Refer to the previous exercise.
a. For this example, it seems that the average sodium content is as good a predictor as the one resulting from the regression equation. Do you expect r² to be large or small? Why?
b. For this data, r = -0.017. Interpret r².
c. Show the algebraic relationship between the correlation of -0.017 and the slope of the regression equation b = -0.25, using the fact that the standard deviations are 5.32 g for sugar and 77.3 mg for sodium.

Previous exercise

The following figure shows the result of a regression analysis of the explanatory variable x = sugar and the response variable y = sodium for the breakfast cereal data set discussed in Chapter 2 (the Cereal data file on the book’s website).