Question

01 of 6 - Select all the scatter plots that indicate a violation of one or more of the assumptions of linear regression: Residual 30 40 50 60 70 80 90 100 Response variable Explanatory value 0.5 11. 52 253 Explanatory variable Residual Response variable 100 110 120 130 140 150 160 170 180 10 20 30 40 Explanatory variable 50 60 Explanatory value O2 of 6 Geoff is abou, 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 (X11), average price of a dish (xi) 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: O Y = -20,000 - 60,000X11 + 40,000X2i 0 # = 20,000 - 40,000x1 + 60,000X2I Y = -20,000 + 40,000x11 - 60,000x2i ĝi = 20,000 + 60,000X11 - 40,000X2i

Answer 1

1) Among the 2 residual plots the 2nd one shows a pattern indicating that the residuals are not independent. Hence assumptio of linearity is violated.

Among the 2 (response vs explanatory) scatter plots, the 1st one clearly shows that it is not linear in nature.

Hence the 2nd and the 3rd scatter plots shows violation of the assumptions.

2) Geoff noticed that moving 1 mile away from CBD result in a decrease of $60,000 in annual revenues.

Hence b1 = - 60000

Geoff ha also noticed that increasing the average price of a dish by $1 will result in an increase of $40000 in annual revenue

Hence b2 = 40000

The restaurant at the centre of CBD that gave away its food for free would have an annual loss of $20,000

Hence b0 = -20000

The regression equation that corresponds to Geoff's Analysis is:

$\hat{y_{i}}=-20,000-60,000 x_{1i}+40,000x_{2i}$