Problem 1 The regression model was estimated of Price on Food (food quality), De
ID: 3047626 • Letter: P
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Problem 1 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) Test statistical significance of each predictor at -0.05. (For each predictor state and interpret the hypothesis test, state rejection rule and your conclusion) c) What is the correlation coefficient between Price and Food? d)Is the coefficient of Food statistically significant at a - 0.05 in the simple regression of Price on Food? (Explain) e) What is the sign of the coefficient of Food in the simple linear regres- sion of Price on Food? f) Is the coefficient of Food statistically significant at -0.05 in the multiple regression model? (State and interpret the hypothesis test, state the rejection rule and your conclusion g) Explain the reason for your different answers to b) and d). In par ticular why does coefficient of Food have a different sign in the multiple regression compared to simple linear regression!Explanation / Answer
answering 4 parts as per chegg policies
a) Ho: model is not significant
H1: model is significant
With F=330.49 and p-value < 1%, I reject Ho at 1% level of significance and conclude that model is significant
b) Ho: coefficient of food is not significant. Beta1 = 0
H1: coefficient of food is significant. Beta1 =/= 0
T=beta/SE = -0.103/.167 = -0.61677
p-value = 2*(1-P(T<|t|) = 2*(1-P(T<|-0.61677|) = 0.537869
I reject ho If p-value < 5%
since p-value > 5%, I fail to reject Ho and conclude that coefficient of food is not significant. Beta1 = 0
Ho: coefficient of decor is not significant. Beta2 = 0
H1: coefficient of decor is significant. Beta2 =/= 0
T=beta/SE = 1.026/.127 = 8.07874
p-value = 2*(1-P(T<|t|) = 2*(1-P(T<|8.07874|) = 0.000
I reject ho If p-value < 5%
Since p-value < 5%, I reject Ho and conclude that coefficient of decor is significant. Beta2 =/= 0
Ho: coefficient of service is not significant. Beta1 = 0
H1: coefficient of service is significant. Beta1 =/= 0
T=beta/SE = 2.555/.234 = 10.9188
p-value = 2*(1-P(T<|t|) = 2*(1-P(T<|10.9188|) = 0.000
I reject ho If p-value < 5%
Since p-value < 5%, I reject Ho and conclude that coefficient of service is significant. Beta3 =/= 0
c) Price and food, correlation coefficient = 0.528
d) Ho: there is no significant linear relationship between food and price. That is r=0
H1: there is significant linear relationship between food and price. That is r=/=0
With r=0.528 and p-value < 5%, I reject ho and conclude that there is significant linear relationship between food and price. That is r=/=0
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