Chapter 13, Problem 80CP

True or false: Slopes For data on y = college GPA, x₁ = high school GPA, and x₂ = average of mathematics and verbal entrance exam score, we get $\hat{y}=2.70+0.45x_1$ for simple regression and $\hat{y}=0.3+0.40x_1+0.003x_2$ multiple regression. For each of the following statements, indicate whether it is true or false. Give a reason for your answer.

1. a. The correlation between y and x₁ is positive.
2. b. A one-unit increase in x₁ corresponds to a change of 0.45 in the predicted value of y, controlling for x₂.
3. c. Controlling for x₁, a 100-unit increase in x₂ corresponds to a predicted increase of 0.30 in college GPA.