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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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https://brainmass.com/math/interpolation-extrapolation-and-regression/regression-analysis-124846

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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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Statistics Problems - Regression Analysis, Autocorrelation, Multicollinearity

1. Suppose an appliance manufacturer is doing a regression analysis, using quarterly time-series data, of the factors affecting its sales of appliances. A regression equation was estimated between appliance sales (in dollars) as the dependent variable and disposable personal income and new housing starts as the independent variables. The statistical tests of the model showed large t-values for both independent variables, along with a high r2 value. However, analysis of the residuals indicated that substantial autocorrelation was present.

a. What are some of the possible causes of this autocorrelation?

b. How does this autocorrelation affect the conclusions concerning the significance of the individual explanatory variables and the overall explanatory power of the regression model?

c. Given that a person uses the model for forecasting future appliance sales, how does this autocorrelation affect the accuracy of these forecasts?

d. What techniques might be used to remove this autocorrelation from the model?

2. Suppose the appliance manufacturer discussed in Exercise 1 also developed another model, again using time-series data, where appliance sales was the dependent variable and disposable personal income and retail sales of durable goods were the independent variables. Although the r2 statistic is high, the manufacturer also suspects that serious multicollinearity exists between the two independent variables.

a. In what ways does the presence of this multicollinearity affect the results of the regression analysis?

b. Under what conditions might the presence of multicollinearity cause problems in the use of this regression equation in designing a marketing plan for appliance sales?

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