ECN 206E PS#4.pdf - ECN 206E Statistics II Problem Set 4...

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ECN 206E — Statistics II Problem Set 4 Spring ’18 Exercise 11.13 Consider the sales prediction model developed for Northern Household Goods in Example 11.2. (a) Estimate per capita sales if the mean disposable income is $56,000. (b) Interpret the coefficients b 0 and b 1 for Northern’s management. (c) You have been asked to estimate per capita sales if mean disposable income grows to $64,000. Discuss how you would proceed and indicate your cautions. Solution: Y = 559 + . 3815 X (a) ˆ y = 559 + 0 . 3815(56 , 000) = 21 , 923 (b) The coefficient b 0 = 559 states that for $0 per capita disposable family income, the expected value of retail sales is $559. This is not a realistic value and has no meaning in this problem. The coefficient b 1 = 0 . 3815 states that every $1 increase in per capita disposable family income, the expected value of retail sales increases by $0.38. (c) Because the disposable income is outside the range of data values, the model, and the underlying assump- tions should be checked to make sure that it would make sense to extrapolate. If it makes sense to estimate,
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