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(I need a detailed solution because I have already gotten the answer key) Use the following to answer the next six questions. Zagat Survey, LLC., is...

Please help! I need a detailed solution! Thanks.(I have a stat final tmr! My question is in the attachment.

(I need a detailed solution because I have already gotten the answer key) Use the following to answer the next six questions . Zagat Survey, LLC., is a company that compiles and publishes ratings for restaurants. Each restaurant included in the survey is rated on a scale of 1-30 in three categories: food, décor, and service. The survey also provides a price for each restaurant, which is the reviewer’s estimate of the dollar cost of dinner (one entrée from the regular menu plus one drink, including tip). I am interested in how and whether these survey ratings are related to prices. I obtained survey data on 114 restaurants from the same metro area. The table below shows the computer output from a multiple regression with price as the dependent variable and food, décor, and service as independent (explanatory) variables. Summary measures R 2 0.69 R 2 adjusted 0.68 Standard error of estimate 6.3 ANOVA table Source DF SS MS F P-value Explained ?? 9598.8855 3199.6288 80.6553 0 Unexplained ?? ?? ?? Regression coefficients Coefficient Standard error t-value p- value Constant -30.66 4.79 -6.41 0.0000 food 1.38 0.35 3.9 0.0002 décor 1.10 0.18 ?? ?? service 1.05 0.38 2.75 0.0070 1. Suppose a restaurant has ratings: food = 18,décor = 22, service = 17. What is the 95% prediction interval for this restaurant’s price ? Choose the answer closest to correct. A) (35.06,37.40) B) (23.73,37.40) C) (35.06,48.75) D) (23.73,48.75) E) (35.26,37.20) When I ran this regression, I also asked Minitab to output columns of Fitted Values and Residuals. Below are the first two rows of the output: food décor service price Fitted value Resi dual 18 22 17 41 ?? ??
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2. What numbers should appear in the “Fitted Values” and “Residuals” columns? A) Fitted value=35.06, Residual=5.94 B) Fitted value=48.75, Residual=- 7.75 C) Cannot be determined D) Fitted value=23.73, Residual=17.27 E) Fitted value=36.23, Residual=4.77 3. Suppose we tested the null hypothesis that “an increase in the décor rating (given fixed values for food and service) has no effect on price”. Calculate the test statistic: A) 6.11 B) 2.65 C) 3.47 D) 2.41 E) None of the above 4. A certain restaurant just hired a new head chef with a very good reputation. As a result, their food rating is expected to increase from 24 to 25 (their décor and service ratings will stay the same). By about how much should their price increase? Construct an appropriate 95% interval. A) (-11.12,13.88) B) (0.69,2.07) C) (0.00,13.88) D) (-2.08,2.08) E) None of the above 5. What is the unexplained sum of squares (i.e., what number should appear in place of ?? under the “SS” column of the ANOVA table)? A) 4364 B) 3465 C) 6435 D) 6354 E) None of the above 6. What is the correlation between price and Fitted Values ? A) 0.69 B) 0.68 C) 0.831 D) 80.655 E) 0.557
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