A second predictor in Exercise 13 improved the regression model of Exercise 1, so let’s try a third. Here’s a model with average ACT score of the entering class included:

a) The coefficient of SAT in this model is quite different from the SAT coefficient in the original model of Exercise 1 or the multiple regression model of Exercise 13. Why the change?
b) Find a 95% confidence interval for the coefficient of SAT. How does it compare with the one you found in Exercise 13?
c) The t-ratio associated with the SAT coefficient is now much smaller and the corresponding P-value much larger.

Data From Exercise 13

Continuing with the data from Exercise 1, here’s a regression with the percent of students who receive merit-based financial aid included in the model:

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Response variable is: Earn R squared = 36.5% s = 5372 with 687 - 4 = 683 degrees of freedom Variable Intercept SAT %need ACT Coefficient 25162.8 10.1117 -8564.03 551.243 SE(Coeff) 2340 4.355 1320 170.0 3.24 t-ratio 10.8 2.32 -6.49 P-value <0.0001 0.0205 <0.0001 0.0012