URGENT PLEASE HELP
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.
b. Interpret the meaning of the slopes B1 and B2 in this problem
c. Explain why the regression coefficient, b0, has no practical meaning in the context of this problem.
d. Predict the mean quality rating for wines that have 8% alcohol content and chlorides of 0.10
e. Construct a 95% confidence interval estimate for the mean quality rating for wines that have 8%alcohol and .10 chlorides.
f. Construct a 95% prediction interval estimate for the quality rating for an individual wine that has 8% alcohol and .10
chlorides.
h. What conclusions can you reach concerning this regression model?
Let's carry out regression in Excel (go to Data tab -> Data Analysis -> Regression, choose Quality as Y-column, and Alcohol Content, Chlorides as Y-columns). The output is:
Regression Statistics | |
Multiple R | 0.93164272 |
R Square | 0.867958158 |
Adjusted R Square | 0.852423824 |
Standard Error | 1.172348171 |
Observations | 20 |
Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | |
Intercept | -11.90786112 | 1.808850665 | -6.583109017 | 4.64988E-06 | -15.72420243 | -8.091519812 |
Alcohol Content (%) | 1.625394856 | 0.24835144 | 6.544736977 | 5.00049E-06 | 1.101419118 | 2.149370594 |
Chlorides | 9.014905454 | 14.17419472 | 0.636008298 | 0.533240795 | -20.89003137 | 38.91984228 |
a) = -11.91 + 1.63 * + 9.01 *
b) Slope b1 for X1 is 1.63, which means the quality rating increases by 1.63 every % increase in alcohol content.
Slope b2 for X2 is 9.01, which indicates quality rating increases by 9.01 per unit increase in amount of chlorides.
c) The -ve value -11.91 of b0 tells us that the rating is -11.91 in cases where both the alcohol content and chlorides content are 0. But, given a quality rating below 0 is meaningless, the intercept is meaningless.
d) For 8% alcohol content and chlorides of 0.1, predicted quality rating,
= -11.91 + 1.63 * 8 + 9.01 * 0.1 = 2.031 ~ 2
e) 95% confidence interval for this prediction is given by:
= (0.596, 3.466)
f) 95% prediction interval for this prediction is given by:
= (-4.54, 8.6)
g) Given the high p-value of chloride amount (0.533), chloride isn't a significant predictor of quality rating. However, given the low p-value of alcohol content % (5e-06), alcohol content is a very significant predictor of wine quality rating. Also, given the R-squared value ~ 0.87, nearly 87% of the variation in quality ratings is explained by these 2 predictors (which should hopefully improved if we remove the less significant predictor, chloride content).
URGENT PLEASE HELP The production of wine is a multibillion-dollar worldwide industry. In an attempt to...
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 w ne quality, measured on a scale from 0 very bad to 10 excellent based on a cohol content(%) and the amount of chlo dos. Complete parts a through...
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(%) Chlorides0 7.1 0.0610 7.6 0.0632...
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. Alcohol Chlorides 10.1 0.067 11.8 0.064 9 0.076...
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The production of wine is a multi-billion-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 from a particular type of foreign wine. A multiple linear regression model was developed from a sample of 45 wines. The model was used to predict wine quality, measured on a scale from 0 (very bad) to 10 (excellent) based on the alcohol content (%) and the amount of...
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