Regression Analysis

SUMAIRA YOUSUF Registration Number: 2025-BBA/FMS/F07 E-mail ID: [email protected] Assignment: TRANSFORMATION OF DATA INTO VIABLE INFORMATION Course: STATISTICAL INTEFERENCE Course Title: QNT-401

INTERNATIONAL ISLAMIC UNIVERSITY, ISLAMABAD

ACNOWLEDGEMENT 1

Firstly, I would like to thank whole-heartedly to ALLAH, THE ALMIGHTY. Who gave me courage, knowledge and confidence to carry out & complete this project. I am also thankful to our respected Sir, Mr. Khushnoor, who gave the useful information and guidance to complete this project. I would also like to thank my PARENTS who are there to motivate me and build my confidence which helps me in walk of my life.

Scenario 2

Data has been gathered to find the impact of various educational factors on CGPA of Students. We have taken a sample of 38 students, 19 males and 19 females, of fourth semester doing BBA (HONS) in International Islamic University.

Relationship of dependent variable (CGPA) has been made with various Impendent variables (Inter pct, Medium of Instruction, Institute, Quantitative Subjects (Principles of Accounting1, Principles of Accounting2 and Cost Accounting) and Verbal Subjects (Functional English1, Functional English 2 and Oral Communication)) using the software SPSS (Statistical Package for Social Sciences).

First we used Scatter Matrix, Correlations Matrix and Mean mutually for all students. Secondly, we split the results according to gender, and separately observed Scatter Matrix, Correlation Matrix and Mean. After this, we took out Simple Regressions Correlation and Multiple Regression Correlation in order to find the impact of cause (Quant1, Inter pct, Institute, Verbal 1 and MOIM) and effect (CGPA) according to the highest correlation.

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CONTENTS Mean and Standard Deviation.............................................................................................5 RESULTS and INTERPRETATIONS...............................................................................7 SCATTER MATRIX.......................................................................................................9 RESULTS and INTERPRETATIONS...............................................................................9 CORRELATIONS.........................................................................................................11 RESULTS and INTERPRETATIONS.............................................................................12 MEASUREMENTS ACCORDING TO GENDER.................................................................15 MEAN AND Standard Deviation.......................................................................................15 RESULTS and INTERPRETATIONS for Males................................................................15 RESULTS and INTERPRETATIONS for Females.............................................................16 SCATTER MATRIX for Males........................................................................................17 RESULTS and INTERPRETATIONS.............................................................................18 SCATTER MATRIX for Females......................................................................................20 RESULTS and INTERPRETATIONS.............................................................................21 CORRELATION According to Gender...............................................................................22 RESULTS and INTERPRETATIONS for Males................................................................24 RESULTS and INTERPRETATIONS for Females.............................................................27 SIMPLE REGRESSION CORRELATION..........................................................................29 REGRESSION EQUATION/MODEL with Quant 1 as Predictor Variable and CGPA as response Variable...................................................................................................................32 TESTING OF HYPOTHESIS FOR MODEL 1(with QUANT1 as predictor):.............................33 REGRESSION EQUATION/MODEL with INTER PCT as Predictor Variable and CGPA as response Variable...................................................................................................................41 TESTING OF HYPOTHESIS FOR MODEL 1(with INTER PCT as predictor):..........................42 REGRESSION EQUATION/MODEL with INSTITUTE as Predictor Variable and CGPA as response Variable...................................................................................................................47 TESTING OF HYPOTHESIS FOR MODEL 1(with INSTITUTE as predictor):.........................48

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REGRESSION EQUATION/MODEL with VERBAL1 as Predictor Variable and CGPA as response Variable...................................................................................................................53 TESTING OF HYPOTHESIS FOR MODEL 1(with Verbal1 as predictor):...............................54 REGRESSION EQUATION/MODEL with MOIM as Predictor Variable and CGPA as response Variable...................................................................................................................58 TESTING OF HYPOTHESIS FOR MODEL 1(with MOIM as predictor):.................................60 MULTIPLE REGRESSION EQUATION/MODEL.............................................................67 TESTING OF HYPOTHESIS (with ‘Quant1’, ‘Inter pct’, ‘Institute’, ‘Verbal1’ and ‘MOIM’ as predictors):...............................................................................................................68 TESTING OF HYPOTHESIS (with ‘Inter pct’ ‘Quant1’, ‘Institute’, ‘Verbal1’ and ‘MOIM’ as predictors):...............................................................................................................70 TESTING OF HYPOTHESIS (with ‘Institute’, ‘Inter pct’ ‘Quant1’ , ‘Verbal1’ and ‘MOIM’ as predictors):...............................................................................................................72 TESTING OF HYPOTHESIS (with ‘Verbal1’ ‘Institute’, ‘Inter pct’ ‘Quant1’ and ‘MOIM’ as predictors):...............................................................................................................74 TESTING OF HYPOTHESIS (with ‘MOIM’ ‘Institute’, ‘Inter pct’ ‘Quant1’ and ‘Verbal1’ as predictors):...............................................................................................................76 TESTING OF HYPOTHESIS (with ‘MOIM’ ‘Institute’, ‘Inter pct’ ‘Quant1’ and ‘Verbal1’ as predictors):

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A Brief Introduction to SPSS SPSS provides facilities for analyzing and displaying information using a variety of techniques. This document uses version 15 of SPSS for Windows. It looks a lot like Microsoft excel as they are both spread sheets. However there are at least two features of SPSS which distinguish from excel which makes it particularly useful for employment in social sciences.

Prerequisites

Basic familiarity with Windows and at least an elementary knowledge of simple statistics (statistical theory is not explained).

Mean and Standard Deviation

6

7

Descriptive Statistics

Mean

CGPA

Std. Deviation

N

3.2439

.41850

38

73.03

6.780

38

.11

.311

38

1.29

.460

38

QUANT1

4.1535

1.29817

38

Verbal1

4.6316

.68790

38

Intercept

MOIM

Institute

8

RESULTS and INTERPRETATIONS A2: Result (Conclusion) When mean of Intercept is 73.04, mean CGPA is 3.2439. Interpretation (Discussion) As mean intercept increases, CGPA increases.

A3: Result (Conclusion) When mean of MOIM is .11, mean CGPA is 3.2439. Interpretation (Discussion)

As mean of Urdu MOIM increases, CGPA decreases.

A4: Result (Conclusion) When mean of Public is 1.29, mean CGPA is 3.2439. Interpretation (Discussion) As mean of Urdu MOIM increases, CGPA decreases.

A5: Result (Conclusion) When mean of Quantitative subjects is 4.15, mean CGPA is 3.2439. Interpretation (Discussion) As mean of Quantitative subjects increases, CGPA increases. 9

A6: Result (Conclusion) When mean of Verbal subjects is 4.63, mean of CGPA is 3.2439. Interpretation (Discussion) As mean of verbal subjects’ increases, CGPA increases.

SCATTER MATRIX Gender

Verbal1

QUANT1

Instiute

MOIM

Intercept

CGPA

M ale Fem ale Fit line for Total

CGPA Intercept M OIM

Instiute QUANT1 Verbal1

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RESULTS and INTERPRETATIONS A2: Result (Conclusion) There is a positive correlation between CGPA and Intercept. Interpretation (Discussion) When Inter pct increases, CGPA also increases.

A3: Result (Conclusion) There is a slightly negative relationship between CGPA and Urdu Medium of Instruction. Interpretation (Discussion) When the ratio of Urdu medium intermediate pass-outs increases, CGPA decreases.

A4: Result (Conclusion) There is a positive correlation between CGPA and Public Institutions. Interpretation (Discussion) When the ratio of Public Institution pass outs increases, CGPA increases.

A5: Result (Conclusion) There is a positive correlation between CGPA and Quantitative Results. Interpretation (Discussion) When marks obtained by students in quantitative subjects increase, CGPA also increases.

11

A6: Result (Conclusion) There is a positive correlation between CGPA and Verbal Results. Interpretation (Discussion) When marks obtained by students in verbal subjects increase, CGPA also increases.

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CORRELATIONS Correlations CGPA CGPA

Pearson Correlation

1

Sig. (2-tailed) Intercept

N Pearson Correlation Sig. (2-tailed) N

MOIM

Pearson Correlation Sig. (2-tailed) N

Instiute

Pearson Correlation Sig. (2-tailed) N

QUANT1

Pearson Correlation Sig. (2-tailed) N

Verbal1

Pearson Correlation Sig. (2-tailed) N

38 .593(**)

Intercept .593(**)

MOIM -.010

Instiute .489(**)

QUANT1 .791(**)

Verbal1 .419(**)

.000

.955

.002

.000

.009

38 1

38 .037

38 .422(**)

38 .505(**)

38 .334(*)

.000

.825

.008

.001

.040

38

38

38

38

38

38

-.010

.037

1

-.030

-.086

.228

.955

.825

.859

.609

.168

38

38

38

38

38

38

.489(**)

.422(**)

-.030

1

.309

.147

.002

.008

.859

.059

.379

38

38

38

38

38

38

.791(**)

.505(**)

-.086

.309

1

.309

.000

.001

.609

.059

38

38

38

38

38

38

.419(**)

.334(*)

.228

.147

.309

1

.009

.040

.168

.379

.059

38

38

38

38 38 ** Correlation is significant at the 0.01 level (2-tailed). * Correlation is significant at the 0.05 level (2-tailed)

.059

38

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VALIDITY COFFICIENTS

RESULTS and INTERPRETATIONS Result (Conclusion)

rci (38) = .593 ; p<.01 Interpretation (Discussion)

As ρ<α , we reject Ho, results are highly statistically significant i.e. at 1% level of significance. The sample data supports the alternative hypothesis (HA). I.e. Population correlation coefficient is 14

significantly different from zero. (The relationship between the variables in the sample also holds for same variables in the Population). To put it in other words we can generalize the sample results for the whole Population. In the current situation, the correlation between the CGPA and intermediate percentage for students is .635 which holds for the sample as well for the whole Population of students.

Result (Conclusion)

rcm (38) = -.010 ; p>.05 Interpretation (Discussion)

As ρ>α , o we do not reject Ho, the results are not statistically significant at 5% level of significance. The sample data does not support the alternative hypothesis (HA). I.e. the Population correlation coefficient is not significantly different from zero. (The relationship between the variables in the sample does not hold for same variables in the Population). To put it in other words we cannot generalize the sample results for the whole Population. In the current situation, the correlation between the CGPA and Institution for students is -0.10 which only holds for the sample and not for the whole Population of students.

Result (Conclusion)

rci (38) = .489; p<.01 Interpretation (Discussion)

As ρ<α , we reject Ho, results are highly statistically significant i.e. at 1% level of significance. The sample data supports the alternative hypothesis (HA). I.e. Population correlation coefficient is significantly different from zero. (The relationship between the variables in the sample also holds for same variables in the Population). To put it in other words we can generalize the sample results for the 15

whole Population. In the current situation, the correlation between the CGPA and intermediate percentage for students is .489 which holds for the sample as well for the whole Population of students. Result (Conclusion)

rcq (38) = .791; p<.01 Interpretation (Discussion)

As ρ<α , we reject Ho, results are highly statistically significant i.e. at 1% level of significance. The sample data supports the alternative hypothesis (HA). I.e. Population correlation coefficient is significantly different from zero. (The relationship between the variables in the sample also holds for same variables in the Population). To put it in other words we can generalize the sample results for the whole Population. In the current situation, the correlation between the CGPA and intermediate percentage for students is .791 which holds for the sample as well for the whole Population of students.

Result (Conclusion)

rcv (38) = .419; p<.01 Interpretation (Discussion)

As ρ<α , we reject Ho, results are highly statistically significant i.e. at 1% level of significance. The sample data supports the alternative hypothesis (HA). I.e. Population correlation coefficient is significantly different from zero. (The relationship between the variables in the sample also holds for same variables in the Population). To put it in other words we can generalize the sample results for the whole Population. In the current situation, the correlation between the CGPA and intermediate percentage for students is .419 which holds for the sample as well for the whole Population of students.

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MEASUREMENTS ACCORDING TO GENDER MEAN AND Standard Deviation Descriptive Statistics Gender Male

CGPA Intercept MOIM

Std. Deviation .47080 7.945

N 19 19

.11

.315

19

1.47

.513

19

QUANT1

4.2456

1.32796

19

Verbal1

4.7193

.68730

19

CGPA

3.2021

.36698

19

72.37

5.520

19

.11

.315

19

Institute

Female

Mean 3.2858 73.68

Intercept MOIM Institute

1.11

.315

19

QUANT1

4.0614

1.29721

19

Verbal1

4.5439

.69576

19

RESULTS and INTERPRETATIONS for Males  A2: Result (Conclusion) When mean of Intercept is 73.68, mean CGPA is 3.2858  Interpretation (Discussion) As mean intercept increases, CGPA increases.

17

 A3: Result (Conclusion) When mean of MOIM is .11, mean CGPA is 3.2858  Interpretation (Discussion) As mean Urdu MOIM increases, CGPA decreases.

 A4: Result (Conclusion) When mean of Institution is 1.47, mean of CGPA is 3.2858  Interpretation (Discussion) As mean of Urdu MOIM increases, CGPA decreases.  A5: Result (Conclusion) When mean of Quantitative subjects is 4.24, mean CGPA is 3.2858  Interpretation (Discussion) As mean of Quantitative subjects increases, CGPA increases

 A6: Result (Conclusion) When mean of Verbal subjects is 4.63, mean of CGPA is 3.2858  Interpretation (Discussion) As mean of verbal subjects’ increases, CGPA increases

RESULTS and INTERPRETATIONS for Females  A2: Result (Conclusion) When mean of Intercept is 72.47, mean CGPA is 3.202  Interpretation (Discussion) As mean intercept increases, CGPA increases.

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 A3: Result (Conclusion) When mean of MOIM is .11, mean of CGPA is 3.202  Interpretation (Discussion) As mean of MOIM increases, CGPA decreases.  A4: Result (Conclusion) When mean of Public is 1.11, mean of CGPA is 3.202  Interpretation (Discussion) As mean of Urdu MOIM increases, CGPA decreases.  A5: Result (Conclusion) When mean of Quantitative subjects is 4.06, mean of CGPA is 3.202  Interpretation (Discussion) As mean of Quantitative subjects increases, CGPA increases

 A6: Result (Conclusion) When mean of Verbal subjects is 4.54, mean of CGPA is 3.202  Interpretation (Discussion) As mean of verbal subjects increase, CGPA increases

SCATTER MATRIX for Males Graph  Legacy Dialogues  Scatter plot  Matrix Scatter

19

Gender: Male

CGPA

Gender

Verbal1

QUANT1

Instiute

MOIM

Intercept

Male Fit line for Total

CGPA

Intercept

MOIM

Instiute

QUANT1

Verbal1

RESULTS and INTERPRETATIONS  A2: Result (Conclusion) There is a positive correlation between CGPA and Intercept.  Interpretation (Discussion) When Inter pct of male students increases, CGPA also increases.

 A3: Result (Conclusion) 20

There is a slightly negative relationship between CGPA and Urdu Medium of Instruction.  Interpretation (Discussion) When the ratio of Urdu medium intermediate pass-outs of males increases, CGPA decreases.

 A4: Result (Conclusion) There is a positive correlation between CGPA and Public Institutions.  Interpretation (Discussion) When the ratio of Public Institution pass outs of males increases, CGPA increases.

 A5: Result (Conclusion) There is a positive correlation between CGPA and Quantitative Results.  Interpretation (Discussion) When marks obtained by male students in quantitative subjects increase, CGPA also increases.

 A6: Result (Conclusion) There is a positive correlation between CGPA and Verbal Results.  Interpretation (Discussion) When marks obtained by male students in verbal subjects increase, CGPA also increases.

21

SCATTER MATRIX for Females

Gender: Female

CGPA

Gender

Verbal1

QUANT1

Instiute

MOIM

Intercept

Female Fit line for Total

CGPA

Intercept

MOIM

Instiute QUANT1 Verbal1

22

RESULTS and INTERPRETATIONS  A2: Result (Conclusion) There is a positive correlation between CGPA and Intercept.  Interpretation (Discussion) When Inter pct of female students increases, CGPA also increases.

 A3: Result (Conclusion) There is a negative relationship between CGPA and Urdu Medium of Instruction.  Interpretation (Discussion) When the ratio of Urdu medium intermediate pass-outs of females increases, CGPA decreases.

 A4: Result (Conclusion) There is a positive correlation between CGPA and Public Institutions.  Interpretation (Discussion) When the ratio of Public Institution pass outs of females increases, CGPA increases.

 A5: Result (Conclusion) There is a positive correlation between CGPA and Quantitative Results.  Interpretation (Discussion) When marks obtained by female students in quantitative subjects increase, CGPA also increases.

 A6: Result (Conclusion) There is a positive correlation between CGPA and Verbal Results.  Interpretation (Discussion) 23

When marks obtained by female students in verbal subjects increase, CGPA also increases.

CORRELATION According to Gender Correlations Gender

Male

CGPA

CGPA

Pearson Correlation

Intercept

1

Intercept

Pearson Correlation

Sig. (2-tailed)

N

MOIM

QUANT1

Verbal1

.052

.558(*)

.675(**)

.598(**)

.003

.833

.013

.002

.007

19

19

19

19

19

19

.635(**)

1

.058

.557(*)

.448

.505(*)

.812

.013

.054

.027

.003

19

19

19

19

19

19

Pearson Correlation

.052

.058

1

.018

-.154

.400

Sig. (2-tailed)

.833

.812

.941

.530

.089

19

19

19

19

19

19

.558(*)

.557(*)

.018

1

.282

.398

.013

.013

.941

.242

.091

19

19

19

19

19

N

Institute

Institute

.635(**)

Sig. (2-tailed)

N

MOIM

Pearson Correlation

Sig. (2-tailed)

N

19

24

QUANT1

Pearson Correlation

Sig. (2-tailed)

.675(**)

.448

-.154

.282

.002

.054

.530

.242

19

19

19

19

19

19

.598(**)

.505(*)

.400

.398

.486(*)

1

.007

.027

.089

.091

.035

19

19

19

19

19

19

1

.505(*)

-.088

.363

.952(**)

.184

N

Verbal1

Pearson Correlation

Sig. (2-tailed)

N Female

CGPA

Pearson Correlation Sig. (2-tailed) Pearson Correlation Sig. (2-tailed) Pearson Correlation Sig. (2-tailed)

.719

.127

.000

.451

19

19

19

19

19

.505(*)

1

.008

.104

.597(**)

.085

.027

.973

.671

.007

.730

19

19

19

19

19

19

-.088

.008

1

-.118

-.017

.062

.719

.973

.631

.946

.800

19

19

19

19

19

19

.363

.104

-.118

1

.368

-.360

.127

.671

.631

.121

.130

19

19

19

19

19

19

.952(**)

.597(**)

-.017

.368

1

.118

.000

.007

.946

.121

19

19

19

19

19

19

.184

.085

.062

-.360

.118

1

.451

.730

.800

.130

.630

19

19

19

19

19

N Institute

Pearson Correlation Sig. (2-tailed) N

QUANT1

Pearson Correlation Sig. (2-tailed) N

Verbal1

Pearson Correlation Sig. (2-tailed)

.035

.027

N MOIM

.486(*)

19

N Intercept

1

N

.630

19

** Correlation is significant at the 0.01 level (2-tailed). * Correlation is significant at the 0.05 level (2-tailed).

25

VALIDITY COFFICIENTS

RESULTS and INTERPRETATIONS for Males Result (Conclusion)

rci (19) = .635 ; p<.01

26

Interpretation (Discussion) As ρ<α , we reject Ho, results are highly statistically significant i.e. at 1% level of significance. The sample data supports the alternative hypothesis (HA). I.e. Population correlation coefficient is significantly different from zero. (The relationship between the variables in the sample also holds for same variables in the Population). To put it in other words we can generalize the sample results for the whole Population. In the current situation, the correlation between the CGPA and intermediate percentage for male students is .635 which holds for the sample as well for the whole Population of male students.

Result (Conclusion)

rcm (19) = .052; p>.05

Interpretation (Discussion) As ρ>α , o we do not reject Ho, the results are not statistically significant at 5% level of significance. The sample data does not support the alternative hypothesis (HA). I.e. the Population correlation coefficient is not significantly different from zero. (The relationship between the variables in the sample does not hold for same variables in the Population). To put it in other words we cannot generalize the sample results for the whole Population. In the current situation, the correlation between the CGPA and Institution for male students is 0.5 which only holds for the sample and not for the whole Population of male students.

Result (Conclusion)

rci (19) = .558 ; p<.05

27

Interpretation (Discussion) As ρ<α , we reject Ho, results are statistically significant i.e. at 5% level of significance. The sample data supports the alternative hypothesis (HA). I.e. Population correlation coefficient is significantly different from zero. (The relationship between the variables in the sample also holds for same variables in the Population). To put it in other words we can generalize the sample results for the whole Population. In the current situation, the correlation between the CGPA and intermediate percentage for male students is .558 which holds for the sample as well for the whole Population of male students.

Result (Conclusion)

rcq (19) = .675; p<.01

Interpretation (Discussion) As ρ<α , we reject Ho, results are highly statistically significant i.e. at 1% level of significance. The sample data supports the alternative hypothesis (HA). I.e. Population correlation coefficient is significantly different from zero. (The relationship between the variables in the sample also holds for same variables in the Population). To put it in other words we can generalize the sample results for the whole Population. In the current situation, the correlation between the CGPA and intermediate percentage for male students is .675 which holds for the sample as well for the whole Population of male students.

Result (Conclusion)

rcv (19) = .598; p<.01

Interpretation (Discussion) As ρ<α , we reject Ho, results are highly statistically significant i.e. at 1% level of significance. The sample data supports the alternative hypothesis (HA). I.e. Population correlation coefficient is significantly different from zero. (The relationship between the variables in the sample also holds for 28

same variables in the Population). To put it in other words we can generalize the sample results for the whole Population. In the current situation, the correlation between the CGPA and intermediate percentage for male students is .598 which holds for the sample as well for the whole Population of male students.

29

RESULTS and INTERPRETATIONS for Females Result (Conclusion)

rci (19) = .505 ; p<.05

Interpretation (Discussion) As ρ<α , we reject Ho, results are statistically significant i.e. at 5% level of significance. The sample data supports the alternative hypothesis (HA). I.e. Population correlation coefficient is significantly different from zero. (The relationship between the variables in the sample also holds for same variables in the Population). To put it in other words we can generalize the sample results for the whole Population. In the current situation, the correlation between the CGPA and intermediate percentage for female students is .505 which holds for the sample as well for the whole Population of female students.

Result (Conclusion)

rcm (19) = -.088 ; p>0.5

Interpretation (Discussion) As ρ>α , o we do not reject Ho, the results are not statistically significant at 5% level of significance. The sample data does not support the alternative hypothesis (HA). I.e. the Population correlation coefficient is not significantly different from zero. (The relationship between the variables in the sample does not hold for same variables in the Population). To put it in other words we cannot generalize the sample results for the whole Population. In the current situation, the correlation between the CGPA and Institution for female students is -.088 which only holds for the sample and not for the whole Population of female students.

30

Result (Conclusion)

rci (19) = .363 ; p>.05

Interpretation (Discussion) As ρ>α , o we do not reject Ho, the results are not statistically significant at 5% level of significance. The sample data does not support the alternative hypothesis (HA). I.e. the Population correlation coefficient is not significantly different from zero. (The relationship between the variables in the sample does not hold for same variables in the Population). To put it in other words we cannot generalize the sample results for the whole Population. In the current situation, the correlation between the CGPA and Institution for female students is .363 which only holds for the sample and not for the whole Population of female students.

Result (Conclusion)

rcq (19) = .952; p<.01

Interpretation (Discussion) As ρ<α , we reject Ho, results are statistically significant i.e. at 1% level of significance. The sample data supports the alternative hypothesis (HA). I.e. Population correlation coefficient is significantly different from zero. (The relationship between the variables in the sample also holds for same variables in the Population). To put it in other words we can generalize the sample results for the whole Population. In the current situation, the correlation between the CGPA and intermediate percentage for female students is .952 which holds for the sample as well for the whole Population of female students.

Result (Conclusion)

rcv (19) =.184; p>.05

31

Interpretation (Discussion) As ρ>α , o we do not reject Ho, the results are not statistically significant at 5% level of significance. The sample data does not support the alternative hypothesis (HA). I.e. the Population correlation coefficient is not significantly different from zero. (The relationship between the variables in the sample does not hold for same variables in the Population). To put it in other words we cannot generalize the sample results for the whole Population. In the current situation, the correlation between the CGPA and Institution for female students is .184 which only holds for the sample and not for the whole Population of female students.

SIMPLE REGRESSION CORRELATION

32

33

4.00

3.50

A P G C

3.00

2.50

2.00 2.00

3.00

4.00

5.00

6.00

QUANT1

Double Click on this Graph And click on the REFERENCE LINE

34

REGRESSION EQUATION/MODEL with Quant 1 as Predictor Variable and CGPA as response Variable

Y= a + b x

Response Variable Predictor Variable

35

CGPA = 2.185 + 0.255(Quant1)

Response Variable

Predictor Variable

The interpretation of regression equation is as follows: In the given data, response variable is ‘CGPA’ and predictable variable is ‘Quant1’ As it is evidenced from the estimated regression model calculated from sample data, we have (a) The constant(Intercept) Value

bo = 2.185 The above value is the predicted value of response variable i.e. CGPA, when the predictor variable i.e. Quant1 is zero (b)

b1 = 0.255

The slope b1, which is equal to 0.255 is the change in response variable i.e. CGPA when the predictor variable i.e. Quant1 increases by 1 unit. To simplify our interpretation we can say that with an increase of 1 unit in Quant1 CGPA increases by 0.255 units.

TESTING OF HYPOTHESIS FOR MODEL 1(with QUANT1 as predictor):

STEP #1 State the null hypothesis and alternative hypothesis: H0: β = 0(IV is not a significant predictor of response variable) Ha:β 0(IV is a significant predictor of response variable) 36

STEP #2 Level of significance: Predetermined level of significance: α = 5%

= 0.05

STEP #3 Test statistic: tcal = b - β = b - β Sb

Se Sx

= 0.237 - 0 0.034

= 7.056

STEP #4 Critical region (Depends on HA &): P = 0.000 α = .05

STEP #5 Result/Conclusion: 37

As p = 0.000 < = 0.05 (Observed value Significance)

of

significance

is

less

than

determined

value

of

STEP #6 Interpretation/Discussion P<α , therefore we reject Ho i.e. the Population correlation regression coefficient is significantly different from zero. So, the results are statistically significant at α 5% level of significance. In other words, we can say that the sample data provides sufficient evidence to support alternative hypothesis. Therefore, we say that the sample result holds for the whole Population as well. In the current scenario, the IV (Quant1) is a positive and significant predictor of the response variable (CGPA) i.e. it enhances the predictive ability of the model.

38

39

40

41

Model Summary is the heart of regression; it tells us about the goodness of fit, which means how good the model fits the data.

Standard Error: S S is measured in units of the response variable i.e. CGPA and represents the standard distance, data values fall from the regression line. In the given study, the better the equation predicts the response the lower the “S” is. The value of S is . 25967, which is less as compared to the response variable i.e. CGPA well. 42

R-Sq This is the coefficient of determination. It describes the amount of variation the amount of variation in the observed response variable (CGPA) that is explained by the predictor variable (Quant1). In this model the predictor CGPA explains 62.5% of the variation in the dependent/response variable i.e. CGPA. Is due to the independent variable/ predictor i.e. Quant1. R R is the square root of R-Squared and is the correlation between the observed and predicted values of dependent variable. The R-vale is .791, which is equal to sample correlation coefficient between the dependent variable (CGPA) and the dependent variable (Quant1).

The ANOVA table shows the overall impact of the model. It depicts the amount of variation in the response data explained by the predictor and the amount of variation left un-explained. In the ANOVA table we have p values in the last column, which is 0.000 for this model (with Quant1 as predictor variable). If p<α (we reject Ho) If p> (we do not reject Ho) In this model, the observed level of significance i.e. p-value is less than the specified level of significance. i.e. α =5%, therefore we reject Ho and conclude that the test results are statistically significant at 5% i.e. at 5% level of significance, the sample data provides sufficient evidence to support the alternative hypothesis (HA: β ≠ 0). So we can say that the predictor variables Quant1 is making a significant contribution in predicting the response variable i.e. CGPA.

43

Y = 2.185 + 0.255(Quant1) T-Calculated = 0.255 = 7.27 0.033

B is 7.27 times greater than its standard error. International Convention, if the value of t> 2.5, it is a healthy sign. S.D or Standard error is also known as ‘bouncing error’. QUANT1

Lower Bond

Upper Bond

0.188

0.322

P<, therefore we reject Ho i.e. the Population correlation regression coefficient is significantly different from zero. So, the results are statistically significant at α 5% level of significance. In other words, we can say that the sample data provides sufficient evidence to support alternative hypothesis. Therefore, we say that the sample result holds for the whole Population as well. In the current scenario, the IV (Quant1) is a positive and significant predictor of the response variable (CGPA) i.e. it enhances the predictive ability of the model. Since the hypothesized value of beta is 0 is not contained in the 95% confidence interval, it is also a reflection that results are statistically significant.

44

REGRESSION EQUATION/MODEL with INTER PCT as Predictor Variable and CGPA as response Variable

4.00

3.80

CGPA of respondents

3.60

3.40 0.05 * x + -0.25 3.20

3.00

2.80

2.60

55

60

65

70

75

80

85

Interpct of respondents

CGPA = .572 + 0.0375 (Inter pct)

Response Variable

45

Predictor Variable

The interpretation of regression equation is as follows: In the given data, response variable is ‘CGPA’ and predictable variable is ‘Inter pct’ As it is evidenced from the estimated regression model calculated from sample data, we have (a) The constant(Intercept) Value

bo = .572 The above value is the predicted value of response variable i.e. CGPA, when the predictor variable i.e. Inter pct is zero (b)

b1 = 0.0375

The slope b1, which is equal to 0.255 is the change in response variable i.e. CGPA when the predictor variable i.e. Inter pct increases by 1 unit. To simplify our interpretation we can say that with an increase of 1 unit in Interpct CGPA increases by 0.255 units

TESTING OF HYPOTHESIS FOR MODEL 1(with INTER PCT as predictor):

STEP #1 State the null hypothesis and alternative hypothesis: H0: = 0(IV is not a significant predictor of response variable) Ha:β  0(IV is a significant predictor of response variable)

STEP #2 46

Level of significance: Predetermined level of significance: α = 5%

= 0.05

STEP #3 Test statistic: tcal = b - β = b - β Sb

Se Sx

= 0.0375 - 0 0.008

= 4.68

STEP #4 Critical region (Depends on HA &α ): P = 0.000 α = .05

STEP #5 Result/Conclusion: 47

As p = 0.000   = 0.05 (Observed value Significance)

of

significance

is

less

than

determined

value

of

STEP #6 Interpretation/Discussion P<α , therefore we reject Ho i.e. the Population correlation regression coefficient is significantly different from zero. So, the results are statistically significant at α 5% level of significance. In other words, we can say that the sample data provides sufficient evidence to support alternative hypothesis. Therefore, we say that the sample result holds for the whole Population as well. In the current scenario, the IV (Inter pct) is a positive and significant predictor of the response variable (CGPA) i.e. it enhances the predictive ability of the model.

Model Summary is the heart of regression; it tells us about the goodness of fit, which means how good the model fits the data.

Standard Error: S S is measured in units of the response variable i.e. CGPA and represents the standard distance, data values fall from the regression line. In the given study, the better the equation predicts the response the lower the “S” is. The value of S is . 34169, which is less as compared to the response variable i.e. CGPA well.

48

R-Sq This is the coefficient of determination. It describes the amount of variation the amount of variation in the observed response variable (CGPA) that is explained by the predictor variable (Inerpct). In this model the predictor CGPA explains 35.1% of the variation in the dependent/response variable i.e. CGPA. Is due to the independent variable/ predictor i.e. Inter pct. R R is the square root of R-Squared and is the correlation between the observed and predicted values of dependent variable. The R-vale is .593, which is equal to sample correlation coefficient between the dependent variable (CGPA) and the dependent variable (Inter pct).

The ANOVA table shows the overall impact of the model. It depicts the amount of variation in the response data explained by the predictor and the amount of variation left un-explained. In the ANOVA table we have p values in the last column, which is 0.000 for this model (with CGPA as Inter pct variable). If p< (we reject Ho) If p> (we do not reject Ho) In this model, the observed level of significance i.e. p-value is less than the specified level of significance. i.e.  =5%, therefore we reject Ho and conclude that the test results are statistically significant at 5% i.e. at 5% level of significance, the sample data provides sufficient evidence to support the alternative hypothesis (HA: β ≠ 0). So we can say that the predictor variables Inter pct is making a significant contribution in predicting the response variable i.e. CGPA.

49

Y = .572 + 0.0375(Inter pct) T-Calculated = 0.0375= 4.68 0.008

B is 4.68 times greater than its standard error. International Convention, if the value of t> 2.5, it is a healthy sign. S.D or Standard error is also known as ‘bouncing error’. Inter pct

Lower Bond

Upper Bond

.020

.053

P<, therefore we reject Ho i.e. the Population correlation regression coefficient is significantly different from zero. So, the results are statistically significant at α 5% level of significance. In other words, we can say that the sample data provides sufficient evidence to support alternative hypothesis. Therefore, we say that the sample result holds for the whole Population as well. In the current scenario, the IV (Inter pct) is a positive and significant predictor of the response variable (CGPA) i.e. it enhances the predictive ability of the model. Since the hypothesized value of beta is 0 is not contained in the 95% confidence interval, it is also a reflection that results are statistically significant.

REGRESSION EQUATION/MODEL with INSTITUTE as Predictor Variable and CGPA as response Variable

50

4.00

3.80

CGPA of respondents

3.60

3.40 1.5 * x + 1 3.20

3.00

2.80

2.60

1

1.2

1.4

1.6

1.8

2

institution of respondents

CGPA = 2.670 + + .445(Institute)

Response Variable

Predictor Variable

The interpretation of regression equation is as follows: 51

In the given data, response variable is ‘CGPA’ and predictable variable is ‘Institute’ As it is evidenced from the estimated regression model calculated from sample data, we have (a) The constant(Intercept) Value

bo = 2.670 The above value is the predicted value of response variable i.e. CGPA, when the predictor variable i.e. Institute is zero

b1 = .445

(b)

The slope b1, which is equal to .445 is the change in response variable i.e. CGPA when the predictor variable i.e. Institute increases by 1 unit. To simplify our interpretation we can say that with an increase of 1 unit in Institute, CGPA increases by .445 units.

TESTING OF HYPOTHESIS FOR MODEL 1(with INSTITUTE as predictor):

STEP #1 State the null hypothesis and alternative hypothesis: H0: β = 0(IV is not a significant predictor of response variable) Ha:β  0(IV is a significant predictor of response variable)

STEP #2 Level of significance: Predetermined level of significance: α = 5%

= 0.05

STEP #3 52

Test statistic: tcal = b - β = b - β Sb

Se Sx

= .445 - 0 .132

= 3.371

STEP #4 Critical region (Depends on HA &α ): P = 0.000 = .05

STEP #5 Result/Conclusion:

As p = 0.002 <  = 0.05 53

(Observed value Significance)

of

significance

is

less

than

determined

value

of

STEP #6 Interpretation/Discussion P<α , therefore we reject Ho i.e. the Population correlation regression coefficient is significantly different from zero. So, the results are statistically significant at α 5% level of significance. In other words, we can say that the sample data provides sufficient evidence to support alternative hypothesis. Therefore, we say that the sample result holds for the whole Population as well. In the current scenario, the IV (Institute) is a positive and significant predictor of the response variable (CGPA) i.e. it enhances the predictive ability of the model.

Model Summary is the heart of regression; it tells us about the goodness of fit, which means how good the model fits the data.

Standard Error: S S is measured in units of the response variable i.e. CGPA and represents the standard distance, data values fall from the regression line. In the given study, the better the equation predicts the response the lower the “S” is. The value of S is . 37021, which is less as compared to the response variable i.e. CGPA well.

54

R-Sq This is the coefficient of determination. It describes the amount of variation the amount of variation in the observed response variable (CGPA) that is explained by the predictor variable (Institute). In this model the predictor CGPA explains 23.9% of the variation in the dependent/response variable i.e. CGPA. Is due to the independent variable/ predictor i.e. Inter pct. R R is the square root of R-Squared and is the correlation between the observed and predicted values of dependent variable. The R-vale is .489, which is equal to sample correlation coefficient between the dependent variable (CGPA) and the dependent variable (Institute).

The ANOVA table shows the overall impact of the model. It depicts the amount of variation in the response data explained by the predictor and the amount of variation left un-explained. In the ANOVA table we have p values in the last column, which is 0.002 for this model (with Institute as predictor variable). If p< (we reject Ho) If p>α (we do not reject Ho) In this model, the observed level of significance i.e. p-value is less than the specified level of significance. i.e. α =5%, therefore we reject Ho and conclude that the test results are statistically significant at 5% i.e. at 5% level of significance, the sample data provides sufficient evidence to support the alternative hypothesis (HA: β ≠ 0). So we can say that the predictor variables Institute is making a significant contribution in predicting the response variable i.e. CGPA.

55

Y = 2.670 + .445(Inter pct) T-Calculated = .445= 3.371 .132

B is 3.371 times greater than its standard error. International Convention, if the value of t> 2.5, it is a healthy sign. S.D or Standard error is also known as ‘bouncing error’. Inter pct

Lower Bond

Upper Bond

.176

.713

P<, therefore we reject Ho i.e. the Population correlation regression coefficient is significantly different from zero. So, the results are statistically significant at α 5% level of significance. In other words, we can say that the sample data provides sufficient evidence to support alternative hypothesis. Therefore, we say that the sample result holds for the whole Population as well. In the current scenario, the IV (Institute) is a positive and significant predictor of the response variable (CGPA) i.e. it enhances the predictive ability of the model. Since the hypothesized value of beta is 0 is not contained in the 95% confidence interval, it is also a reflection that results are statistically significant.

56

REGRESSION EQUATION/MODEL with VERBAL1 as Predictor Variable and CGPA as response Variable

CGPA = 2.063 + .255(Verbal1)

Response Variable

57

Predictor Variable

The interpretation of regression equation is as follows: In the given data, response variable is ‘CGPA’ and predictable variable is ‘Verbal1’ As it is evidenced from the estimated regression model calculated from sample data, we have (a) The constant(Intercept) Value

bo = 2.063 The above value is the predicted value of response variable i.e. CGPA, when the predictor variable i.e. Verbal1 is zero (b)

b1 = .255

The slope b1, which is equal to .255is the change in response variable i.e. CGPA when the predictor variable i.e. Verbal1 increases by 1 unit. To simplify our interpretation we can say that with an increase of 1 unit in Verbal1, CGPA increases by .255 units.

TESTING OF HYPOTHESIS FOR MODEL 1(with Verbal1 as predictor):

STEP #1 State the null hypothesis and alternative hypothesis: H0: β = 0(IV is not a significant predictor of response variable) Ha:  0(IV is a significant predictor of response variable)

STEP #2 Level of significance: Predetermined level of significance: 58

α = 5%

= 0.05

STEP #3 Test statistic:

tcal = b - β = b - β Sb

Se Sx

= .091 - 0 .062

= 1.467

STEP #4 Critical region (Depends on HA &α ): P = .000 α = .05

STEP #5 Result/Conclusion:

As p = 0.009 <  = 0.05

59

(Observed value Significance)

of

significance

is

more

than

determined

value

of

STEP #6 Interpretation/Discussion P<, therefore we do reject Ho i.e. the Population correlation regression coefficient is significantly different from zero. So, the results are statistically significant at α 5% level of significance. In other words, we can say that the sample data provides sufficient evidence to support alternative hypothesis. Therefore, we say that the sample result holds for the whole Population as well. In the current scenario, the IV (Verbal1) is a positive and significant predictor of the response variable (CGPA) i.e. it enhances the predictive ability of the model.

Model Summary is the heart of regression; it tells us about the goodness of fit, which means how good the model fits the data.

Standard Error: S S is measured in units of the response variable i.e. CGPA and represents the standard distance, data values fall from the regression line. In the given study, the better the equation predicts the response the lower the “S” is. The value of S is . 38520, which is less as compared to the response variable i.e. CGPA well.

R-Sq

60

This is the coefficient of determination. It describes the amount of variation the amount of variation in the observed response variable (CGPA) that is explained by the predictor variable (Verbal1). In this model the predictor CGPA explains 17.6% of the variation in the dependent/response variable i.e. CGPA. Is due to the independent variable/ predictor i.e. Verbal1. R R is the square root of R-Squared and is the correlation between the observed and predicted values of dependent variable. The R-vale is .419, which is equal to sample correlation coefficient between the dependent variable (CGPA) and the dependent variable (Verbal1).

The ANOVA table shows the overall impact of the model. It depicts the amount of variation in the response data explained by the predictor and the amount of variation left un-explained. In the ANOVA table we have p values in the last column, which is 0.009 for this model (with Verbal1 as predictor variable). If p< (we reject Ho) If p> (we do not reject Ho) In this model, the observed level of significance i.e. p-value is less than the specified level of significance. i.e. α =5%, therefore we reject Ho and conclude that the test results are statistically significant at 5% i.e. at 5% level of significance, the sample data provides sufficient evidence to support the alternative hypothesis (HA: β ≠ 0). So we can say that the predictor variables Verbal1 is making a significant contribution in predicting the response variable i.e. CGPA.

61

Y = 2.063 + .255(Verbal1) T-Calculated = .255= 2.77 .092

B is 2.77 times larger than its standard error. Verbal1

Lower Bond

Upper Bond

.068

.442

P<, therefore we reject Ho i.e. the Population correlation regression coefficient is significantly different from zero. So, the results are statistically significant at α 5% level of significance. In other words, we can say that the sample data provides sufficient evidence to support alternative hypothesis. Therefore, we say that the sample result holds for the whole Population as well. In the current scenario, the IV (Verbal1) is a positive and significant predictor of the response variable (CGPA) i.e. it enhances the predictive ability of the model. Since the hypothesized value of beta is 0 is not contained in the 95% confidence interval, it is also a reflection that results are statistically significant.

62

REGRESSION EQUATION/MODEL with MOIM as Predictor Variable and CGPA as response Variable 4.00

3.80

CGPA of respondents

3.60

3.40 1.5 * x + 2.5 3.20

3.00

2.80

2.60

0

0.2

0.4

0.6

0.8

1

MOIM of respondents

63

CGPA = 3.245 + -.013(MOIM)

Response Variable

Predictor Variable

The interpretation of regression equation is as follows: In the given data, response variable is ‘CGPA’ and predictable variable is ‘MOIM’ As it is evidenced from the estimated regression model calculated from sample data, we have (a) The constant(MOIM) Value

bo = 3.245 The above value is the predicted value of response variable i.e. CGPA, when the predictor variable i.e. Verbal1 is zero (b)

b1 = -.0.13

The slope b1, which is equal to -.255is the change in response variable i.e. CGPA when the predictor variable i.e. Verbal1 increases by 1 unit. To simplify our interpretation we can say that with an increase of 1 unit in MOIM, CGPA decreases by -.255 units.

TESTING OF HYPOTHESIS FOR MODEL 1(with MOIM as predictor):

STEP #1 State the null hypothesis and alternative hypothesis: H0:  = 0(IV is not a significant predictor of response variable) Ha:β ≠ 0(IV is a significant predictor of response variable)

64

STEP #2 Level of significance: Predetermined level of significance: α = 5%

= 0.05

STEP #3 Test statistic:

tcal = b - β = b - β Sb

Se Sx

= -.013 - 0 .224

= -0.058

STEP #4 Critical region (Depends on HA &α ): P = 0.000 = .05

65

STEP #5 Result/Conclusion:

As p = 0.955 >  = 0.05 (Observed value Significance)

of

significance

is

more

than

determined

value

of

STEP #6 Interpretation/Discussion If the value of the parameter as specified in the null hypothesis is contained in confidence interval then we do not reject (accept) Ho.If the before mentioned value is not contained in the confidence interval, then we reject Ho.

Model Summary is the heart of regression; it tells us about the goodness of fit, which means how good the model fits the data.

Standard Error: S S is measured in units of the response variable i.e. CGPA and represents the standard distance, data values fall from the regression line. In the given study, the better the equation predicts the response the lower the “S” is. The value of S is . 42425, which is less as compared to the response variable i.e. CGPA well.

66

R-Sq This is the coefficient of determination. It describes the amount of variation the amount of variation in the observed response variable (CGPA) that is explained by the predictor variable (Verbal1). In this model the predictor CGPA explains O% of the variation in the dependent/response variable i.e. CGPA. Is due to the independent variable/ predictor i.e. MOIM. R R is the square root of R-Squared and is the correlation between the observed and predicted values of dependent variable. The R-vale is .010, which is equal to sample correlation coefficient between the dependent variable (CGPA) and the dependent variable (MOIM).

The ANOVA table shows the overall impact of the model. It depicts the amount of variation in the response data explained by the predictor and the amount of variation left un-explained. In the ANOVA table we have p values in the last column, which is .955 for this model (with MOIM as predictor variable). If p< (we reject Ho) If p> (we do not reject Ho) In this model, the observed level of significance i.e. p-value is greater than the specified level of significance. i.e. α =5%, therefore we do not reject Ho and conclude that the test results are not statistically significant at 5% i.e. At 5% level of significance, the sample data does not provide sufficient evidence to support the alternative hypothesis (HA: β ≠ 0). So we can say that the predictor variables MOIM is not making a significant contribution in predicting the response variable i.e. CGPA.

67

Y = 3.245 + -.013(Verbal1) T-Calculated = -.013= -0.058 .224

B is -2.77 times smaller than its standard error. Verbal1

Lower Bond -.468

Upper Bond .442

P>α , therefore we do not reject Ho i.e. the Population correlation regression coefficient is not significantly different from zero. So, the results are not statistically significant at α 5% level of significance. In other words, we can say that the sample data does not provide sufficient evidence to support alternative hypothesis. Therefore, we say that the sample result does not hold for the whole Population. In the current scenario, the IV (MOIM) is a negative and insignificant predictor of the response variable (CGPA) i.e. it does not enhance the predictive ability of the model. Since the hypothesized value of beta is 0 is contained in the 95% confidence interval, it is also a reflection that results are not statistically significant.

68

MUTIPLE REGRESSION

69

70

71

MULTIPLE REGRESSION EQUATION/MODEL

Y= a + b x + b2 x2 + b3 x3+ b4 x4+ b5 x5

Response Variable Predictor Variable Predictor Variable Predictor Variable Predictor Variable Predictor Variable

CGPA = 1.102 + .195(Quant1) + .009 (Inter pct) + .199(Institute) + .091(Verbal1) + .013(MOIM)

Response Variable

Predictor VariablePredictor VariablePredictor VariablePredictor VariablePredictor Variable

The interpretation of regression equation is as follows: In the given data, response variable is ‘CGPA’ and predictable variables are ‘Quant1’, ‘Inter pct”, ‘Institute’, ‘Verbal1’ and ‘MOIM’. As it is evidenced from the estimated regression model calculated from sample data, we have: (a) The constant(Intercept) Value

bo = 1.102 This is the predicted value of response variable i.e. ‘Quant1’, ‘Inter pct’, ‘Institute’, ‘Verbal1’ and ‘MOIM’. 72

In other words we can say that when ‘Quant1’, ‘Inter pct”, ‘Institute’, ‘Verbal1’ and ‘MOIM’ is zero, the CGPA is 1.102. So, the figure of zero is of no significance in our analysis.

(b)

b1 = .195

The slope b1, which is equal to .195 is the change in response variable i.e. CGPA when the predictor variable i.e. Quant1 increases by 1 unit. To simplify our interpretation we can say that with an increase of 1 unit in Quant1, CGPA increases by .195 units, when the proportion of marks is held constant. (c)

b2 = .009

The slope b2, which is equal to .009 is the change in response variable i.e. CGPA when the predictor variable i.e. Inter pct increases by 1 unit. To simplify our interpretation we can say that with an increase of 1 unit in Inter pct, CGPA increases by .195 units, when the proportion of marks is held constant. (d)

b3 = .199

The slope b1, which is equal to .199 is the change in response variable i.e. CGPA when the predictor variable i.e. Institute increases by 1 unit. To simplify our interpretation we can say that with an increase of 1 unit in Institute, CGPA increases by .199 units, when the proportion of marks is held constant.

(e)

b4 = .091

The slope b1, which is equal to .091 the change in response variable i.e. CGPA when the predictor variable i.e. Verbal1 increases by 1 unit. To simplify our interpretation we can say that with an increase of 1 unit in Verbal1, CGPA increases by .091 units, when the proportion of marks is held constant. (f)

b5 = .013

The slope b1, which is equal to .091 the change in response variable i.e. CGPA when the predictor variable i.e. MOIM increases by 1 unit. To simplify our interpretation we can say that with an increase of 1 unit in MOIM, CGPA increases by .091 units, when the proportion of marks is held constant.

73

The coefficient table tells us whether the predictor variables included in the model makes a significant contribution or not, if not then we will exclude the predictor variable which is not contributing significantly to our linear regression model. For the given data, the results of coefficient table can be summarized as follows:

TESTING OF HYPOTHESIS (with ‘Quant1’, ‘Inter pct’, ‘Institute’, ‘Verbal1’ and ‘MOIM’ as predictors): ‘QUNAT1’ IN THE PRESENCE OF ‘INTER PCT’, ‘INSTITUTE’, ‘VERBAL1’ AND ‘MOIM’ AS PREDICTORS

STEP #1 State the null hypothesis and alternative hypothesis: H0: β = 0(IV is not a significant predictor of response variable) Ha:  0(IV is a significant predictor of response variable)

STEP #2 Level of significance: Predetermined level of significance:  = 5%

= 0.05

STEP #3 Test statistic:

74

tcal = b - β = b - β Sb

Se Sx

= .195 - 0 .035

= 5.57

STEP #4 Critical region (Depends on HA &): P = 0.000 = .05

STEP #5 Result/Conclusion:

As p = 0.000 <  = 0.05 (Observed value Significance)

of

significance

is

less

than

determined

value

of

STEP #6 Interpretation/Discussion P<α , therefore we reject Ho i.e. the Population correlation regression coefficient is significantly different from zero. So, the results are statistically significant at α 5% level of significance.

75

In other words, we can say that the sample data provides sufficient evidence to support alternative hypothesis. Therefore, we say that the sample result holds for the whole Population as well. In the current scenario, the IV (Quant1) is a positive and significant predictor of the response variable (CGPA) i.e. it enhances the predictive ability of the model.

TESTING OF HYPOTHESIS (with ‘Inter pct’ ‘Quant1’, ‘Institute’, ‘Verbal1’ and ‘MOIM’ as predictors): ‘INTER PCT’ IN THE PRESENCE OF, ‘QUNAT1’ ‘INSTITUTE’, ‘VERBAL1’ AND ‘MOIM’ AS PREDICTORS

STEP #1 State the null hypothesis and alternative hypothesis: H0: β = 0(IV is not a significant predictor of response variable) Ha:β  0(IV is a significant predictor of response variable)

STEP #2 Level of significance: Predetermined level of significance: α = 5%

= 0.05

STEP #3 Test statistic:

76

tcal = b -  = b - β Sb

Se Sx

= .009 - 0 .007

= 1.28

STEP #4 Critical region (Depends on HA &α ): P = .000 α = .05

STEP #5 Result/Conclusion: As p = 0.215 > α = 0.05 (Observed value Significance)

of

significance

is

more

than

determined

value

of

STEP #6 Interpretation/Discussion

77

P>, therefore we do not reject Ho i.e. the Population correlation regression coefficient is not significantly different from zero. So, the results are not statistically significant at α 5% level of significance. In other words, we can say that the sample data does not provide sufficient evidence to support alternative hypothesis. Therefore, we say that the sample result does not hold for the whole Population as well. In the current scenario, the IV (Inter pct) is a positive and insignificant predictor of the response variable (CGPA) i.e. it does not enhance the predictive ability of the model.

TESTING OF HYPOTHESIS (with ‘Institute’, ‘Inter pct’ ‘Quant1’ , ‘Verbal1’ and ‘MOIM’ as predictors): ‘INSTITUTE’ IN THE PRESENCE OF, ‘QUNAT1’,’INTERP PCT’ ‘VERBAL1’ AND ‘MOIM’ AS PREDICTORS

STEP#1 State the null hypothesis and alternative hypothesis: H0:  = 0(IV is not a significant predictor of response variable) Ha:β  0(IV is a significant predictor of response variable)

STEP#2 Level of significance: Predetermined level of significance: α = 5%

= 0.05

STEP#3 78

Test statistic:

tcal = b - β = b - β Sb

Se Sx

= .199 - 0 .092

= 2.163

STEP#4 Critical region (Depends on HA &α ): P = 0.000 α = .05

STEP#5 Result/Conclusion:

As p = 0.002 <  = 0.05 (Observed value of significance is less than determined value of Significance)

79

STEP#6 Interpretation/Discussion P<, therefore we reject Ho i.e. the Population correlation regression coefficient is significantly different from zero. So, the results are statistically significant at α 5% level of significance. In other words, we can say that the sample data provides sufficient evidence to support alternative hypothesis. Therefore, we say that the sample result holds for the whole Population as well. In the current scenario, the IV (Institute) is a positive and significant predictor of the response variable (CGPA) i.e. it enhances the predictive ability of the model.

TESTING OF HYPOTHESIS (with ‘Verbal1’ ‘Institute’, ‘Inter pct’ ‘Quant1’ and ‘MOIM’ as predictors): ‘VERBAL1’ IN THE PRESENCE OF, ‘QUNAT1’,’INTERP ‘INSTITUTE’ AND ‘MOIM’ AS PREDICTORS

PCT’

STEP#1 State the null hypothesis and alternative hypothesis: H0: β = 0(IV is not a significant predictor of response variable) Ha:β  0(IV is a significant predictor of response variable)

STEP#2 Level of significance: Predetermined level of significance: 80

α = 5%

= 0.05

STEP#3 Test statistic:

tcal = b - β = b - β Sb

Se Sx

= .091 - 0 .062

= 1.467

STEP#4 Critical region (Depends on HA &): P = .000 α = .05

STEP#5 Result/Conclusion:

As p = 0.009 <  = 0.05 81

(Observed value Significance)

of

significance

is

more

than

determined

value

of

STEP#6 Interpretation/Discussion P<α , therefore we do reject Ho i.e. the Population correlation regression coefficient is significantly different from zero. So, the results are statistically significant at α 5% level of significance. In other words, we can say that the sample data provides sufficient evidence to support alternative hypothesis. Therefore, we say that the sample result holds for the whole Population as well. In the current scenario, the IV (Verbal1) is a positive and significant predictor of the response variable (CGPA) i.e. it enhances the predictive ability of the model.

TESTING OF HYPOTHESIS (with ‘MOIM’ ‘Institute’, ‘Inter pct’ ‘Quant1’ and ‘Verbal1’ as predictors): ‘MOIM’ IN THE PRESENCE OF, ‘QUNAT1’,’INTERP PCT’ ‘INSTITUTE’ AND ‘VERBAL1’ AS PREDICTORS

STEP #1 State the null hypothesis and alternative hypothesis: H0: β = 0(IV is not a significant predictor of response variable) Ha:β  0(IV is a significant predictor of response variable)

STEP#2 Level of significance: 82

Predetermined level of significance: α = 5%

= 0.05

STEP#3 Test statistic:

tcal = b - β = b - β Sb

Se Sx

= -.013 - 0 .128

= 0.101

STEP#4 Critical region (Depends on HA &): P = 0.000 = .05

STEP#5 Result/Conclusion:

83

As p = 0.922 >  = 0.05 (Observed value Significance)

of

significance

is

more

than

determined

value

of

STEP#6 Interpretation/Discussion P>, therefore we do not reject Ho i.e. the Population correlation regression coefficient is not significantly different from zero. So, the results are not statistically significant at α 5% level of significance. In other words, we can say that the sample data does not provide sufficient evidence to support alternative hypothesis. Therefore, we say that the sample result does not hold for the whole Population as well. In the current scenario, the IV (MOIM) is a positive and insignificant predictor of the response variable (CGPA) i.e. it does not enhance the predictive ability of the model.

Model Summary is the heart of regression; it tells us about the goodness of fit, which means how good the model fits the data.

Standard Error: S S is measured in units of the response variable i.e. CGPA and represents the standard distance, data values fall from the regression line. In the given study, the better the equation predicts the response the lower the “S” is. The value of S is . 23221, which is less as compared to the response variable i.e. CGPA well.

R-Sq 84

This is the coefficient of determination. It describes the amount of variation the amount of variation in the observed response variable (CGPA) that is explained by the predictor variables (‘Quant1’, ‘Inter pct”, ‘Institute’, ‘Verbal1’ and ‘MOIM’). In this model the predictor CGPA explains 73.4% of the variation in the dependent/response variable i.e. CGPA. Is due to the independent variables/ predictors i.e. ‘Quant1’, ‘Inter pct”, ‘Institute’, ‘Verbal1’ and ‘MOIM’. R R is the square root of R-Squared and is the correlation between the observed and predicted values of dependent variables. The R-vale is .857, which is equal to sample correlation coefficient between the dependent variable (CGPA) and the dependent variables (‘Quant1’, ‘Inter pct”, ‘Institute’, ‘Verbal1’ and ‘MOIM’).

The ANOVA table shows the overall impact of the model. It depicts the amount of variation in the response data explained by the predictor and the amount of variation left un-explained. In the ANOVA table we have p values in the last column, which is 0.000 for this model (with ‘Quant1’, ‘Inter pct”, ‘Institute’, ‘Verbal1’ and ‘MOIM’ as predictor variable). If p<α (we reject Ho) If p> (we do not reject Ho) In this model, the observed level of significance i.e. p-value is less than the specified level of significance. i.e.  =5%, therefore we reject Ho and conclude that the test results are statistically significant at 5% i.e. at 5% level of significance, the sample data provides sufficient evidence to support the alternative hypothesis (HA: β ≠ 0). So we can say that the predictor variables ‘Quant1’, ‘Inter pct”, ‘Institute’, ‘Verbal1’ and ‘MOIM’ are making a significant contribution in predicting the response variable i.e. CGPA.

REMARKS 85

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SIGNATURES 86