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In: Statistics and Probability

The production of wine is a​ multibillion-dollar worldwide industry. In an attempt to develop a model...

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.

Quality   Alcohol_Content(%)   Chlorides
2   7.7   0.067
1   7.9   0.065
3   8.2   0.074
1   8.7   0.071
2   8.5   0.067
4   8.7   0.074
4   9.4   0.071
3   9.1   0.076
6   10.1   0.077
5   10.4   0.078
7   10.3   0.078
6   11.1   0.083
7   11.3   0.081
8   11.5   0.085
6   11.8   0.095
7   11.3   0.093
7   12.5   0.128
8   11.5   0.111
10   12.2   0.157
10   12.8   0.156

1. Construct a​ 95% confidence interval estimate for the mean quality rating for wines that have 11​% alcohol and 0.08 chlorides.

2. Construct a​ 95% prediction interval estimate for the quality rating for an individual wine that has 11​% alcohol and 0.08 chlorides.

Solutions

Expert Solution

Answer:

Given that:

The production of wine is a multibillion-dollar worldwide industry.

Regression Analysis
Regression Statistics
Multiple R 0.9274
R Square 0.8601
Adjusted R square 0.8437
Standard Error 1.0906
Observations 20
ANOVA
df SS MS F Significance F
Regression 2 124.3296 62.1648 52.2641 0.0000
Residual 17 20.2204 1.1894
Total 19 44.5500
Coefficient Standard Error t-Stat P-value Lower 95% Upper 95%
Intercept -9.8600 1.7608 -5.5997 0.0000 -13.5750 -6.1450
Alcohol_content 1.3338 0.2542 5.2476 0.0001 0.7976 1.8701
Chlorides 17.2144 14.9375 1.1524 0.2651 -14.3010 48.7299

1.

95% confidence interval estimate for the mean quality rating for wines that have 10% alcohol and 0.08 chlorides.:

Lower limit = 4.3018

Upper Limit = 5.4094

2.

95% prediction interval estimate for the quality rating for an individual wine that has 10% alcohol and 0.08 chlorides.

Lower limit = 2.4889

Upper Limit = 7.2223

orchestra answered 1 year ago
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