For each of the following statements, indicate whether it is true or false. If false, explain why it is false.
a. The multiple correlation is always the same as the ordinary correlation computed between the values of the response variable and the values ŷ predicted by the regression model.
b. The multiple correlation is like the ordinary correlation in that it falls between -1 and 1.
c. R2 describes how well you can predict y using x1 when you control for the other variables in the multiple regression model.
d. It’s impossible for R2 to go down when you add explanatory variables to a regression model.