Question

The owner of a movie theater company used multiple regression
analysis to predict gross revenue (* y*) as a
function of television advertising
(

*ŷ* = 83.1 + 2.23*x*_{1} +
1.30*x*_{2}.

The computer solution, based on a sample of eight weeks, provided SST = 25.4 and SSR = 23.395.

(a) Compute and interpret *R*^{2} and
*R*_{a}^{2}.
(Round your answers to three decimal places.)

The proportion of the variability in the dependent variable that can be explained by the estimated multiple regression equation is (?) . Adjusting for the number of independent variables in the model, the proportion of the variability in the dependent variable that can be explained by the estimated multiple regression equation is (?).

(b) When television advertising was the only independent
variable, R^{2} = 0.653 and R_{a}^{2} =
0.595. Do you prefer the multiple regression results?

Multiple regression analysis [---Select One--- (is)/(is not)
]preferred since both *R*^{2} and
*R*_{a}^{2} show [---Select One---
(an increased)/(a decreased)] percentage of the variability of
*y* explained when both independent variables are used.

Answer #1

a)

R^{2}=SSR/SST = |
0.921 |

R^{2}_{adj}=1-(1-R^{2})*(n-1)/(n-k-1)= |
0.889 |

The proportion of the variability in the dependent variable that can be explained by the estimated multiple regression equation is 0.921 Adjusting for the number of independent variables in the model, the proportion of the variability in the dependent variable that can be explained by the estimated multiple regression equation is 0.889

b)

Multiple regression analysis is preferred since both
*R*^{2} and
*R*_{a}^{2} show an increased
percentage of the variability of *y* explained when both
independent variables are used.

The owner of a movie theater company used multiple regression
analysis to predict gross revenue (y)
as a function of television advertising
(x1) and newspaper advertising
(x2). The estimated regression
equation was
ŷ = 82.5 + 2.26x1 +
1.30x2.
The computer solution, based on a sample of eight weeks,
provided SST = 25.3 and SSR = 23.415.
(a)Compute and interpret R2
and Ra2.
(Round your answers to three decimal places.)
The proportion of the variability in the dependent variable that...

The owner of a movie theater company used multiple regression
analysis to predict gross revenue (y) as a
function of television advertising
(x1) and newspaper
advertising (x2). The
estimated regression equation was
ŷ = 83.8 + 2.26x1 +
1.50x2.
The computer solution, based on a sample of eight weeks,
provided SST = 25.8 and SSR = 23.385.
(a) Compute and
interpret R2 and
Ra2.
(Round your answers to three decimal places.)
The proportion of the variability in the dependent variable that
can be...

The owner of Showtime
Movie Theaters, Inc., used multiple regression analysis to predict
gross revenue (y) as a function of television advertising
(x1) and newspaper advertising (x2).
Weekly Gross Revenue
( s)
Televison Advertising
( s)
Newspaper Advertising
( s)
97
5
2.5
91
2
2
96
5
2.5
93
2.5
3.5
96
4
4.3
95
4.5
2.3
95
3.5
5.2
95
4
3.5
The estimated
regression equation was y^ = 86.7 + 1.66x1 -
.54x2
The computer solution
provided...

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...

The following estimated regression equation relating sales to
inventory investment and advertising expenditures was given.
ŷ = 25 + 11x1 +
9x2
The data used to develop the model came from a survey of 10
stores; for those data, SSyy (Total Sum of Squares) = 16,000 and
SSR (Regression Sum of Squares) = 11,360.
(a)
For the estimated regression equation given, compute
R2.(Round your answer to two decimal
places.)
R2 = ____
(b)
Compute the adjusted r-square,
Ra2.
(Round your...

The following estimated regression equation relating sales to
inventory investment and advertising expenditures was given.
ŷ = 24 + 12x1 +
7x2
The data used to develop the model came from a survey of 10
stores; for those data, SSyy (Total Sum of Squares) = 17,000 and
SSR (Regression Sum of Squares) = 12,070.
(a)For the estimated regression equation given, compute
R2.(Round your answer to two decimal
places.)
R2 =
(b) Compute the adjusted r-square,
Ra2.(Round
your answer to two...

In a regression analysis, _____ represents the proportion of
variations in the dependent variable, Y, could be explained by the
independent variables (all the Xs).
R2
F statistics
t statistics
p value

8. Consider the following data for a dependent variable
y and two independent variables, x1 and
x2.
x1
x2
y
30
12
94
47
10
108
25
17
112
51
16
178
40
5
94
51
19
175
74
7
170
36
12
117
59
13
142
76
16
211
(a) Develop an estimated regression equation relating y
to x1. (Round your numerical values to one decimal
place.)
ŷ = ______
Predict y if x1 = 51. (Round
your answer...

1. The owner of a movie theater company 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
1.5
91
2
2
95
4
1.5
93
2.5
2.5
95
3
3.3
94
3.5
2.2
94
2.5
4.1
94
3
2.5
(a) Use α = 0.01 to test the hypotheses
H0:
β1 = β2 = 0
Ha:...

The following data describes weekly gross revenue, television
advertising, and newspaper advertising for Showtime Movie
Theaters.
Weekly Gross Revenue ($1000s)
Televison Advertising ($1000s)
Newspaper Advertising ($1000s)
96
5
1.5
90
2
2
95
4
1.5
92
2.5
2.5
95
3
3.3
94
3.5
2.3
94
2.5
4.2
94
3
2.5
1. Find an estimated regression equation relating weekly gross
revenue to television advertising expenditures and newspaper
advertising expenditures (Round to 2 decimals).
where = Television Advertising ($1000s)
and = Newspaper Advertising ($1000s)....

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