Fixed Acidity Volatile Acidity Citric Acid Residual Sugar Chlorides Free Sulfur Dioxide

11.5 0.3 0.6 2 0.067 12

7.7 0.715 0.01 2.1 0.064 31

10.4 0.575 0.61 2.6 0.076 11

9.2 0.63 0.21 2.7 0.097 29

7.9 0.35 0.46 3.6 0.078 15

8.9 0.745 0.18 2.5 0.077 15

7.6 0.51 0.24 2.4 0.091 8

10.8 0.5 0.46 2.5 0.073 5

6.4 0.47 0.4 2.4 0.071 8

9.9 0.63 0.24 2.4 0.077 6

6.9 0.685 0 2.5 0.105 22

7.3 0.45 0.36 5.9 0.074 12

6.8 0.81 0.05 2 0.07 6

7.5 0.51 0.02 1.7 0.084 13

10.4 0.34 0.58 3.7 0.174 6

7.1 0.46 0.14 2.8 0.076 15

9.1 0.5 0.3 1.9 0.065 8

7.3 0.69 0.32 2.2 0.069 35

7.7 0.6 0 2.6 0.055 7

6.7 0.46 0.24 1.7 0.077 18

8.6 0.47 0.27 2.3 0.055 14

8.3 0.65 0.1 2.9 0.089 17

6 0.31 0.47 3.6 0.067 18

8.6 0.49 0.28 1.9 0.11 20

7.9 0.54 0.34 2.5 0.076 8

10.2 0.49 0.63 2.9 0.072 10

8 0.33 0.53 2.5 0.091 18

7.6 0.39 0.31 2.3 0.082 23

7.1 0.59 0 2.1 0.091 9

8.3 0.6 0.13 2.6 0.085 6

8.8 0.46 0.45 2.6 0.065 7

8.5 0.47 0.27 1.9 0.058 18

10.2 0.645 0.36 1.8 0.053 5

11.6 0.32 0.55 2.8 0.081 35

6.3 0.55 0.15 1.8 0.077 26

7.5 0.38 0.48 2.6 0.073 22

9.1 0.765 0.04 1.6 0.078 4

8.4 1.035 0.15 6 0.073 11

6.2 0.56 0.09 1.7 0.053 24

7.3 0.74 0.08 1.7 0.094 10

7.8 0.39 0.42 2 0.086 9

10.4 0.44 0.42 1.5 0.145 34

11.6 0.47 0.44 1.6 0.147 36

8.3 0.65 0.1 2.9 0.089 17

6.3 0.55 0.15 1.8 0.077 26

6.7 1.04 0.08 2.3 0.067 19

7.2 0.33 0.33 1.7 0.061 3

6.8 0.815 0 1.2 0.267 16

5.5 0.49 0.03 1.8 0.044 28

7.4 0.59 0.08 4.4 0.086 6

Below is data for the problems. Help would be much appreciated!

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 of Portuguese "Vinho Verde" wine. A sample of 50 wines is stored in table 4. 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. Interpret the meaning of the slope for Alcohol. For every 1 unit of Quality, Alcohol increases by 0.496, holding Chlorides constant. For every 1 unit of Alcohol, Quality increases by 0.496, holding Chlorides constant. For every 0.496 unit of Quality, Alcohol increases by 1, holding Chlorides constant. For every 0.496 unit of Alcohol, Quality increases by 1, holding Chlorides constant. Referring to Table 4, interpret R.2 40.09% of the variation in Alcohol and Chlorides is being explained by Quality, once we have taken a penalty for the number of X's we are using. 42.54% of the variation in Alcohol and Chlorides is being explained by Quality, once we have taken a penalty for the number of X's we are using. 40.09% of the variation in Quality is being explained by Alcohol and Chlorides, once we have taken a penalty for the number of X's we are using. 42.54% of the variation in Quality is being explained by Alcohol and Chlorides, once we have taken a penalty for the number of X's we are using. Referring to Table 4, predict the mean wine quality rating for wines that have 10% alcohol and chlorides of 0.08. Referring to Table 4, construct a 95% confidence interval estimate for the mean wine quality rating for wines that have 10% alcohol and chlorides of 0.08. What is the lower limit of that confidence interval? Referring to Table 4, construct a 99% prediction interval for the wine quality rating for an individual wine that has 10% alcohol and chlorides of 0.08. What is the upper limit of that prediction interval? Referring to Table 4, which phrase would be part of the interpretation of the 99% prediction interval? O If a group of wines that all had 10% alcohol and chlorides of 0.08 were selected, we would be 99% confident that their average wine quality rating would be between and If a group of wines that all had 10% alcohol and chlorides of 0.08 were selected, we would be 99% confident that their wine quality rating would be between and If an individual wine with 10% alcohol and chlorides of 0.08 was selected, we would be 99% confident that the wine quality rating would be between and If an individual wine with 10% alcohol and chlorides of 0.08 was selected, we would be 99% confident that their average wine quality rating would be between and Referring to Table 4, what is the test statistic to conduct the test of H: B, = B2 = 0 Referring to Table 4, what is the conclusion of the test of H: B, = B2 = 0 at a 0.05 level of significance? We do have evidence that both variables of Alcohol and Chlorides are significant predictors of Quality. We do not have evidence that both variables of Alcohol and Chlorides are significant predictors of Quality. We do not have evidence that at least 1 of the variables of Alcohol and Chlorides are significant predictors of Quality. We do have evidence that at least 1 of the variables of Alcohol and Chlorides are significant predictors of Quality. Referring to Table 4, what is the p-value to conduct the test of H: Bchlorides = 0? Referring to Table 4, what is the conclusion of the test of H: Bchlorides = 0 if alpha = 0.01? We do not have evidence that Chlorides is a significant predictor of Quality. We do have evidence that Chlorides is a significant predictor of Quality. We do not have evidence that Quality is a significant predictor of Chlorides. We do have evidence that Quality is a significant predictor of Chlorides. Referring to Table 4, look at the Residuals vs. Chlorides plot. From this plot you conclude: The equal variance assumption is met. The equal variance assumption is violated. The normality assumption is met. The normality assumption is violated. Referring to Table 4, look at the Residuals vs. Alcohol plot. From this plot you conclude: The independence assumption is met. The independence assumption is violated. The linearity assumption is met The linearity assumption is violated. Referring to Table 4: Create a dummy variable where pH above 3.5 is high and 3.5 or below is low. Let high=1. Add this dummy variable to a model with the percentage of alcohol, chlorides to predict the quality of red wines. What is the p-value of the dummy variable? Referring to Table 4, what is the decision in regards to the significance of the dummy variable in the previous question at 0.05 significance level? We do Reject Ho. We do have evidence that the dummy variable is a significant predictor of wine quality. We do Reject Ho. We do not have evidence that the dummy variable is a significant predictor of wine quality. We do not Reject Ho. We do have evidence that the dummy variable is a significant predictor of wine quality. We do not Reject Ho. We do not have evidence that the dummy variable is a significant predictor of wine quality. Referring to Table 4, how do you interpret the dummy variable for pH? If the pH is high, the quality decreases by 0.68. If the pH is high, the quality decreases by 0.68, holding Alcohol and Chlorides constant. For every 1 unit of pH added, the quality decreases by 0.68. For every 1 unit of pH added, the quality decreases by 0.68, holding Alcohol and Chlorides constant. Referring to Table 4, create an interaction term between the percentage of alcohol and chlorides and build a new model, not including the dummy variable. What is the p-value of the interaction term? Referring to the previous question, at a significance level of 0.10, what is the decision in regards to the interaction term? It is a significant predictor of wine quality. It is not a significant predictor of wine quality. We are unable to determine if it is a significant predictor of wine quality. 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 of Portuguese "Vinho Verde" wine. A sample of 50 wines is stored in table 4. 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. Interpret the meaning of the slope for Alcohol. For every 1 unit of Quality, Alcohol increases by 0.496, holding Chlorides constant. For every 1 unit of Alcohol, Quality increases by 0.496, holding Chlorides constant. For every 0.496 unit of Quality, Alcohol increases by 1, holding Chlorides constant. For every 0.496 unit of Alcohol, Quality increases by 1, holding Chlorides constant. Referring to Table 4, interpret R.2 40.09% of the variation in Alcohol and Chlorides is being explained by Quality, once we have taken a penalty for the number of X's we are using. 42.54% of the variation in Alcohol and Chlorides is being explained by Quality, once we have taken a penalty for the number of X's we are using. 40.09% of the variation in Quality is being explained by Alcohol and Chlorides, once we have taken a penalty for the number of X's we are using. 42.54% of the variation in Quality is being explained by Alcohol and Chlorides, once we have taken a penalty for the number of X's we are using. Referring to Table 4, predict the mean wine quality rating for wines that have 10% alcohol and chlorides of 0.08. Referring to Table 4, construct a 95% confidence interval estimate for the mean wine quality rating for wines that have 10% alcohol and chlorides of 0.08. What is the lower limit of that confidence interval? Referring to Table 4, construct a 99% prediction interval for the wine quality rating for an individual wine that has 10% alcohol and chlorides of 0.08. What is the upper limit of that prediction interval? Referring to Table 4, which phrase would be part of the interpretation of the 99% prediction interval? O If a group of wines that all had 10% alcohol and chlorides of 0.08 were selected, we would be 99% confident that their average wine quality rating would be between and If a group of wines that all had 10% alcohol and chlorides of 0.08 were selected, we would be 99% confident that their wine quality rating would be between and If an individual wine with 10% alcohol and chlorides of 0.08 was selected, we would be 99% confident that the wine quality rating would be between and If an individual wine with 10% alcohol and chlorides of 0.08 was selected, we would be 99% confident that their average wine quality rating would be between and Referring to Table 4, what is the test statistic to conduct the test of H: B, = B2 = 0 Referring to Table 4, what is the conclusion of the test of H: B, = B2 = 0 at a 0.05 level of significance? We do have evidence that both variables of Alcohol and Chlorides are significant predictors of Quality. We do not have evidence that both variables of Alcohol and Chlorides are significant predictors of Quality. We do not have evidence that at least 1 of the variables of Alcohol and Chlorides are significant predictors of Quality. We do have evidence that at least 1 of the variables of Alcohol and Chlorides are significant predictors of Quality. Referring to Table 4, what is the p-value to conduct the test of H: Bchlorides = 0? Referring to Table 4, what is the conclusion of the test of H: Bchlorides = 0 if alpha = 0.01? We do not have evidence that Chlorides is a significant predictor of Quality. We do have evidence that Chlorides is a significant predictor of Quality. We do not have evidence that Quality is a significant predictor of Chlorides. We do have evidence that Quality is a significant predictor of Chlorides. Referring to Table 4, look at the Residuals vs. Chlorides plot. From this plot you conclude: The equal variance assumption is met. The equal variance assumption is violated. The normality assumption is met. The normality assumption is violated. Referring to Table 4, look at the Residuals vs. Alcohol plot. From this plot you conclude: The independence assumption is met. The independence assumption is violated. The linearity assumption is met The linearity assumption is violated. Referring to Table 4: Create a dummy variable where pH above 3.5 is high and 3.5 or below is low. Let high=1. Add this dummy variable to a model with the percentage of alcohol, chlorides to predict the quality of red wines. What is the p-value of the dummy variable? Referring to Table 4, what is the decision in regards to the significance of the dummy variable in the previous question at 0.05 significance level? We do Reject Ho. We do have evidence that the dummy variable is a significant predictor of wine quality. We do Reject Ho. We do not have evidence that the dummy variable is a significant predictor of wine quality. We do not Reject Ho. We do have evidence that the dummy variable is a significant predictor of wine quality. We do not Reject Ho. We do not have evidence that the dummy variable is a significant predictor of wine quality. Referring to Table 4, how do you interpret the dummy variable for pH? If the pH is high, the quality decreases by 0.68. If the pH is high, the quality decreases by 0.68, holding Alcohol and Chlorides constant. For every 1 unit of pH added, the quality decreases by 0.68. For every 1 unit of pH added, the quality decreases by 0.68, holding Alcohol and Chlorides constant. Referring to Table 4, create an interaction term between the percentage of alcohol and chlorides and build a new model, not including the dummy variable. What is the p-value of the interaction term? Referring to the previous question, at a significance level of 0.10, what is the decision in regards to the interaction term? It is a significant predictor of wine quality. It is not a significant predictor of wine quality. We are unable to determine if it is a significant predictor of wine quality