A magazine used the rating of 10 restaurants to predict the cost of a restaurant
ID: 3265345 • Letter: A
Question
A magazine used the rating of 10 restaurants to predict the cost of a restaurant meal. For that data, SSR = 132, 061.43 and SST = 143,000.06. Complete parts (a) through (c). a. Determine the coefficient of determination., r^2, and implement its meaning. r^2 = (Round to four decimal place as needed.) Interpret the meaning of r^2. It means that % of the variation in the cost of a meal be explaining by the variation in summated ratings. (Round to two decimal place as needed.) b. Determine the standard error of the estimate. S_YX = (Round to four decimal place as needed.) c. How useful do you think regression model is for predicting the cost of a meal? A. 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. B. 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. C. 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 estimate is fairly small. D. 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.Explanation / Answer
SSR = 132061.43 and SST = 143860.68
so r2 = ( SSR/ SST) = ( 132061.43/ 143860.58) = 0.9180
it means that 91.80 % of the variation in the cost of the meal can be explained by varaition in summated ratings.
(b) Standard error of the estimate sYX = ?
MSE = SSE / (n-k-1) = (SST - SSR)/ (n-k-1) = (143860.58 - 132061.43)/ (10 - 1-1) = 1474.89375
SYX = sqrt (MSE) = sqrt (1474.89375) = 38.4043
(c) Part a is correct. It is very useful for predicting the cost for a meal becuas ethe coefficient of determination is close to 1. The standard error of the estimate does not indicate whether a regression model is useful or not.
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