Group report on
Multiple Linear Regression and Correlation Analysis
Business statistics II
Section: A
Submitted By
Mustakim Billah
(111193087)
Sumiya Haque Mim
(114191009)
Md. Rahat -Ul- Ashekin
(111192108)
Shahriar Tanvir Rakib
(111202016)
Submitted to
Md. Kazimul Hoque
Assistant professor
School of Business & Economics, UIU
Date of Submission: 18 September 2022
Developed questionnaire for the survey:
1.What is your average grade point till now?





less than 2
2-2.5
2.5-3
3-3.5
3.5-4
2. How many classes do you miss





missed less than 2 classes
missed up to3-4 classes
missed up to 5-6 classes
missed up to 7-8 classes
more
3. How much do you time spend on studying?





less then .5 hours
.5-1 hours
1-1.5 hours
1.5-2 hours
over 2 hours
4. How much motivated do you feel while studying?





highly motivated .( I am extremely curious to learn.)
moderately motivated. ( I feel sufficient amount of motivation)
average. (my study time is not enough to motivate myself.)
less motivated. (my study time is not enough to motivate myself.)
not motivated. ( I don't study at all)
5. How much stressful do you feel to study?





high stress.( I feel extremely stress while studying.)
moderate stress. (I feel noticeable amount of stress while studying.)
average stress. ( I feel some stress while studying.)
less stress. (I feel a little stress, but it's okay.)
no stress. ( I don't feel any stress at all)
6. How much engagement do you feel towards your courses?





highly engagement . ( I am extremely curious to learn.)
moderate engagement.(I find sufficient amount of motivation)
average engagement. ( I find some courses interesting)
less engagement. ( I find only few courses boring)
no engagement. ( I don't find any courses interesting)
Survey data:
Student
no.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
CGPA
Study time
4
5
4
4
5
3
4
5
2
4
5
3
3
4
5
4
2
4
5
4
3
5
5
2
4
3
5
3
4
5
Motivation
3
3
4
3
4
2
3
5
1
5
5
3
2
4
3
5
1
3
4
4
4
5
4
1
5
2
5
3
2
4
3
3
3
4
4
1
3
4
1
3
5
2
3
4
3
4
2
5
5
4
4
4
5
2
5
2
4
3
3
5
Engagement
toward
courses
4
4
3
3
4
1
4
4
1
4
4
2
4
4
4
4
1
4
4
4
3
4
4
1
5
1
4
3
3
4
Stress
level
Attendance
2
1
3
2
3
5
2
1
4
3
1
4
3
2
2
3
5
2
2
1
3
3
1
5
4
5
2
3
1
2
4
5
5
3
5
2
3
5
1
5
J5
3
4
5
4
4
1
5
4
5
4
5
5
3
5
3
5
3
4
4
Findings:
Descriptive Statistics
Mean
Std. Deviation
N
cGPA
3.93
.980
30
Study_time
3.40
1.276
30
Motivation
3.30
1.179
30
Attendance
3.43
1.165
30
Stress
2.67
1.295
30
Attitude
3.97
1.189
30
Comment: We have taken 30 samples in total. The mean cGPA of 30 samples scores 3.93 in a 15 range of scale, indicating the mean students are having a cGPA of just below 3.00. The
standard deviation for cGPA is 0.980, which indicated that 68% of the data are clustered very
closely around the mean score.
Correlations
cGPA
Pearson Correlation
cGPA
Attendance
Stress
Attitude
.739
.794
.721
-.751
.768
Study_time
.739
1.000
.766
.738
-.480
.782
Motivation
.794
.766
1.000
.806
-.723
.820
Attendance
.721
.738
.806
1.000
-.632
.733
-.751
-.480
-.723
-.632
1.000
-.635
.768
.782
.820
.733
-.635
1.000
.
.000
.000
.000
.000
.000
Study_time
.000
.
.000
.000
.004
.000
Motivation
.000
.000
.
.000
.000
.000
Attendance
.000
.000
.000
.
.000
.000
Stress
.000
.004
.000
.000
.
.000
Attitude
.000
.000
.000
.000
.000
.
cGPA
30
30
30
30
30
30
Study_time
30
30
30
30
30
30
Motivation
30
30
30
30
30
30
Attendance
30
30
30
30
30
30
Stress
30
30
30
30
30
30
Attitude
30
30
30
30
30
30
Attitude
N
Motivation
1.000
Stress
Sig. (1-tailed)
Study_time
cGPA
Comment: The strongest correlation of the dependent variable cGPA is with the independent
variable Motivation. So, among all the factors, the level of Motivation a student is having is the
strongest influencer of the student’s performance. Here, as the value is positive (0.739), we can
say there is a direct positive relationship between these two variables. It seems obvious, because
the more motivation a student feels towards her study, the better cGPA she will be able to
achieve.
Model Summary
Model
1
R
R Square
.874
Adjusted R
Std. Error of the
Square
Estimate
.764
a
.715
Change Statistics
R Square Change
.523
F Change
.764
df1
15.567
df2
5
Sig. F Change
24
a. Predictors: (Constant), Attitude, Stress, Attendance, Study_time, Motivation
Comment:
R is the correlation between the predicted values and the observed values of the dependent
variable (Here, cGPA). As the value is positive and close to 1.00, there is a strong direct
relationship between the actual and observed values.
R square is the square of this coefficient and indicates the percentage of variation in the
dependent variable explained by the variation in the dependent variables. Here the adjusted R
square value (which is more accurate than R square) indicates that the 5 independent variables
altogether are explaining 76.4% of the data in the the variation of cGPA of a typical student.
The rest of 23.6% of the variation in cGPA can be explained by the presence of some controlled
variables or some insignificant variables.
ANOVAa
Model
1
Sum of Squares
Regression
Residual
Total
df
Mean Square
21.299
5
4.260
6.568
24
.274
27.867
29
a. Dependent Variable: cGPA
b. Predictors: (Constant), Attitude, Stress, Attendance, Study_time, Motivation
F
15.567
Sig.
.000b
.000
Comment: Here, the calculated F value 15.567 indicates a P value which is very close to 0, ( Far
less than the significance level 0.05). So we reject the null hypothesis.
Coefficientsa
Unstandardized Coefficients
Model
1
B
Std. Error
(Constant)
3.045
.723
Study_time
.251
.140
Motivation
.090
Attendance
Stress
Attitude
Standardized
95.0% Confidence Interval for
Coefficients
B
Beta
t
Sig.
Lower Bound
Correlations
Upper Bound
Zero-order
Partial
Part
4.211
.000
1.553
4.538
.326
1.790
.086
-.038
.540
.739
.343
.177
.188
.108
.475
.639
-.299
.478
.794
.097
.047
.026
.151
.031
.174
.864
-.286
.339
.721
.035
.017
-.307
.114
-.406
-2.699
.013
-.542
-.072
-.751
-.483
-.267
.118
.161
.143
.736
.469
-.213
.450
.768
.149
.073
a. Dependent Variable: Cgpa
Comment: Here, the regression equation will be:
Y= 3.045+ 0.251 x^1 + 0.090x^2+ 0.026x^3- 0.307x^4+ 0.118x^5
Here, the regression coefficient of mean study time is 0.251. The coefficient is positive and
shows a direct relationship between cGPA and Study time. As the study time increases, the
cGPA of a student increases.
Here, like the study time, Motivation, Attendance and Attitude toward study are also having
direct positive relationship with cGPA; indicating the more Study time, Motivation, Attendance
and Attitude a student is having, better she will be able to achieve a good grade.
Among the five independent variables, only Stress Level has a negative coefficient value,
indicating an indirect relationship between stress and cGPA. It is also obvious, because more
stress a student is having in her study life, the more difficulties she will be facing to achieve a
good grade.
Reference:
http://article.scieducationalresearch.com/pdf/EDUCATION-2-9-8.pdf