Question 1 - Describing a multiple regression. As part of a study entitled "Predicting Success for Actuarial Students in Undergraduate Mathematics Courses," data from 106 Bryant University actuarial graduates were obtained.2 The researchers were interested in describing how students' overall math grade point averages are explained by SAT Math and Verbal scores, class rank, and Bryant University's mathematics placement score.
(a) What is the response variable?
(b) What is n, the number of cases?
(c) What is p, the number of explanatory variables?
(d) What are the explanatory variables?
Question 2 - Significance tests for regression coefficients. Recall Question 1. Due to missing values for some students, only 86 students were used in the multiple regression analysis. The following table contains the estimated coefficients and standard errors:
|
Variable
|
Estimate
|
SE
|
|
Intercept
|
-0.764
|
0.651
|
|
SAT math
|
0.00156
|
0.00074
|
|
SAT Verbal
|
0.00164
|
0.00076
|
|
High school rank
|
1.470
|
0.430
|
|
Bryant University placement
|
0.889
|
0.402
|
(a) All the estimated coefficients for the explanatory variables are positive. Is this what you would expect? Explain.
(b) What are the degrees of freedom for the model and error?
(c) Test the significance of each coefficient and state your conclusions.