# Regression analysis

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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

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

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

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

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

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See attached file for full problem description.

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##### Solution Summary

Step by step method for regression analysis is discussed here. Regression coefficients, coefficient of determination, scatter diagram and significance of regression model are explained in the solution.

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