Referring to Problem 14.41 on page 506, you have decided to analyze whether there are differences in fixed acidity, chlorides, and pH between white wines and red wines (0 = white 1 = red). Using the data stored in Red and White.
a. Develop a logistic regression model to predict whether the wine is red based on the fixed acidity, chlorides, and pH.
b. Explain the meaning of the regression coefficients in the model developed in (a).
c. Predict the probability that a wine is red if it has a fixed acidity of 7.0, chlorides of 0.04, and pH of 3.5.
d. At the 0.05 level of significance, is there evidence that the logistic regression model developed in (a) is a good-fitting model?
e. At the 0.05 level of significance, is there evidence that fixed acidity, chlorides, and pH each make a significant contribution to the model?
f. What conclusions concerning the probability of a wine selected being red can you reach?

Problem 14.41

In Problem 14.5 on page 483, you developed a multiple regression model to predict wine quality for red wines. Now, you wish to determine whether there is an effect on wine quality due to whether the wine is white (0) or red (I). These data are organized and stored in Red and White.
Develop a multiple regression model to predict wine quality bas ed on the percentage of alcohol and the type of wine. For (a) through (m), do not include an interaction term.
a. State the multiple regression equation that predicts wine quality based on the percentage of alcohol and the type of wine.
b . Interpret the regression coefficients in (a).
c. Predict the mean quality for a red wine that has 10% alcohol. Construct a 95 % confidence interval estimate and a 95% prediction interval.
d. Perform a residual analysis on the model and determine whether the regress ion assumptions are valid.
e. Is there a significant relationship between wine quality and the two independent variables (percentage of alcohol and the type of wine) at the 0.05 level of significance?
f . At the 0.05 level of significance, determine whether each independent variable makes a contribution to the regression model. Indicate the most appropriate regression model for this set of data.
g. Construct and interpret 95 % confidence interval estimates of the population slope for the relationship between wine quality and the percentage of alcohol and between wine quality and the type of wine.
h. Compare the slope in (b) with the slope for the simple linear regress ion model of Problem 13.4 on page 439. Explain the difference in the results.
i. Compute and interpret the meaning of the coefficient of multiple determination, r²
j. Compute and interpret the adjusted r²
k. Compare r² with the r² value computed in Problem 13.16 (a) on page 445.
I. Compute the coefficients of partial determination and interpret their meaning.
m. What assumption about the s lope of type of wine with wine quality do you need to make in this problem?
n. Add an interaction term to the mode l and, at the 0 .05 level of significance, determine whether it makes a significant contribution to the model.
o. On the basis of the results of (f) and (n) , which model is most appropriate? Explain.
p. What conclusions can you reach concerning the effect of alcohol percentage and type of wine on wine quality?

Problem 14.5

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 were collected from red wine variants of Portuguese  " Vinho Verde" wine. A sample of 50 wines is stored in Vinho Verde.
Develop a multiple linear regress ion model to predict wine quality, measured on a scale from 0 (very bad) to I 0 (excellent) based on  alcohol content (%) and the amount of chlorides.
a. State the multiple regression equation.
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 wine quality rating for wines that have 10% alcohol a nd chlorides of 0.08.
e. Construct a 95% confidence interval estimate for the mean wine  quality rating for wines that have 10% alcohol and chlorides of  0.08.
f. Construct a 95 % prediction interval for the wine quality rating for an individual wine that has 10 % alcohol and chlorides of 0.08.
g. What conclusions can you reach concerning this regression model?

Problem 13.4 (b)

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 were collected from red wine variants of Portuguese "Vinho Verde" wine.
A sample of 50 wines is stored in Vinho Verde. Develop a simple  linear regression model to predict wine quality, measured on a scale from 0 (very bad) to 10 (excellent), based on alcohol content (%).
a. Construct a scatter plot. For these data, b₀ = -0.3529 and b₁ = 0.5624.
b. Interpret the meaning of the slope, b₁, in this problem.
c. Predict the mean wine quality for wines with a 10% alcohol content.
d. What conclusion can you reach based on the results of (a)-(c)?

Problem 13.16(a)

In Problem 13.4 on page 439, the percentage of .mm alcohol was used to predict wine quality (stored in Vinho Verde). For those data, SSR = 21.8677 and SST = 64.0000.
a. Determine the coefficient of determination, r² , and interpret its meaning.
b. Determine the standard error of the estimate.
c. How useful do you think this regression model is for predicting  sales?