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 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 10​% alcohol and 0.08 chlorides.

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

Answer 1

Output using excel:

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	144.5500
	Coefficients	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