15.2

1.

The estimated regression equation for a model involving two independent variables and 10 observations follows.

?=26.1170+0.5808x₁+0.4940x₂

(a)

Interpretb₁

in this estimated regression equation.

b₁= 0.5808 is an estimate of the change inycorresponding to a 1 unit change inx₁whenx₂is held constant.

b₁= 0.4940 is an estimate of the change inycorresponding to a 1 unit change inx₁whenx₂is held constant.

b₁= 0.4940 is an estimate of the change inycorresponding to a 1 unit change inx₂whenx₁is held constant.

b₁= 0.5808 is an estimate of the change inycorresponding to a 1 unit change inx₂whenx₁is held constant.

b₁= 26.1170 is an estimate of the change inycorresponding to a 1 unit change inx₁whenx₂is held constant.

Interpretb₂

in this estimated regression equation.

b₂= 0.4940 is an estimate of the change inycorresponding to a 1 unit change inx₁whenx₂is held constant.

b₂= 0.5808 is an estimate of the change inycorresponding to a 1 unit change inx₁whenx₂is held constant.

b₂= 0.4940 is an estimate of the change inycorresponding to a 1 unit change inx₂whenx₁is held constant.

b₂= 26.1170 is an estimate of the change inycorresponding to a 1 unit change inx₁whenx₂is held constant.

b₂= 0.5808 is an estimate of the change inycorresponding to a 1 unit change inx₂whenx₁is held constant.

(b)

Predictywhenx₁=180andx₂=320.

2.

A shoe store developed the following estimated regression equation relating sales to inventory investment and advertising expenditures.

?=21+12x₁+6x₂

where

x₁=inventory investment ($1,000s)x₂=advertising expenditures ($1,000s)y=sales ($1,000s).

(a)

Predict the sales (in dollars) resulting from a $15,000investment in inventory and an advertising budget of $10,000.

$

(b)

Interpretb₁andb₂

in this estimated regression equation.

Sales can be expected to increase by $for every dollar increase in inventory investment when advertising expenditure is held constant. Sales can be expected to increase by$for every dollar increase in advertising expenditure when inventory investment is held constant.

3.

The owner of Showtime Movie Theaters, Inc., would like to predict weekly gross revenue as a function of advertising expenditures. Historical data for a sample of eight weeks follow.

Weekly Television Gross Newspaper Revenue Advertising Advertising ($1,000s) ($1,000s) ($1,000s) 96 5.0 1.5 90 2.0 2.0 95 4.0 1.5 92 2.5 2.5 95 3.0 3.3 94 3.5 2.3 94 2.5 4.2 94 3.0 2.5Selling Price Baths Sq Ft Beds Selling Price Baths Sq Ft Beds 160,000 1.5 1,786 3 295,000 2.5 1,860 3 170,000 2 1,768 3 325,000 2 2,056 4 178,000 1 1,219 3 325,000 3.5 2,776 4 182,500 1 1,578 2 328,400 2 1,408 4 195,100 1.5 1,125 4 331,000 1.5 1,972 3 212,500 2 1,196 2 344,500 2.5 1,736 3 245,900 2 2,128 3 365,000 2.5 1,990 4 250,000 3 1,280 2 385,000 2.5 3,640 4 255,000 2 1,596 3 395,000 2.5 1,928 4 258,000 3.5 2,374 4 399,000 2 2,108 3 267,000 2.5 2,439 3 430,000 2 2,462 4 268,000 2 1,470 4 430,000 2 2,615 4 275,000 2 1,688 4 454,000 3.5 3,700 4