Question

A magazine used the summated rating of 10 restaurants to predict the cost of a restaurant meal. For that data, SSR 132,502.37 and SST 143,937.29. Complete parts (a) through (c) a. Determine the coefficient of determination, r, and interpret its meaning. I (Round to four decimal places as needed.) Interpret the meaning of It means that 96 of the variation in the cost of a meal Round to two decimal places as needed.) b. Determine the standard error of the estimate. ▼ be explained by the variation in summated ratings SYx®□ (Round to four decimal places as needed ) c. How useful do you think this regression model is for predicting the cost of a meal? O A. It is not very useful for predicting the cost of a meal because although the coefficient of determination is close to 1, the standard error of the estimate is fairly small O B. It is not very useful for predicting the cost of a meal because the coefficient of determination is close to 0 and the standard error of the estimate is fairly large. ° C. It is very useful for predicting the cost of a meal because the coefficient of determination is close to 1. The standard error of the estimate does not indicate whether a regression model is useful. O D. It is very useful for predicting the cost of a meal because the coefficient of determination is close to 1 and the standard error of the estimate is fairly smal

Answer 1

Answer

(A) we know the formula that

where we have SSR = 132502.37 and SST = 143937.29

setting the values, we get

converting it into %, we get 0.9206*100 = 92.06%

So, it means that 92.06% of the variation in the cost of a meal can be explained by the variation in the summated ratings.

(B) We know the formula that

we have SSE = SST-SSR = 143937.29 - 132502.37 = 11434.92

and n = 10

setting the values, we get

(C) Option C is correct answer because the model is useful for predicting as the r square value is 92.06%, but we dont know whether the model is good or not based on the standard error.