A shoe store developed the following estimated regression equation relating sales to inventory investment and advertising expenditures. y = 21 + 10X1 + 7x2 where X1 = inventory investment ($1,000s) X2 = advertising expenditures ($1,000s) y = sales ($1,000s). (a) Predict the sales (in dollars) resulting from a $14,000 investment in inventory and an advertising budget of $10,000. $ 241 (b) Interpret b, and by in this estimated regression equation. Sales can be expected to increase by $ 1000 X for every dollar increase in inventory investment when advertising expenditure is held constant. Sales can be expected to increase by $ 1000 X for every dollar increase in advertising expenditure when inventory investment is held constant.A statistical program is recommended. 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 Gross Television 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 2.5 (a) Develop an estimated regression equation with the amount of television advertising as the independent variable. (Round your numerical values to two decimal places. Let x, represent the amount of television advertising in $1,000s and y represent the weekly gross revenue in $1,000s.) D = 88.64 + 1.604x] (b) Develop an estimated regression equation with both television advertising and newspaper advertising as the independent variables. (Round your numerical values to two decimal places. Let x, represent the amount of television advertising in $1,000s, x, represent the amount of newspaper advertising in $1,000s, and y represent the weekly gross revenue in $1,000s.) V = 83.23 + 2.290x, + 1.301x2 (c) Is the estimated regression equation coefficient for television advertising expenditures the same in part (a) and in part (b)? No v , it is 1.604 v in part (a) and 2.290 in part (b). Interpret the coefficient in each case. O In part (a) it represents the change in revenue due to a one-unit increase in television advertising expenditure with newspaper advertising held constant. In part (b) it represents the change in revenue due to a one-unit increase in newspaper advertising with television advertising held constant. In part (a) it represents the change in revenue due to a one-unit increase in television advertising expenditure. In part (b) it represents the change in revenue due to a one-unit increase in newspaper advertising with television advertising held constant In part (a) it represents the change in revenue due to a one-unit increase in television advertising with newspaper advertising held constant. In part (b) it represents the change in revenue due to a one-unit increase in television advertising expenditure. O In part (a) it represents the change in revenue due to a one-unit increase in television advertising expenditure. In part (b) it represents the change in revenue due to a one-unit increase in television advertising with newspaper advertising held constant. In part (a) it represents the change in revenue due to a one-unit increase in newspaper advertising expenditure with television advertising held constant. In part (b) it represents the change in revenue due to a one-unit increase in television advertising with newspaper advertising held constant. X (d) Predict weekly gross revenue (in dollars) for a week when $3,800 is spent on television advertising and $1,900 is spent on newspaper advertising. (Round your answer to the nearest cent.) $ 10216.33 XSpring is a peak time for selling houses. The table below contains the selling price, number of bathrooms, square footage, and number of bedrooms of 26 homes in a certain city. Selling Price Baths Sq Ft Beds Selling Price Baths Sq Ft Beds 160,000 1.5 1,766 3 295,000 2.5 1,860 170,000 2 1,768 3 325,000 2 2,056 178,000 1 1,219 3 325,000 3.5 2,776 182,500 1 1,558 2 328,400 2 1,408 4 195,100 1.5 1,125 3 331,000 1.5 1,972 3 212,500 2 1,196 344,500 2.5 1,736 3 245,900 2 2,128 3 365,000 2.5 1,990 250,000 3 1,280 3 385,000 2.5 3,640 4 255,000 2 1,596 3 395,000 2.5 1,908 258,000 3.5 2,374 399,000 2 2,108 267,000 3.5 2,439 3 430,000 2 2,462 268,000 2 1,470 4 430,000 2,615 4 275,000 2 1,688 4 454,000 3.5 3,700 4(a) Develop scatter plots of selling price versus number of bathrooms. 500 000 500 000 450 000 450 000 . .. 400 000 400 000 - ... 350 000 350 000 . . . 300 000 300 000 . . . Selling Price 250 000 Selling Price 250 000 200 000 200 000 150 000 150 000 100 000 100 000 50 000 50 000 0- 0.5 1. 1.5 2. 25 3. 3.5 0.5 1. 1.5 2. 25 3. 3.5 O Number of Bathrooms Number of Bathrooms 500 000 - 500 000 450 000 450 000 400 000 400 000 350 000 - 350 000 300 000 300 000 Selling Price 250 000 .. . . Selling Price 250 000 200 000 - 200 000 150 000 150 000 100 000 100 000 50 000 - 50 000 0.5 1. 1.5 2 . 2.5 3. 3.5 0.5 1. 1.5 2. 2.5 3. 3.5 Number of Bathrooms O Number of Bathrooms What is the relationship between the selling price of a house and the number of bathrooms in it? As the number of bathrooms increases, the selling price increases. O As the number of bathrooms increases, the selling price decreases. X(b) Develop an estimated regression equation that can be used to predict the selling price given the three independent variables (number of baths, square footage, and number of bedrooms). (Round your numerical values to two decimal places. Let x, represent the number of baths, x, represent the square footage, x3 represent the number of bedrooms, and y represent the selling price.) 27208.24x, + 47.17x, + 40900.34x, + 91331.34 x (c) It is argued that we do not need both number of baths and number of bedrooms. Develop an estimated regression equation that can be used to predict selling price given square footage and the number of bedrooms. (Round your numerical values to two decimal places. Let x, represent the square footage, x, represent the number of bedrooms, and y represent the selling price.) = 60.88x + 41885.48x, + 37155.81 X (d) Suppose your house has four bedrooms and is 2,650 square feet. What is the predicted selling price (in $) using the model developed in part (c). (Round your answer to the nearest cent.) $ 366029.73 X