Question

The production of wine is a multibillion dollar worldwide industry. In an attempt to develop a model of wine quality as judged by wine experts, data was collected from red wine variants. A sample of 20 wines is provided in the accompanying table. Develop a multiple linear regression model to predict w ne quality, measured on a scale from 0 very bad to 10 excellent based on a cohol content(%) and the amount of chlo dos. Complete parts a through g below. Click the icon to view the table. Ys-898 + ( 1.26 )x, + ( 16.78 ) (Round to two decimal places as needed.) b. Interpret the meaning of the slopes, b, and b2. in this problem. A. For a given number of chlorides, each increase of one percentage of alcohol content is estimated to result in a mean increase of wine quality of b, units. For a given alcohol content, each increase of one unit in chlorides is estimated to result in the mean increase in wine quality of b2 units. OB. For a given quality, each decrease of the value of b units in chlorides is estimated to reeult in a mean increase in alcohol content of one unit For a given alcohol content, each decrease of the value of b2 units in quality is estimated to result in the ○ C. For every increase of one unit of alcohol content, the estimated number of chlorides and mean wine quality decreases by the values of b1 and b2 units, respectively 0 D. The slopes, b1 and b2, cannot be interpreted individually. c. Explain why the regression coefficient, bo, has no practical meaning in the context of this problem. 0 A. The interpretation of bo has no practical meaning here because it would correspond to the estimated mean alcohol content and mean chlondes when there is no quality mean increase in chlonides of one unit. B. The interpretation of b0 has no practical meaning here because it would correspond to the estimated mean chlorides when a wine has a 0% alcohol content and 0 quality. Xc. The interpretation of bo has no practical meaning here because it would oorrespond to the estimated mean alcohol content when a wine has a 0 quality and 0 chlorides. *D The interpretation of b0 has no practical meaning here because it would correspond to the estimated mean quality when a wine has a 0% alcohol content and 0 chlorides. d. Predict the mean quality rating for wines that have 10% alcohol content and chlorides of 0.08. The wine quality prediction for a wine that has 10% alcohol and 0.08 chlorides is 4.96 (Round to two decimal places as needed.) Construct a 95% confidence interval estimate for the mean quality rating for wines that have 10% alcohol and 0.08 chlorides ing for wines that have 10% al 01 and 0.08 chlorides is The 95% co dence interval estimate of the mean quality Round to one decimal place as needed.)

Answer 1

R R Console > quality [1 2 2 2 2 3 3 2 3 6 6 76 6 8 7979 9 10 > alcohol [1 7.6 7.2 8.3 7.1 8.8 8.9 9.9 9.8 10.8 10.9 10.5 10.9 11.5 11.5 11.8 [16 11.3 11.9 11.6 12.5 12.5 > chloride [1 0.064 0.067 0.072 0.065 0.069 0.071 0.071 0.072 0.076 0.084 0.082 0.081 [131 0.087 0.086 0.092 0.094 0.149 0.103 0.156 0.154 > fit=lm (quality-alcohol-chloride) > new data.frame (alcohol-10,chloride-0.08) > predict (fit,new, interval="confidence") fit lwr upr 1 4.952862 4.325438 5.580286 > #### Answer: > # 95 % confidence interval is 4.3 to 5.6