The stock market Some people think that the behavior of the stock market in January predicts its behavior for the rest of the year. Take the explanatory variable x to be the percent change in a stock market index in January and the response variable y to be the change in the index for the entire year. We expect a positive correlation between x and y because the change during January contributes to the full year’s change.

Calculation from data for an 18-year period gives x– = 1.75% sx = 5.36% y– = 9.07%

sy = 15.35% r = 0.596

(a) Find the equation of the least-squares line for predicting full-year change from January change. Show your work.

(b) Suppose that the percent change in a particular January was 2 standard deviations above average. Predict the percent change for the entire year, without using the least-squares line. Show your work.