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

2020

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.

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Part 1

a. State the multiple regression equation. Let

Upper X Subscript 1 iX1i

represent the alcohol content​ (%) of wine i and let

Upper X Subscript 2 iX2i

represent the number of chlorides for wine i.

ModifyingAbove Upper Y with caret Subscript iYiequals=negative 10.74−10.74plus+​(1.391.39​)Upper X Subscript 1 iX1iplus+​(25.5025.50​)Upper X Subscript 2 iX2i

​(Round to two decimal places as​ needed.)

Part 2

b. Interpret the meaning of the​ slopes,

b 1b1

and

b 2b2​,

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 1b1

and

b 2b2

​units, respectively.

B.

For a given​ quality, each decrease of the value of

b 1b1

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 2b2

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 1b1

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 2b2

units.

Your answer is correct.

D.

The​ slopes,

b 1b1

and

b 2b2​,

cannot be interpreted individually.

Part 3

c. Explain why the regression​ coefficient,

b 0b0​,

has no practical meaning in the context of this problem.

A.

The interpretation of

b 0b0

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 0b0

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 0b0

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 0b0

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

99​%

alcohol content and chlorides of

0.090.09.

The wine quality prediction for a wine that has

99​%

alcohol and

0.090.09

chlorides is

enter your response here.

​(Round to two decimal places as​ needed.)