d) What percent of the total variation in MBA applicant GPAS can be explained by the straight-line relationship for each of the continuous explanatory variables separately (Hint run simple linear regression models)? How much does self-esteem (SE) contribute to explaining GPA after the effect of IQ on GPA is taken into account? (StatCrunch) e) Now, perform another multiple regression analysis including GPA as the response or dependent variable, IQ and SE as the continuous explanatory variables and SEX as a categorical variable (Note: refer to this model as Model 2 which includes the categorical variable SEX without any interaction terms); comment on the validity and significance of this model. (StatCrunch) f) Which model (Model 1 or Model 2) is a better model? (Justify your answer) g) Write the regression equation for the full model 2 and the separate regression equations for males and females and compare their coefficients (Hint: create a male and a female subset of the base data and run separate multiple regressions on
d) What percent of the total variation in MBA applicant GPAS can be explained by the straight-line relationship for each of the continuous explanatory variables separately (Hint run simple linear regression models)? How much does self-esteem (SE) contribute to explaining GPA after the effect of IQ on GPA is taken into account? (StatCrunch) e) Now, perform another multiple regression analysis including GPA as the response or dependent variable, IQ and SE as the continuous explanatory variables and SEX as a categorical variable (Note: refer to this model as Model 2 which includes the categorical variable SEX without any interaction terms); comment on the validity and significance of this model. (StatCrunch) f) Which model (Model 1 or Model 2) is a better model? (Justify your answer) g) Write the regression equation for the full model 2 and the separate regression equations for males and females and compare their coefficients (Hint: create a male and a female subset of the base data and run separate multiple regressions on
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Data given:
| Applicant | GPA | IQ | SE | SEX |
| 1 | 7.94 | 111 | 67 | 1 |
| 2 | 8.292 | 107 | 43 | 1 |
| 3 | 4.643 | 100 | 52 | 1 |
| 4 | 7.47 | 107 | 66 | 1 |
| 5 | 8.882 | 114 | 58 | 0 |
| 6 | 7.585 | 115 | 51 | 1 |
| 7 | 7.65 | 111 | 71 | 1 |
| 8 | 2.412 | 97 | 51 | 1 |
| 9 | 6 | 100 | 49 | 0 |
| 10 | 8.833 | 112 | 51 | 1 |
| 11 | 7.47 | 104 | 35 | 0 |
| 12 | 5.528 | 89 | 54 | 0 |
| 13 | 7.167 | 104 | 54 | 1 |
| 14 | 7.571 | 102 | 64 | 0 |
| 15 | 4.7 | 91 | 56 | 0 |
| 16 | 8.167 | 114 | 69 | 0 |
| 17 | 7.822 | 114 | 55 | 0 |
| 18 | 7.598 | 103 | 65 | 0 |
| 19 | 4 | 106 | 40 | 1 |
| 20 | 6.231 | 105 | 66 | 0 |
| 21 | 7.643 | 113 | 55 | 1 |
| 22 | 1.76 | 109 | 20 | 1 |
| 24 | 6.419 | 108 | 56 | 0 |
| 26 | 9.648 | 113 | 68 | 1 |
| 27 | 10.7 | 130 | 69 | 0 |
| 28 | 10.58 | 128 | 70 | 1 |
| 29 | 9.429 | 128 | 80 | 1 |
| 30 | 8 | 118 | 53 | 1 |
| 31 | 9.585 | 113 | 65 | 1 |
| 32 | 9.571 | 120 | 67 | 0 |
| 33 | 8.998 | 132 | 62 | 0 |
| 34 | 8.333 | 111 | 39 | 0 |
| 35 | 8.175 | 124 | 71 | 1 |
| 36 | 8 | 127 | 59 | 1 |
| 37 | 9.333 | 128 | 60 | 0 |
| 38 | 9.5 | 136 | 64 | 1 |
| 39 | 9.167 | 106 | 71 | 1 |
| 40 | 10.14 | 118 | 72 | 0 |
| 41 | 9.999 | 119 | 54 | 0 |
| 43 | 10.76 | 123 | 64 | 1 |
| 44 | 9.763 | 124 | 58 | 1 |
| 45 | 9.41 | 126 | 70 | 1 |
| 46 | 9.167 | 116 | 72 | 1 |
| 47 | 9.348 | 127 | 70 | 1 |
| 48 | 8.167 | 119 | 47 | 1 |
| 50 | 3.647 | 97 | 52 | 1 |
| 51 | 3.408 | 86 | 46 | 0 |
| 52 | 3.936 | 102 | 66 | 1 |
| 53 | 7.167 | 110 | 67 | 1 |
| 54 | 7.647 | 120 | 63 | 1 |
| 56 | 6.173 | 115 | 67 | 1 |
| 57 | 7.295 | 93 | 61 | 1 |
| 58 | 7.295 | 72 | 54 | 0 |
| 59 | 8.938 | 111 | 60 | 0 |
| 60 | 7.882 | 103 | 60 | 0 |
| 61 | 8.353 | 123 | 63 | 1 |
| 62 | 5.062 | 79 | 30 | 1 |
| 63 | 8.175 | 119 | 54 | 1 |
| 64 | 8.235 | 110 | 66 | 1 |
| 65 | 7.588 | 110 | 44 | 1 |
| 68 | 7.647 | 107 | 49 | 1 |
| 69 | 5.237 | 74 | 44 | 0 |
| 71 | 7.825 | 105 | 67 | 1 |
| 72 | 7.333 | 112 | 64 | 0 |
| 74 | 9.167 | 105 | 73 | 1 |
| 76 | 7.996 | 110 | 59 | 1 |
| 77 | 8.714 | 107 | 37 | 0 |
| 78 | 7.833 | 103 | 63 | 0 |
| 79 | 4.885 | 77 | 36 | 1 |
| 80 | 8 | 98 | 64 | 0 |
| 83 | 3.82 | 90 | 42 | 1 |
| 84 | 5.936 | 96 | 28 | 0 |
| 85 | 9 | 112 | 60 | 0 |
| 86 | 9.5 | 112 | 70 | 0 |
| 87 | 6.057 | 114 | 51 | 1 |
| 88 | 6.057 | 93 | 21 | 0 |
| 89 | 6.938 | 106 | 56 | 1 |
Transcribed Image Text:d) What percent of the total variation in MBA applicant GPAs can be explained by the
straight-line relationship for each of the continuous explanatory variables separately
(Hint run simple linear regression models)? How much does self-esteem (SE)
contribute to explaining GPA after the effect of IQ on GPA is taken into account?
(StatCrunch)
e) Now, perform another multiple regression analysis including GPA as the response or
dependent variable, IQ and SE as the continuous explanatory variables and SEX as
a categorical variable (Note: refer to this model as Model 2 which includes the
categorical variable SEX without any interaction terms); comment on the validity and
significance of this model. (StatCrunch)
f) Which model (Model 1 or Model 2) is a better model? (Justify your answer)
g) Write the regression equation for the full model 2 and the separate regression
equations for males and females and compare their coefficients (Hint: create a male
and a female subset of the base data and run separate multiple regressions on
each subset) (StatCrunch)
Transcribed Image Text:The admission committee of an MBA program at a Canadian university is considering
using a psychometric test of self-esteem (SE) in addition to the IQ test they administer
to MBA applicants to help in their selection process. They want to assess the influence
of self-esteem on candidate bachelor's GPA above and beyond IQ and sex. The
Assign4Data.xlsx file contains a random sample of 77 GPA records of MBA applicants
with the corresponding IQ, SE, and sex information (Female=0, Male=1). Treating GPA
as the response variable and IQ, SE, and SEX as explanatory variables, answer the
following questions using a 1% significance level.
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