. The mathematics department at a university is interested in learning more about the grades that

students earn in an introductory calculus class. A sample of

n

= 80 students who have taken this

introductory calculus course during any semester of the three last three academic years is selected.

The academic record for each selected student is reviewed. The professors in the math department

determine that, of the available information for all students, the relevant variables are their final grade

in the calculus course, their high school percentile rank, their score on the algebra placement test given

to all incoming students who plan to take a calculus course, their ACT Math score, and their ACT

Natural Sciences score.

A. The professors in the math department believe that the score on the algebra placement test and

the high school percentile rank will be the best explanatory variables for the final grade in calculus.

The partially complete ANOVA table below shows relevant values for the model containing these

two explanatory variables. Conduct the

F

test for whether this model is useful or not.

SS

df

MS

F

p-value

Regression

2840.4

2

1420.2

blah

Residuals

7491.8

77

97.3

Total

10332.2

79

B. What is the minimum number of values that need to be known to be able to fill in the ANOVA

table completely?

C. One of the professors suggests testing whether adding the two ACT scores to the regression model

would improve the model. The ANOVA table below shows the relevant values for the model

containing all four explanatory variables. Conduct the appropriate

F

test to determine if adding

the ACT scores improves the model.

SS

df

MS

F

p-value

Regression

2986.2

4

746.5

7.6

3.5e

5

Residuals

7346.0

75

97.9

Total

10332.2

79

D. Which of the two suggested models should the math department use?

E. In an attempt to further improve the model, the professors decide to look at the a

t

-tests for each

of the coefficients in the model that you chose in part D.. Using the Python output for both

models shown below, conduct each

t

-test for slope.

2

F. Based on the conclusions from part E., which explanatory variable, if any, would you try removing

first?