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?
let x represent the djia indexes.
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?
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?
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.