2 2 1. Analyze R, R, Adjusted R, Significance F for each of the four regressions

Question

2 2 1. Analyze R, R, Adjusted R, Significance F for each of the four regressions and talk about inconsistencies between each regression. Be sure to interpret the multiple regression as a whole. 2. If relevant, discuss possible multicollinearity and its correction. Suggest alternative models you might use to test the robustness of the results. See the Supplemental Topics in Regression for this topic 3. Predict the salary for a female whose GMAT score is 624 and who graduates from a school with an acceptance rate of 27. What about for a male? Look at the sample data to see if these salaries seem reasonable with what you have observed. 4. Can you predict the salary for a female whose GMAT score is 550? Why or why not? See the Supplemental Topics in Regression for the answer.

Explanation / Answer

1)

R

We can see above 4 regression So basically R is correlation between dependent variable and idependent variable which is diffreant in all regression because evry time new independent variable .

R2

Coeficient of Determination(R2) we can see above 4 Regression If add idependent variable in the regression the R2 is increases So this is not good messure of chaking goodness of model

Adj R2

Adj R2 we used for chaking goodness of model ,Suppose you add new independant variable in regression Adj R2 Increases when this variable is important for that regression.

You see our case if add new independent variable in regression our Adj R2 going to decreses

that means our model is not good .

Significance F

You can see our P-value of all the models which are greater than 0.05 that means all the model's

are insignificant or inconsistant.

2)Multicolinearity

Multicolinearity  is basically High correlation between independent variables

So we need to check is there really high correlation between independant variables are highly correlated then we need used differeant model.

3)

For this question we are using 4th regression model

So our model is

Salary= -1965.55 +89.47* GMAT - 11.57 Acc.Rate + 1798.067*Gender

Given

GMAT = 624

Acc.Rate = 27

Gender = 0

Salary= -1965.55 +89.47* GMAT - 11.57 Acc.Rate + 1798.067*Gender

= -1965.55 +89.47*624 - 11.57*27+ 1798.067*0
= 53551.34

If you can see sample data our prediction looks good .

4)

We can't predict the Salary based on GMAT and Gender beacuse we need new regression model based on dependent variable Salary and independent variable GMAT and Gender

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