Suppose you want to examine what factors influence a student’s college GPA. (ANS

Question

Suppose you want to examine what factors influence a student’s college GPA. (ANSWER Question C and D only)

A. Create a dummy variable “female” that is equal to 1 if the student is female and 0 if the student is male.

(NO need to answer)

B. Run an OLS regression of colgpa on hsize, hrank, female, black, and female*black. How do we interpret the coefficient on female and the coefficient on black? Comment on their statistical significance. (NO need to answer)

C. What is the estimated difference in colgpa for a black female and a non-black female, holding everything else constant? Test for the statistical significance of this difference.

D. You hypothesize that a high school’s size could have a different predicted impact on a student’s college GPA depending on the student’s sex. Re-specify your model from part B to test for this difference and run the regression. Holding everything else constant, what is the estimated difference of the impact of high school size on college GPA for non-black females, black males, and black females, compared to non-black males (the reference group)?   

Explanation / Answer

C) To estimate difference in colgpa for black female and non-black female we need to define indicator (dummy ) variable as fallows

D1=1,for a black female and 0, for otherwise (ie for non black female)

Now consider the model as

colgpa=2.625456+0.099646415*hsize-0.0050282*hsrank+0.0840616*female-0.3848531*female-0.0947995*D1

if D1=0 then the model becomes

colgpa=2.625456-0.0947995(0)+0.099646415*hsize-0.0050282*hsrank+0.0840616*female-0.3848531*female

colgpa=2.625456+0.099646415*hsize-0.0050282*hsrank+0.0840616*female-0.3848531*female

if D1=1

colgpa=2.7250975+0.099646415*(1)*hsize-0.0050282*hsrank+0.0840616*female-0.3848531*female

draw the graph for both tthe model and from that you may observe the estimated difference.

Now to test the significance of the test difference

as p-value for female_black is large so we may say that the difference is the significant . on the other haand from the 95% confidence interval we may observe that the value of the coefficient does not lies in the confidence interval so their is a statistical evidence that we fail to accept H0 ie we may say that the difference is significant.

D) here we define dummy variable for specifying gender of student

D2=1, for male student and 0, othewise (ie for female student)

if D2=1 then the model is given by

colgpa=2.625456+0.099646415*D2-0.0050282*hsrank+0.0840616*female-0.3848531*female-0.0947995*female _black

colgpa=2.625456+0.099646415*1-0.0050282*hsrank+0.0840616*female-0.3848531*female-0.0947995*female _black

colgpa=2.2.7250975-0.0050282*hsrank+0.0840616*female-0.3848531*female-0.0947995*female _black

if D2=0 then model is given by

colgpa=2.625456+0.099646415*0-0.0050282*hsrank+0.0840616*female-0.3848531*female-0.0947995*female _black

colgpa=2.625456-0.0050282*hsrank+0.0840616*female-0.3848531*female-0.0947995*female _black

draw the graph for both the model on same graph we may get the estimated difference.

And from the anova table the p value is small so we may say that the difference is not significant.

Now in the 2nd part we have given 4 classification so we have to specify 3 dummy variables

D1=1,for male student and 0,otherwise(ie for female student)

D2=1,for black male and 0, othewise (ie for non black male)

D3 =1,for black female and 0,otherwise (ie for non black female)

to obain estimated difference

put D1=0 and D3=0,for Non black female

put D2=1, and D3=1 ,for black male and black female

put D1=1 and D2=0 ,for non black male

You get 3 model draw the graph for that you will get the estimated difference

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