For data on y = college GPA, x1 = high school GPA, and x2 = average of mathematics and verbal entrance exam score, we get ŷ = 2.70 + 0.45x1 for bivariate regression and ŷ = 0.3 + 0.40x1 + 0.003x2 for multiple regression. For each of the following statements, indicate whether it is true or false. Give a reason for your answer.
a. The correlation between y and x1 is positive.
b. A one-unit increase in x1 corresponds to a change of 0.45 in the predicted value of y, controlling for x2.
c. Controlling for x1, a 100-unit increase in x2 corresponds to a predicted increase of 0.30 in college GPA.