Question

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. Weekly Gross Revenue ($100s) Television Advertising Newspaper Advertising ($100s) ($100s) Market Mobile 101.3 4.9 1.4 Shreveport 52.9 3.1 3.2 Jackson 75.8 4.2 1.5 Birmingham 127.2 4.5 4.3 Little Rock 137.8 3.6 4 Biloxi 102.4 3.5 2.3 New Orleans 236.8 5 8.4 Baton Rouge 220.6 6.8 5.9 (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 three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300) + 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? The input in the box below will not be graded, but may be reviewed and considered by your instructor. blank (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. 51.81 %

Answer 1

In order to solve this question I used R software.

R codes and output:

> d=read.table('data.csv',header=T,sep=',')

> head(d)

Revenue TV Newspaper

1   101.3 4.9       1.4

2    52.9 3.1       3.2

3    75.8 4.2       1.5

4   127.2 4.5       4.3

5   137.8 3.6       4.0

6   102.4 3.5       2.3

> attach(d)

> fit=lm(Revenue ~ TV)

> summary(fit)

Call:

lm(formula = Revenue ~ TV)

Residuals:

    Min      1Q Median      3Q     Max

-49.221 -28.623 -7.739 17.779 82.130

Coefficients:

            Estimate Std. Error t value Pr(>|t|)

(Intercept)   -52.783 70.89 -0.745   0.4847

TV             41.491 15.47   2.682   0.0364 *

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Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 47.79 on 6 degrees of freedom

Multiple R-squared: 0.5452, Adjusted R-squared: 0.4694

F-statistic: 7.192 on 1 and 6 DF, p-value: 0.03645

> fit2=lm(Revenue ~ TV + Newspaper)

> summary(fit2)

Call:

lm(formula = Revenue ~ TV + Newspaper)

Residuals:

      1       2       3       4       5       6       7       8

5.858 -34.433 -5.100 -13.891 23.540 22.755   6.147 -4.875

Coefficients:

            Estimate Std. Error t value Pr(>|t|)  

(Intercept) -46.208     33.678 -1.372 0.22841  

TV            23.485      8.302   2.829 0.03672 *

Newspaper     18.980      4.081   4.651 0.00558 **

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Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 22.68 on 5 degrees of freedom

Multiple R-squared: 0.9146, Adjusted R-squared: 0.8804

F-statistic: 26.78 on 2 and 5 DF, p-value: 0.002131

a.

y = -52.783 + 41.491 x

Since p-value for testing slope coefficient of TV is 0.0364, which is less than 0.05, hence we conclude that Slope coefficient is statistically significant. Which ultimately implies that there is significant relationship between television advertising and weekly gross revenue.

b.

54.52% variation.

c.

y =  -46.208 + 23.485 x1 + 18.980 x2

P-value for intercept is greater than 0.05, hence intercept $\small \beta_0$ is not statistically significant. P-value for slope coefficient $\small \beta_1$ and $\small \beta_2$ are less that 0.05, hence these variables are statistically significant.

d.

91.46% variation.

e.

R² and adjusted R² both are high for second model, it means second model will explain more variation in the weekly gross revenue. Hence we choose second model for prediction.

f.

Manager would prefer model 2.