Question

As a statistical consultant, you have been asked to develop a linear model which shall be given to first year executive MBA students.

Variable           Name                                                   Description

X1                   Gender                                                Male or Female

X2                   GMAT Score                                      Score on GMAT Test

X3                   College Degree Previously Earned     Bachelors, Masters, or PhD

Y                     Income                                                            Annual Income in Thousand Dollars

Where 1=Male and 2= Female for X1 and B = Bachelors Degree, M=Master’s Degree, and P= PhD for X3.

1. Given this data, recode the variables so that they may be used as potential predictors for Y in a linear regression model.   Redefine your categorical variables and write them out here.

Variable     

I1, Gender 0=Male Female = 1

I2 = GMAT Score

Education            I3           I4    

Bachelors             1            0         1 if they have bachelors 0 if not same for the other two

Masters                 0           1      

PHD                     0            0      

Y = B0 + B1*I1 + B2*I2 + B3*I3 + B4*I4 + error

b. Now assume that the influence of a Bachelors Degree on Income may depend on Gender and vice versa. In order to answer this question (does the influence of Bachelor’s Degree depend on Gender and vice versa?), rewrite a regression model (using the model from part a ) and describe how you would answer this question with your model.

I think I answered part a correctly. Could you possibly help me in aswering part b? If part a is incorrect could you please help me fix it? There is no data for this question. Just what is provided.

Answer 1

Sol:

If you want to run the multiple regression then you can use these codes in you model

Variable	Name	Codes
X1	Gender	Male : 1, Female : 2
X2	GMAT Score	Continues variable
X3	College Degree Previously Earned	Bachelor: 1, Master:2, PhD: 3
Y	Income	Continues variable

In which Gender taken as qualitative information which divided into two category Male and Female, transform these variable into M-1 , F-2 , second one is GMAT score which is taken as marks on numerical number you can it as a continues variable or you can divide it into the category i.e Low -1 Better-2 High-2 as per seeing the result and the model . similiarly College degree i.e  Bachelor: 1, Master:2, PhD: 3.

these variable predict you response variable Income(Y) taken as continuous .