .357 .361 .201
.
Income
N
83 83 83 83 83 83 83 83 83 83 83 83 83 83 83
Regression Analysis on the Academic Performance of the Bachelor of Science in
Applied Statistics Students in Statistics / Rosalyn S. Bayacsan; et al. 2008
38
Variables Entered/Removed
Model
Variables Entered Variables Removed
Method
1 Annual
Income, . Enter
English 11, Fathers'
Highest Educational
Attainment,
National, High
School Average,
Mathematics 11,
Gender, Mothers'
Highest Educational
Attainment, IT 11,
IQ, Private, City,
University
a Tolerance = .000 limits reached.
b Dependent Variable: Statistics 11
Model Summary
Model
R
R Square
Adjusted R Std. Error of the
Square
Estimate
1 .594 .352 .230 .410
a Predictors: (Constant), Annual Income, English 11, Fathers' Highest
Educational Attainment, National, High School Average, Mathematics 11,
Gender, Mothers' Highest Educational Attainment, IT 11, IQ, Private, City,
University
ANOVA
Model Sum
of
df Mean F Sig.
Squares
Square
1 Regression
6.300 13 .485 2.888 .002
Residual
11.576 69 .168
Total
17.876
82
a Predictors: (Constant), Annual Income, English 11, Fathers' Highest
Educational Attainment, National, High School Average, Mathematics 11,
Gender, Mothers' Highest Educational Attainment, IT 11, IQ, Private, City,
University
b Dependent Variable: Statistics 11
Regression Analysis on the Academic Performance of the Bachelor of Science in
Applied Statistics Students in Statistics / Rosalyn S. Bayacsan; et al. 2008
39
Coefficients
Unstandardized
Standardized
t Sig.
Coefficients
Coefficients
Model
B Std.
Error
Beta
1 (Constant) .540 1.896
.285 .777
Mathematics
.484 .102 .507
4.762
.000
11
English
11 .218 .170 .146 1.287 .203
IT
11 .199 .127
.168
1.568
.121
IQ
-1.507E-02
.012
-.141
-1.266
.210
High
School
1.776E-02 .015 .120 1.159 .250
Average
Gender
5.577E-02
.104 .058 .539
.592
City
3.613E-02
.169
.026
.214
.831
University -.171 .153 -.145 -1.117
.268
National
2.033E-02
.125 .022 .163
.871
Private .192 .245 .088 .783
.437
Fathers'
-8.363E-02 .066 -.134 -1.271 .208
Highest
Educational
Attainment
Mothers'
-3.211E-02 .063 -.053 -.506 .615
Highest
Educational
Attainment
Annual
-4.404E-02 .078 -.058 -.561 .576
Income
a Dependent Variable: Statistics 11
Excluded Variables
Beta
In
t
Sig.
Partial
Collinearity
Correlation Statistics
Model
Tolerance
1
Barangay
. . . .
.000
a Predictors in the Model: (Constant), Annual Income, English 11, Fathers'
Highest Educational Attainment, National, High School Average, Mathematics
11, Gender, Mothers' Highest Educational Attainment, IT 11, IQ, Private, City,
University
b Dependent Variable: Statistics 11
Regression Analysis on the Academic Performance of the Bachelor of Science in
Applied Statistics Students in Statistics / Rosalyn S. Bayacsan; et al. 2008
Document Outline
- Regression Analysis on the Academic Performance of the Bachelor of Science in
Applied Statistics Students in Statistics.
- BIBLIOGRAPHY
- ABSTRACT
- TABLE OF CONTENTS
- INTRODUCTION
- REVIEW OF LITERATURE
- THEORETICAL FRAMEWORK
- METHODOLOGY
- RESULTS AND DISCUSSION
- SUMMARY, CONCLUSIONS AND RECOMMENDATIONS
- LITERATURE CITED
- Appendix