Geoff is about to open a restaurant. He has found two possible locations for the

Question

Geoff is about to open a restaurant. He has found two possible locations for the restaurant; one closer to the Central Business District (CBD) and one in the suburbs. Geoff is concerned that if he chooses the CBD location, he will have to charge higher prices for his food to cover the higher rent. Geoff is uncertain of the affect that this will have on his annual revenue.

To help with his decision, Geoff will carry out a multiple regression analysis to predict the annual revenue earned by restaurants based on their distance from the CBD in miles and the average price in dollars charged for a dish. Geoff has collected a sample of 50 restaurants that are randomly spread around the city. The proximity to the CBD (x1i), average price of a dish (x2i) and annual revenues (yi) were recorded for each of these restaurants (i = 1, 2, ..., 50). Geoff believes that a multiple linear regression is appropriate for this data.

After carrying out some analysis, geoff has noticed that moving one mile away from the CBD (assuming that the average price of a dish is held constant) will result in a decrease of $60,000 in annual revenues. Geoff has also noticed that increasing the average price of a dish by $1 (assuming that the distance from the CBD is held constant) will result in an increase of $40,000 in annual revenues. The data shows that a restaurant at the center of the CBD that gave away its food for free would have an annual loss of $20,000.

Select the multiple linear regression equation that corresponds to Geoff's analysis:

y^i = -20,000 + 40,000x1i - 60,000x2i y^i = 20,000 - 40,000x1i + 60,000x2i y^i = 20,000 + 60,000x1i - 40,000x2i y^i = -20,000 - 60,000x1i + 40,000x2i

Explanation / Answer

we need to focus on how independent variables effect the dependent variables . Please see the below important words from the question

hence the regression equation that satisfies the above "signs" of coefficients is

y^i = -20,000 + 40,000x1i - 60,000x2i

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