Question 2.48

2.48 The “January effect.”

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 based on 38 years of data gives

  1. What percent of the observed variation in yearly changes in the index is explained by a straight-line relationship with the change during January?
  2. What is the equation of the least-squares line for predicting the full-year change from the January change?
  3. The mean change in January is . Use your regression line to predict the change in the index in a year in which the index rises 1.75% in January. Why could you have given this result (up to roundoff error) without doing the calculation?