On the last page of this file you will find the Excel output for a multiple linear regression model. The model was built in an attempt to better understand why students at area high schools perform differently on the state high school mathematics exam. The average test score for a class of students is what we are trying to predict. In our attempt to understand why these exam scores differ, we use 3 independent variables: a rating (0-100) for the quality of the math degree obtained by the instructor, the age of the instructor, and the salary (in thousands) of the instructor. You are to address the following questions based on the output. Worth 25 points total.

a.)Estimate the average math score for a class of students whose instructor is 52 years old, earns $48,000, and got her degree in a math program rated 72.

b.)What percentage of the variations in math scores can be explained by this model?

c.)Conduct a test to determine if the model, taken as a whole, provided us with any significant explanation of the differences in math scores. That is, should the model be retained for further analysis?

d.)Which of the independent variables appear to be significant to the model? Which appear to be insignificant? What leads you to these conclusions?

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.597512233

R Square

0.357020869

Adjusted R Square

0.303439274

Standard Error

7.724526046

Observations

40

ANOVA

df

SS

MS

F

Significance F

Regression

3

1192.732105

397.5774

6.663125

0.001076925

Residual

36

2148.058895

59.6683

Total

39

3340.791

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Intercept

35.67761801

7.278849159

4.901547

2.03E-05

20.9154278

Math Degree

0.247481581

0.069845662

3.543263

0.001115

0.105828014

Age

0.244830604

0.185213036

1.321886

0.194545

-0.130798841

Income

0.133296712

0.152818937

0.872253

0.388851

-0.176634456