You, as a MBA program director at Rowan, developed a multiple regression model t
ID: 3240034 • Letter: Y
Question
You, as a MBA program director at Rowan, developed a multiple regression model to predict
GMAT scores from grade point average(UGPA) and months of business experience(EXPER)
by sex. Data were collected for ten students and are presented in the accompanying table.
The last two independent variables (SEX and UMAJOR) are as follows:
SEX = 1 if male, SEX = 0 if female and .
UMAJOR = 1 if business background in undergraduate, UMAJOR=0 if not.
GMAT score Under GPA Experience(months) Sex Undergraduate Major
(GMAT) (UGPA) (EXPER) (SEX) (UMAJOR)
630 3.53 2.5 1 1
520 2.58 8.5 0 1
480 2.87 7.1 0 0
535 3.25 5.6 1 0
518 2.75 6.2 0 1
495 2.53 4.8 1 1
560 3.72 6.5 0 0
610 3.78 4.9 1 0
540 3.26 3.8 0 0
505 2.68 2.3 1 1
Using SPSS for output or formulas to prove answer.
(1) Which two independent variables are most strongly correlated with dependent variable(GMAT) regardless of different signs in its direction? Show it.
(2) Use the original regression model to predict(estimate) the mean GMAT score for all students with 5 months business experience after holding all other variable constant.
(3) Is there any implication of multicollinearity problem in this model? If yes, explain it using your criteria.
(4) Run the regression again, using only the independent variables that are significant at least at the 5 percent level of significance. Does it make a difference whether our MBA student has a business major in the undergraduate or not ?
(4a) If it does, how much more point in GMAT does a business background in UMAJOR have than a non-business background in UMAJOR?
Explanation / Answer
1)
UGPA and UMAJOR are the two independent variables which have most strongly correlated with dependent variable(GMAT) regardless of different signs in its direction. Brecause the type III sum of square is larger than remaining variables.
(2) Use the original regression model to predict(estimate) the mean GMAT score for all students with 5 months business experience after holding all other variable constant.
Ans:
The original regression model to predict(estimate) the mean GMAT score for all students with 5 months business experience after holding all other variable constant is
GMAT=320.180 - 5.134 EXPER = 320.180 - 5.134 *5=294.51
(3) Is there any implication of multicollinearity problem in this model? If yes, explain it using your criteria.
The correlation between UGPA and EXPER is 0.559. Hence, we can assume that there is no multicollinearity problem in this model.
(4) Run the regression again, using only the independent variables that are significant at least at the 5 percent level of significance. Does it make a difference whether our MBA student has a business major in the undergraduate or not ?
(4a) If it does, how much more point in GMAT does a business background in UMAJOR have than a non-business background in UMAJOR?
Dependent Variable:GMAT Source Type III Sum of Squares df Mean Square F Sig. Corrected Model 19654.050a 4 4913.513 16.378 .004 Intercept 1619.132 1 1619.132 5.397 .068 SEX 119.860 1 119.860 .400 .555 UMAJOR 4080.401 1 4080.401 13.601 .014 UGPA 15359.587 1 15359.587 51.197 .001 EXPER 48.301 1 48.301 .161 .705 Error 1500.050 5 300.010 Total 2929599.000 10 Corrected Total 21154.100 9Related Questions
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