Problem 2 The regression model was estimated of Price on Food (food quality), De

Question

Problem 2 The regression model was estimated of Price on Food (food quality), Decor and Service based on the data for 294 restaurants from 2003 Zagat restaurant guide for New York City. Price is the cost of a dinner with one drink (in dollars). Food, Decor and Service are ratings on a scale from 0 to 30. In the data for 294 restaurants the lowest rating for each predictor is 8 Answer questions below based on the Minitab output on the next page. a) Is the multiple regression model of Price on all three predictors sta- tistically significant at = 0.01? (State the hypothesis test, interpret it, and state your conclusion.) b) What is the correlation between Price and Food? Is the coefficient of Food in the simple regression of Price on Food statistically significant at c) Why is the coefficient of Food negative in the multiple regression d) Is the coefficient of Food statistically significant at = 0.05 in the = 0.057(Explain) model? multiple regression model? (State and interpret the hypothesis test, state the rejection rule and your conclusion) e) The best subsets regression was run to obtain the "best" set of pre- dictors for explaining the variation in Price. What is the criterion, which we discussed in class, for choosing the "best" set of predictors? f) According to the best subsets regression or/and results above, Decor and Service were selected as the best set of predictors for Price. Interpret the constant term and the coefficient of Service in this model

Explanation / Answer

a)

H0: = 0 (no linear relationship)

H1: 0 (at least one independent variable affects Y)

Looking at the p-value in the ANOVA table, it is 0 and hence it is less than a=0.01 and hence reject the null hypothesis. Thus, we conclude that at least one independent variable affects Y

b)

Correlation between price and food is 0.528. Looking at the coefficients, it does not appear to be statistically significant because p-value is greater than a and sign is also not significant. It indicates that price would go down with increase in food quality which ideally does not make sense.

c)

It indicates that price would go down with increase in food quality which ideally does not make sense.

d)

H0: j = 0

H1: j # 0

Looking at the coefficients, it does not appear to be statistically significant because p-value is greater than a and sign is also not significant. It indicates that price would go down with increase in food quality which ideally does not make sense.

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