Problem 7-9
Dixie Showtime Movie Theaters, Inc., owns and operates a chain
of cinemas in several markets in the southern U.S. The owners would
like to estimate weekly gross revenue as a function of advertising
expenditures. Data for a sample of eight markets for a recent week
follow.
Market
Weekly Gross
Revenue
($100s)
Television
Advertising
($100s)
Newspaper Advertising
($100s)
Mobile
101.3
5.0
1.5
Shreveport
51.9
3.0
3.0
Jackson
74.8
4.0
1.5
Birmingham
126.2
4.3
4.3
Little Rock
137.8
3.6
4.0
Biloxi
101.4
3.5
2.3
New Orleans
237.8
5.0
8.4
Baton Rouge
219.6
6.9
5.8
(a)
Use the data to develop an
estimated regression with the amount of television advertising as
the independent variable.
Let x represent
the amount of television advertising.
If required, round your answers to
four decimal places. For subtractive or negative numbers use a
minus sign even if there is a + sign before the blank. (Example:
-300)
ŷ =
(BLANK) + (BLANK) x
Test for a significant relationship
between television advertising and weekly gross revenue at the 0.05
level of significance. What is the interpretation of this
relationship?
(b)
How much of the variation in the
sample values of weekly gross revenue does the model in part (a)
explain?
If required, round your answer to
two decimal places.
(BLANK) %
(c)
Use the data to develop an
estimated regression equation with both television advertising and
newspaper advertising as the independent variables.
Let x1 represent
the amount of television advertising.
Let x2 represent
the amount of newspaper advertising.
If required, round your answers to
four decimal places. For subtractive or negative numbers use a
minus sign even if there is a + sign before the blank. (Example:
-300)
ŷ =
(BLANK) + (BLANK) x1 +
(BLANK) x2
Test whether each of the regression
parameters β0, β1,
and β2 is equal to zero at a 0.05 level of
significance. What are the correct interpretations of the estimated
regression parameters? Are these interpretations reasonable?
(d)
How much of the variation in the
sample values of weekly gross revenue does the model in part (c)
explain?
If required, round your answer to
two decimal places.
(BLANK) %
(e)
Given the results in part (a) and
part (c), what should your next step be? Explain.
(f)
What are the managerial
implications of these results?