You own similarly-sized stores widely scattered across the United States. To examine the

relationship between sales and income of people living near the store, you create the regression

equation

S = 30+.7I

where S = yearly sales of a store (in $100,000's) and I = median income (in $1,000s) of people

living near the store. The R² for this model is 14% and the standard error (SE) is 20.

(a) Give managerial interpretations for the numbers 30, .7, and 20.

(b) If a new industry opening near a given store raises median income for the people living

near the store by $1,000, what can you say about how this would affect sales? Discuss

briefly.

(c) Half the stores are in rural areas and half are in urban areas. You decide to create

separate models and get

S = 50 . 25I, R² = 30%, SE = 18

for the rural areas and

S = 90 . 22I, R² = 31%, SE = 17

for the urban areas. How is it possible that the regression coefficients are negative in the urban and rural equations, but positive in the overall equation above? Explain with a diagram, if necessary.