Math Problem Statement

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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 wine​ quality, measured on a scale from 0​ (very bad) to 10​ (excellent) based on alcohol content​ (%) and the amount of chlorides. Complete parts a through g below. LOADING... Click the icon to view the table. Question content area bottom Part 1 a. State the multiple regression equation. Let Upper X Subscript 1 i represent the alcohol content​ (%) of wine i and let Upper X Subscript 2 i represent the number of chlorides for wine i. ModifyingAbove Upper Y with caret Subscript iequals

negative 10.74plus​(

1.39​)Upper X Subscript 1 iplus​(

25.50​)Upper X Subscript 2 i ​(Round to two decimal places as​ needed.) Part 2 b. Interpret the meaning of the​ slopes, b 1 and b 2​, in this problem. A. For every increase of one unit of alcohol​ content, the estimated number of chlorides and mean wine quality decreases by the values of b 1 and b 2 ​units, respectively. B. For a given​ quality, each decrease of the value of b 1 units in chlorides is estimated to result in a mean increase in alcohol content of one unit. For a given alcohol​ content, each decrease of the value of b 2 units in quality is estimated to result in the mean increase in chlorides of one unit. C. 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 1 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 b 2 units. Your answer is correct.D. The​ slopes, b 1 and b 2​, cannot be interpreted individually. Part 3 c. Explain why the regression​ coefficient, b 0​, has no practical meaning in the context of this problem. A. The interpretation of b 0 has no practical meaning here because it would correspond to the estimated mean alcohol content and mean chlorides when there is no quality. B. The interpretation of b 0 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. C. The interpretation of b 0 has no practical meaning here because it would correspond to the estimated mean alcohol content when a wine has a 0 quality and 0 chlorides. D. The interpretation of b 0 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. Your answer is correct. Part 4 d. Predict the mean quality rating for wines that have 9​% alcohol content and chlorides of 0.09. The wine quality prediction for a wine that has 9​% alcohol and 0.09 chlorides is

enter your response here. ​(Round to two decimal places as​ needed.)

Solution

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Math Problem Analysis

Mathematical Concepts

Multiple Linear Regression
Statistics
Predictive Modeling

Formulas

Y = b0 + b1*X1 + b2*X2
Y = -10.74 + 1.39*Alcohol_Content(%) + 25.50*Chlorides

Theorems

Least Squares Regression

Suitable Grade Level

College/University