XR19-16 The marketing manager for a chain of hardware stores needed more information about the…

XR19-16 The marketing manager for a chain
of hardware stores needed more information about the effectiveness of the three
types of advertising that the chain used. These are localised direct mailing
(in which flyers describing sales and featured products are distributed to
homes in the area surrounding a store), newspaper advertising and local
television advertisements. To determine which type is most effective, the
manager collected one week’s data from 25 randomly selected stores. For each
store, the following variables were recorded:

• Weekly gross sales

• Weekly expenditures on
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XR19-16 The marketing manager for a chain
of hardware stores needed more information about the effectiveness of the three
types of advertising that the chain used. These are localised direct mailing
(in which flyers describing sales and featured products are distributed to
homes in the area surrounding a store), newspaper advertising and local
television advertisements. To determine which type is most effective, the
manager collected one week’s data from 25 randomly selected stores. For each
store, the following variables were recorded:

• Weekly gross sales

• Weekly expenditures on direct mailing

• Weekly expenditures on newspaper
advertising

• Weekly expenditures on television
commercials. All variables were recorded in thousands of dollars.

a Find the regression equation.

b What are the coefficient of determination
(R2) and the coefficient of determination adjusted for degrees of
freedom (R ) 2?

What do these statistics tell you about the
regression equation? Using the ANOVA table, calculate R2, R2
and s_ and confirm that these values are the same as those shown in the
computer output.

c What does the standard error of estimate
tell you about the regression model?

d Test the overall utility of the model.
What does the p-value of the test statistic tell you?

e Which independent variables are linearly
related to weekly gross sales? Explain.

f Predict next week’s gross sales if a
local store spent $800 on direct mailing, $1200 on newspaper advertisements and
$2000 on television commercials.

g Estimate the mean weekly gross sales for
all stores that spend $800 on direct mailing, $1200 on newspaper advertising
and $2000 on television commercials.

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