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...

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 website, April 17, 2012).

Date	DJIA	S&P
January 6	12360	1278
January 13	12422	1289
January 20	12720	1315
January 27	12660	1316
February 3	12862	1345
February 10	12801	1343
February 17	12950	1362
February 24	12983	1366
March 2	12978	1370
March 9	12922	1371
March 16	13233	1404
March 23	13081	1397
March 30	13212	1408
April 5	13060	1398
April 13	12850	1370 Use the data to develop an estimated regression equation showing how S&P 500 is related to DJIA. What is the estimated regression model? Letx represent the DJIA indexes. What is the 95% confidence interval for the regression parameterβ1? Based on this interval, what conclusion can you make about the hypotheses that the regression parameterβ1 is equal to zero? What is the 95% confidence interval for the regression parameterβ0? Based on this interval, what conclusion can you make about the hypotheses that the regression parameterβ0 is equal to zero? How much of the variation in the sample values of S&P 500 does the model estimated in part (b) explain Suppose that the closing price for the DJIA is 13,500. Estimate the closing price for the S&P 500. Should we be concerned that the DJIA value of 13,500 used to predict the S&P 500 value in part (e) is beyond the range of the used to develop the estimated regression equation? Explain.