XR19-16 The marketing manager for a chain
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
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
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
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

 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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