a3764K9F.doc

# a3764K9F.doc - (The next 8 questions are based on the...

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(The next 8 questions are based on the following information.) The general manager of a supermarket chain believes that sales of a product are related to the amount of space the product is given on shelves. Across a sample of stores, she measures the sales of a particular brand of laundry detergent (in boxes per week) and relates sales to the amount of shelf space (in inches) devoted to the detergent. In the sample, shelf space ranges from 12 to 32 inches, while sales ranges from 173 to 395 boxes per week. The general manager estimates two models, a straight-line model, and a quadratic (parabola) model. Selected output from Excel is given below. Straight-Line Model: R 2 = .191 R 2 (Adjusted) = .148 Residual Standard Deviation = 47.8 Coefficients Standard Error t Stat P-value Intercept 191.54 39.31 4.87 0.0001 ShelfSpace 3.64 1.72 2.12 0.0479 Quadratic Model: R 2 = .380 R 2 (Adjusted) = .312 Residual Standard Deviation = 43.0 Coefficients Standard Error t Stat P-value Intercept -109.85 133.14 -0.83 0.4201 ShelfSpace 33.29 12.72 2.62 0.0175 ShelfSpace Squared -0.67 0.29 -2.35 0.0305 320. Determine the correlation coefficient relating Sales to ShelfSpace. (a) r= -0.67 (b) r= 0.44 (c) r= 0.62 (d) r= 0.67 Answer: (b) correlation coefficient measures the straight-line association between X and Y. it’s the sqrt of the R2 value from the straight-line model: r = sqrt(.191) = .44 And the correlation is positive because the slope is positive (3.64) 321. Based on the quadratic model , what are the predicted sales of detergent if there are 20 inches of shelf space devoted to detergent? (a) 264 boxes per week (b) 288 boxes per week (c) 395 boxes per week (d) Cannot be determined, because it would require extrapolating outside of the range of the data. Answer: (b) predicted sales = -109.85 + 33.29*20 - .67*20 2 = 288 322. Suppose one store is considering expanding the shelf space for detergent from 20 inches to 30

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inches. Which model predicts a larger change in sales when changing from 20 inches to 30 inches of shelf space? (a) The straight-line model predicts a larger increase in sales than the quadratic model does. (b) The quadratic model predicts a larger increase in sales than the straight-line model does.
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## This document was uploaded on 06/05/2011.

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a3764K9F.doc - (The next 8 questions are based on the...

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