The production of wine is a multibillion-dollar worldwide industry. In an attemp
ID: 3231457 • Letter: T
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 Click the icon to view the table a. State the multiple regression equation. LetX1i represent the alcohol content of wine iand let X2i represent the number of chlorides for wine i (Round to two decimal places as needed.) b. Interpret the meaning of the slopes, b1 and b2 n this problem O 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 b1 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 O B. 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. O C. For a given quality each decrease of the value of b1 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 units in quality is estimated to result in the mean increase in chlorides of one unit O 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. O A. The interpretation of bo 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. O B. The interpretation of bo has no practical meaning here because it would correspond to the estimated mean alcohol content and mean chlorides when there is no quality. O C. The interpretation of bo 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. O D. The interpretation of bo 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. d. Predict the mean quality rating for wines that have 11% alcohol content and chlorides of 0.08. The wine quality prediction for a wine that has 11% alcohol and 0.08 chlorides is Click to select your answer(s)Explanation / Answer
Answer:
a).
y= -15.12+2.07*x1+(-10.34)*x2
b). option A
c). Option C
d). predicted quality when 11% alcohol and 0.08 chlorides = 6.796
Regression Analysis
R²
0.945
Adjusted R²
0.939
n
20
R
0.972
k
2
Std. Error
0.757
Dep. Var.
Quality
ANOVA table
Source
SS
df
MS
F
p-value
Regression
167.2179
2
83.6090
146.05
1.96E-11
Residual
9.7321
17
0.5725
Total
176.9500
19
Regression output
confidence interval
variables
coefficients
std. error
t (df=17)
p-value
95% lower
95% upper
Intercept
-15.1220
1.4956
-10.111
1.32E-08
-18.2774
-11.9665
Alcohol
2.0678
0.2064
10.018
1.51E-08
1.6323
2.5033
Chlorides
-10.3427
10.3048
-1.004
.3296
-32.0839
11.3985
Predicted values for: Quality
95% Confidence Interval
95% Prediction Interval
Alcohol
Chlorides
Predicted
lower
upper
lower
upper
11
0.08
6.796
6.291
7.302
5.122
8.471
Regression Analysis
R²
0.945
Adjusted R²
0.939
n
20
R
0.972
k
2
Std. Error
0.757
Dep. Var.
Quality
ANOVA table
Source
SS
df
MS
F
p-value
Regression
167.2179
2
83.6090
146.05
1.96E-11
Residual
9.7321
17
0.5725
Total
176.9500
19
Regression output
confidence interval
variables
coefficients
std. error
t (df=17)
p-value
95% lower
95% upper
Intercept
-15.1220
1.4956
-10.111
1.32E-08
-18.2774
-11.9665
Alcohol
2.0678
0.2064
10.018
1.51E-08
1.6323
2.5033
Chlorides
-10.3427
10.3048
-1.004
.3296
-32.0839
11.3985
Predicted values for: Quality
95% Confidence Interval
95% Prediction Interval
Alcohol
Chlorides
Predicted
lower
upper
lower
upper
11
0.08
6.796
6.291
7.302
5.122
8.471
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