Several previous problems have dealt with the College Board changing the format of the SAT test taken by many entering college freshmen. Many reasons were given for changing the format. The class of 2005 was the last to take the former version of the SAT, featuring math and verbal sections. There had been conjecture about whether a relationship between the average math SAT score and the average verbal SAT score and the gender of the student taking the SAT examination existed. Consider the following relationship:

Where:

a. Use the file MathSAT to compute the linear regression equation to predict the average math SAT score using the gender and the average verbal SAT score of the students taking the SAT examination.
b. Interpret the parameters in the model.
c. Conduct a hypothesis test to determine if the gender of the student taking the SAT examination is a significant predictor of the student’s average math SAT score for a given average verbal SAT score.
d. Predict the average math SAT score of female students with an average verbal SAT score of 500.