Chapter 4, Problem 7P

The Dow Jones Industrial Average (DJIA) and the Standard & Poor’s 500 (S&P 500) indexes are used as measures of overall movement in the stock market The DJIA is based on the price movements of 30 large companies: the S&P 500 is an index composed of 500 stocks. Some say the S&P 500 is a better measure of stock market performance because it is broader based. The closing price for the DJIA and the S&P 500 for 15 weeks, beginning with January 6, 2012, follow (Barron’s web site, April 17, 2012).

1. a. Develop a scatter chart for these data with DJIA as the independent variable. What does the scatter chart indicate about the relationship between DJIA and S&P 500?
2. b. Develop an estimated regression equation showing how S&P 500 is related to DJIA. What is the estimated regression model?
3. c. What is the 95% confidence interval for the regression parameter β₁? Based on this interval, what conclusion can you make about the hypotheses that the regression parameter β₁ is equal to zero?
4. d. What is the 95% confidence interval for the regression parameter β₀? Based on this interval, what conclusion can you make about the hypotheses that the regression parameter β₀ is equal to zero?
5. e. How much of the variation in the sample values of S&P 500 does the model estimated in part (b) explain?
6. f. Suppose that the closing price for the DJIA is 13,500. Estimate the closing price for the S&P 500.
7. g. Should we be concerned that the DJIA value of 13,500 used to predict the S&P 500 value in part (f) is beyond the range of the DJIA used to develop the estimated regression equation?