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% s_x = 5.36% y¯ = 9.07% s_y = 15.35% r = 0.596

a. Find the equation of the least-squares line for predicting full-year change from January change.

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.