On March $1,1984,$ the Wall Street Journal published a survey of television

advertisements conducted by Video Board Tests, Inc., a New York ad$-$testing

company that interviewed $4000$ adults. These people were regular product

users who were asked to cite a commercial they had seen for that product

category in the past week. In this case, the response is the number of millions

of retained impressions per week. The regressor is the amount of money spent

by the firm on advertising. The data follow.

Firm

Amount Spent

$($millions$)$

Returned Impressions per week

$($millions$)$

Miller Lite $50\mathrm{.}132\mathrm{.}1$

Pepsi $74\mathrm{.}199\mathrm{.}6$

Stroh$$s $19\mathrm{.}311\mathrm{.}7$

Federal Express $22\mathrm{.}921\mathrm{.}9$

Burger King $82\mathrm{.}460\mathrm{.}8$

Coca$-$Cola $40\mathrm{.}178\mathrm{.}6$

c$02.$indd $6430-01-202114$:$32$:$04$

Problems $65$

$($Continued$)$

Firm

Amount Spent

$($millions$)$

Returned Impressions per week

$($millions$)$

McDonald$$s $185\mathrm{.}992\mathrm{.}4$

MCI $26\mathrm{.}950\mathrm{.}7$

Diet Cola $20\mathrm{.}421\mathrm{.}4$

Ford $166\mathrm{.}240\mathrm{.}1$

Levi$$s $2740\mathrm{.}8$

Bud Lite $45\mathrm{.}610\mathrm{.}4$

ATT Bell $154\mathrm{.}988\mathrm{.}9$

Calvin Klein $512$

Wendy$$s $49\mathrm{.}729\mathrm{.}2$

Polaroid $26\mathrm{.}938$

Shasta $5\mathrm{.}710$

Meow Mix $7\mathrm{.}612\mathrm{.}3$

Oscar Meyer $9\mathrm{.}223\mathrm{.}4$

Crest $32\mathrm{.}471\mathrm{.}1$

Kibbles N Bits $6\mathrm{.}14\mathrm{.}4$

a$.$ Fit the simple linear regression model to these data.

b$.$ Is there a significant relationship between the amount a company spends

on advertising and retained impressions? Justify your answer statistically.

c$.$ Construct the $95\%$ confidence and prediction bands for these data.

d$.$ Give the $95\%$ confidence and prediction intervals for the number of

retained impressions for MCI.