Question: 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).
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?
b. Develop an estimated regression equation showing how S&P 500 is related to DJIA. What is the estimated regression model?
c. What is the 95 percent confidence interval for the regression parameter b1? Based on this interval, what conclusion can you make about the hypotheses that the regression parameter b1 is equal to zero? d. What is the 95 percent confidence interval for the regression parameter b0? Based on this interval, what conclusion can you make about the hypotheses that the regression parameter b0 is equal to zero? e. How much of the variation in the sample values of S&P 500 does the model estimated in part b explain?
f. Suppose that the closing price for the DJIA is 13,500. Estimate the closing price for the S&P 500.
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?