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$\text{'}$s website, April $17,2012).$

a$.$ Develop a scatter diagram with DJIA as the independent variable.

b$.$ Develop the estimated regression equation.

c$.$ Test for a significant relationship. Use $=\mathrm{.}05.$

d$.$ Did the estimated regression equation provide a good fit? Explain.

e$.$ Suppose that the closing price for the DJIA is $13,500.$ Predict the closing price for the

S&P $500.$

f$.$ 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 data used to develop the estimated regres$-$

sion equation?