Question

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 Revenue ($1,000s)	Television Advertising ($1,000s)	Newspaper Advertising ($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 x₁ represent the amount of television advertising in $1,000s and y represent the weekly gross revenue in $1,000s.)

ŷ =

(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 x₁ represent the amount of television advertising in $1,000s, x₂ represent the amount of newspaper advertising in $1,000s, and y represent the weekly gross revenue in $1,000s.)

ŷ =

(c)

Is the estimated regression equation coefficient for television advertising expenditures the same in part (a) and in part (b)?

---Select--- Yes No , 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. 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 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 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 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.

(d)

Predict weekly gross revenue (in dollars) for a week when $3,500 is spent on television advertising and $1,800 is spent on newspaper advertising. (Round your answer to the nearest cent.)

$

Answer 1

a) The estimated regression equation between the gross revenue with the amount of television advertising as the independent variable is given by ŷ = 88.64 + 1.61 x1 (where x₁ represents the amount of television advertising in $1,000s and ŷ represents the predicted weekly gross revenue at $1,000s.)

b) The estimated regression equation with both television advertising and newspaper advertising as the independent variables is given by ŷ = 83.23 + 2.29x1 + 1.30x2 (Where x₁ represents the amount of television advertising in $1,000s, x₂ represents the amount of newspaper advertising in $1,000s, and  ŷ represents the predicted weekly gross revenue in $1,000s.)

c) No, the estimated regression equation coefficient for television advertising expenditures is not the same in part (a) and in part (b).

Option (i) is correct, which says -- 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.

d) Weekly gross revenue for a week when $3,500 is spent on television advertising and $1,800 is spent on newspaper advertising is obtained by putting x1=3500 and x2=1800 in part (b). It comes out to be $94 (rounded to the nearest thousand dollars).

(The calculations are obtained using R-software. Codes and Outputs are attached below).