Regression analysis for Business Statistics - Effect of Shelf Space on Sales of Pet Food.

4 Template

Problem #1 The marketing manager of a large supermarket chain would like
to determine the effect of shelf space on the sales of pet food. A
random sample of 12 equal-sized stores is selected, with the following
results:

Store Shelf Space X (Feet) Weekly Sales Y

(Hundreds of Dollars)



1 5 1.6



2 5 2.2



3 5 1.4



4 10 1.9



5 10 2.4



6 10 2.6



7 15 2.3



8 15 2.7



9 15 2.8



10 20 2.6



11 20 2.9



12 20 3.1



Set up a scatter diagram (NOTE: you can select this as an output with
the regression).

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Assuming a linear relationship, use the least squares method to find the
regression coefficients B0 & B1.

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Interpret the meaning of slope (B1) in this problem.

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Predict the average weekly sales (in hundreds of dollars) of pet food
for stores with 8 feet of shelf space for pet food.

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Suppose that sales in store 12 are 2.6. Repeat b-d with this value and
compare the results to your original results.

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How much shelf space would you recommend that the marketing manager
allocate to pet food? Explain..

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Problem #2 In problem #1 (above), the marketing manager used shelf
space for pet food to predict weekly sales. Using the computer output
you obtained to solve that problem.

Determine the coefficient of determination r2 and interpret its meaning.

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Determine the standard error of the estimate.

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How useful do you think this regression model is for predicting sales?

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Problem #3 In problem #1 (above), the marketing manager used shelf space
for pet food to predict weekly sales. Perform a residual analysis for
these data. Based on the results obtained,

Determine the adequacy of fit of the model.

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Evaluate whether the assumptions of regression have been seriously
violated.

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Problem #4 In problem #1 (above), the marketing manager used shelf space
for pet food to predict weekly sales.

Is it necessary to compute the Durbin Watson statistic? Explain.

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Under what circumstance would it be necessary to compute the Durbin
Watson statistics before proceeding with the least squares method of
regression analysis?

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Problem #5 In problem #1 (above), the marketing manager used shelf
space for pet food to predict weekly sales. Using the output you
obtained to solve that problem.

At the .05 level of significance, is there evidence of a linear
relationship between shelf space and sales?

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Problem #6 In problem #1 (above), the marketing manager used shelf space
for pet food to predict weekly sales.



Set up a 95% confidence interval estimate of the average weekly sales
for all stores that have 8 feet of shelf space for pet food.

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Set up a 95% confidence interval estimate of the average weekly sales of
an individual store that has 8 feet of shelf space for pet food.

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Explain the difference in the results obtained in a & b.

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