Question

12.3

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 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.) 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, Xy represent the amount of newspaper advertising in $1,000s, and y represent the weekly gross revenue in $1,000s.) Is the estimated regression equation coefficient for television advertising expenditures the same in part (a) and in part (b)? D it is in part (a) and in part (b). Interpret the coefficient in each case. 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 television advertising with newspaper 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 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. 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. 0 Predict weekly gross revenue (in dollars) for a week when $3,900 is spent on television advertising and $1,900 is spent on newspaper advertising (Round your answer to the nearest cent.) $

Answer 1

Answer:

a) Estimate the regression equation for the given data by using Minitab as follows: Regression Analysis: Revenue versus TV Ads The regression equation is Revenue 88.6 1.60 TV Ads Predictor Constant Coef SE Coef 88.638 1.582 56.02 0.000 TV Ads 1.6039 0.4778 3.36 0.015 R-Sq (adj)59.5 S 1.21518 R-Sq =65.3% Analysis of Variance Source DF SS MS F Regression 1 16.640 16.640 11.27 0.015 Residual Error 6 8.860 1.477 Total 7 25.500 An estimated regression equation with the amount of television advertising as the independent variable is: y = 88.6+1.60x

b) Estimate the regression equation for the given data by using Minitab as follows: Regression Analysis: Revenue versus TV Ads, News Ads The regression equation is Revenue 83.2 2.29 TV Ads 1.30 News Ads Coef Predictor SE Coef T P Constant 83.230 1.574 52.8e 0.000 TV Ads 2.2902 0.3041 7.53 0.001 News Ads 1.3010 0.3207 4.06 0.010 S 0.642587 R-Sq 91.9 R-Sq(adj) = 88.7% Analysis of Variance Source DF SS MS F Regression 2 23.435 11.718 28.38 0.002 Residual Error 2.065 0.413 Total 7 25.500 The estimated regression equation with both television advertising and newspaper advertising as the independent variables is: y 83.2 + 2.29x, +1.30x

c) The estimated regression coefficient for television advertising expenditure in part (a) is 1.60 and in part (b) it is 2.29 The value of b,is not the same in both cases In simple linear regression, we interpret bas an estimate of the change in weekly gross revenue for a one-unit change in the independent variable that is television advertising expenditure. In multiple regression analysis, this interpretation must be modified somewhat. That is, in multiple regression analysis, we interpret each regression coefficient as follows: b, represents an estimte of the change in y corresponding to a one-unit change in x when all other independent variables are held constant So in this case, involving two independent variables, b-2.29. Thus 2.29 thousand dollars is an estimate of the expected increase in gross revenue corresponding to an increase of one thousand dollars in the television advertising expenditure when the expenditure on newspaper advertising is held constant.

d)

y = 83.2 + 2.29 (3.9) + 1.3 (1.9)

= 94.601

Therefore, the estimate of the weekly gross revenue is $94,601