4. Zagat publishes restaurant ratings for various U.S. locations. Each restaurant receives a separate numerical rating in 3 areas: food, decor, and service. Zagat also reports the average meal cost per person. Your dataset consists of a random sample of 50 restaurants in New York City and 50 restaurants in a nearby suburb. You run a multiple regression to predict the meal cost per person (in $), based on the 3 rating components, and a dummy variable for restaurant location (city or not). Dependent Variable: COST Independent Variable: FOOD, DECOR, SERVICE, CITY Regression Statistics R R Square Adj.RSqr Std.Err. #Cases #Missing Deg.Free t(2.5%,95) 0.787 0.619 0.603 8.454 100 95 1.985 Summary Table Variable Coeff. Std.Err. t Stat P-value Lower95% Upper95% Intercept 38.154 9.605 FOOD 0.204 0.589 DECOR 1.965 0.288 SERVICE 1.887 0.621 CITY 6.326 1.765 (a) State the multiple regression prediction line equation. (b) Check whether each of the 4 independent variables is significantly related to COST (at a = 0.05). (c) Suppose a restaurant implements one of the following: i. Hires new chef and FOOD rating increases by 3 points. ii. Remodels restaurant interior and DECOR rating increases by 1 point. iii. Improves server retention by offering health benefits and SERVICE increases by 2 points. 19 MANAGEMENT 402 DATA AND DECISIONS HOMEWORK 4 - REGRESSION AND DECISION ANALYSIS Which one of these scenarios (holding all other independent variables constant) is associated with the largest change in meal COST? (d) A new restaurant, Z Table, is opening in New York City with a Zagat FOOD rating of 24, a DECOR of 19, and a SERVICE of 26. What is the predicted meal COST at this restaurant? What is the 95% prediction interval