Question

2. A researcher collect information wout in New York. The researcher's goal is to de the restaurant and the average price of ratings vary from 0 to 30 for each category The tables below summarize the sample sa archer collectif researcher's goal is to identify the r and the average price of the ich decor device for 114 a ns between these three characteristics of The meal price is in dollar while the h eation values between the variables fed decor service bies below summarize the t price 33.32 St de 1.16 17.77 1961 2.537 16:58 4.464 2.847 price food decor service Correlation price food 0.599 decor 0.669 0.213 service 0.753 0.707 0.590 a) Which variable is the single best predictor of the price? In other words, if you ran a simple regression, which explanatory variable would explain most of the variation in the meal price? b) Calculate the coefficients in the simple regression with the best predictor as the explanatory variable. c) Calculater for that regression and interpret it. MS Now you run a multiple regression that includes all three explanatory variables and obtain RP=0.687. ANOVA SS Regression 9598.88655 3 199.629 Residual 110 4363.74503 39.670 Total 113 13962.6316 Coefficients Standard Error Star P-value Intercept -30.664 4.787 -6.41 3.82E-09 food 1.380 0.353 I 3.90 0.00016343 decor 1.104 0.176 6.27 7.18E-09 service 1.048 0.381 2.75 0.0069691

Answer 1

a. Service is the single best predictor of the price.
It will be able to explain most of the variation in the meal price.

b. Regression equation.

Let x be the service Let y be the price We are given the following My = 17.77 My = 33.32 or = 2.847 Oy = 11.116 p=0.753 Regression equation : y = a + bx b=px = 0.753 x 13116 = 2.940059 a = Hy+b. Hz = 33.32 + (2.940059). (17.77) = -18.9248486 Regression equation is y = -18.9248486 + (2.940059) X

The coefficient in the simple regression is 2.940059

c.

p2 = V = V0.753 = 0.8677557

Coefficient of determination(rsqaure) = 0.8677557
It is the measure of the amount of variability in y explained by x. Its value lies between 0 and 1. Greater the value, better is the model. In this case, it 86.7%, hence the model is good

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