In an attempt to develop a model of wine quality as judged by wine experts, data on alcohol content and wine quality was collected from variants of a particular wine. From a sample of 12 wines, a model was created using the percentages of alcohol to predict wine quality. For those data, SSR = 18,858 and SST = 29,285. Use this information to complete parts (a) through (c) below. a. Determine the coefficient of determination, r2, and interpret its meaning. = (Round to three decimal places as needed.) Interpret the meaning of r². It means that% of the variation in (Round to one decimal place as needed.) b. Determine the standard error of the estimate. Syx = (Round to four decimal places as needed.) can be explained by the variation in

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In an attempt to develop a model of wine quality as judged by wine experts, data on alcohol content and wine quality was collected from variants of a particular wine. From a sample of 12 wines, a model was created using the percentages of alcohol to predict wine quality. For those data, SSR = 18,858 and SST = 29,285. Use this information to complete parts (a) through (c) below.

a. Determine the coefficient of determination, \( r^2 \), and interpret its meaning.

\( r^2 = \) [box] (Round to three decimal places as needed.)

Interpret the meaning of \( r^2 \).

It means that [box] % of the variation in [dropdown] can be explained by the variation in [dropdown]. (Round to one decimal place as needed.)

b. Determine the standard error of the estimate.

\( S_{YX} = \) [box] (Round to four decimal places as needed.)
Transcribed Image Text:In an attempt to develop a model of wine quality as judged by wine experts, data on alcohol content and wine quality was collected from variants of a particular wine. From a sample of 12 wines, a model was created using the percentages of alcohol to predict wine quality. For those data, SSR = 18,858 and SST = 29,285. Use this information to complete parts (a) through (c) below. a. Determine the coefficient of determination, \( r^2 \), and interpret its meaning. \( r^2 = \) [box] (Round to three decimal places as needed.) Interpret the meaning of \( r^2 \). It means that [box] % of the variation in [dropdown] can be explained by the variation in [dropdown]. (Round to one decimal place as needed.) b. Determine the standard error of the estimate. \( S_{YX} = \) [box] (Round to four decimal places as needed.)
**Educational Exercise: Predicting Wine Quality**

In an attempt to develop a model of wine quality as judged by wine experts, data on alcohol content and wine quality was collected from variants of a particular wine. From a sample of 12 wines, a model was created using the percentages of alcohol to predict wine quality. For these data, SSR (Sum of Squares for Regression) = 18,858 and SST (Total Sum of Squares) = 29,285. Use this information to complete parts (a) through (c) below.

**b. Determine the Standard Error of the Estimate.**

\[ S_{Y|X} = \] [Round to four decimal places as needed.]

**c. How useful do you think this regression model is for predicting wine quality?**

- **A.** It is very useful for predicting wine quality because the coefficient of determination is close to 1.
- **B.** It is not very useful for predicting wine quality because the coefficient of determination is close to 0.
- **C.** It is not very useful for predicting wine quality because the coefficient of determination is close to 1.
- **D.** It is very useful for predicting wine quality because the coefficient of determination is close to 0.

---

**Explaining the Concepts:**

- **Sum of Squares for Regression (SSR):** This represents the explained variation by the model.
- **Total Sum of Squares (SST):** This represents the total variation in the observed data.
- **Standard Error of the Estimate:** This is a measure of the accuracy of predictions made with a regression line. It indicates the average distance that the observed values fall from the regression line.
- **Coefficient of Determination (\(R^2\)):** This represents the proportion of the variance in the dependent variable that is predictable from the independent variable(s). It is calculated as \( R^2 = \frac{SSR}{SST} \). A value close to 1 indicates a useful model, while a value close to 0 indicates a less useful model.
Transcribed Image Text:**Educational Exercise: Predicting Wine Quality** In an attempt to develop a model of wine quality as judged by wine experts, data on alcohol content and wine quality was collected from variants of a particular wine. From a sample of 12 wines, a model was created using the percentages of alcohol to predict wine quality. For these data, SSR (Sum of Squares for Regression) = 18,858 and SST (Total Sum of Squares) = 29,285. Use this information to complete parts (a) through (c) below. **b. Determine the Standard Error of the Estimate.** \[ S_{Y|X} = \] [Round to four decimal places as needed.] **c. How useful do you think this regression model is for predicting wine quality?** - **A.** It is very useful for predicting wine quality because the coefficient of determination is close to 1. - **B.** It is not very useful for predicting wine quality because the coefficient of determination is close to 0. - **C.** It is not very useful for predicting wine quality because the coefficient of determination is close to 1. - **D.** It is very useful for predicting wine quality because the coefficient of determination is close to 0. --- **Explaining the Concepts:** - **Sum of Squares for Regression (SSR):** This represents the explained variation by the model. - **Total Sum of Squares (SST):** This represents the total variation in the observed data. - **Standard Error of the Estimate:** This is a measure of the accuracy of predictions made with a regression line. It indicates the average distance that the observed values fall from the regression line. - **Coefficient of Determination (\(R^2\)):** This represents the proportion of the variance in the dependent variable that is predictable from the independent variable(s). It is calculated as \( R^2 = \frac{SSR}{SST} \). A value close to 1 indicates a useful model, while a value close to 0 indicates a less useful model.
Expert Solution
Step 1

The independent variable is Alcohol content.

The dependent variable is wine quality.

We have to find the coefficient of determination and standard error of the estimate.

This is simple linear regression model.

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