Go to www.pearsonhighered.com/sullivanstats to obtain the data file 14_3_19 using the file format of your choice. The data represent the SAT Math scores for students who took the exam in 2012, along with the percent of students who took the exam in the state, and the average and starting salaries of the teachers (in thousands of dollars).

(a) Find the least-squares regression equation y̅ = b0 + b1x1 + b2x2 + b3x3, where x1 is the percent of students who take the exam in the state, x2 is the average salary, x3 is the starting salary, and y is the SAT Math score.

(b) Does the F-test indicate that we should reject H0: b1 = b2 = b3 = 0? Do any of the explanatory variables have slope coefficients that are not significantly different from zero?

(c) Interpret each of the slope coefficients of the model in part (a). Are they all reasonable? Explain. Hint: Obtain a correlation matrix.

(d) Find the least-squares regression equation yn = b0 + b1x1 + b2x2. Does the F-test indicate that we should reject H0: b1 = b2 = 0? Do any of the explanatory variables have slope coefficients that are not significantly different from zero? Do the slope coefficients have signs that are consistent with what you would expect?