Answered step by step
Verified Expert Solution
Link Copied!

Question

1 Approved Answer

1. 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,

1. 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 collect from red wine variants of Portuguese "Vinho Verde" wine. A sample of 50 wines is storage in VinhoVerde file (below). 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.

a. state the multiple regression equation

b. Interpret the meaning of 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 and chlorides of 0.08.

2. From the above results:

a. Determine whether there is a significant relationship between wine quality and the two independent variables (% of alcohol and chlorides ) at the 0.05 level of significance.

b. Interpret the meaning of the p-value

c. compute the coefficient of multiple determination, r^2, and interpret its meaning.

d. Compute the adjusted r^2.

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.652209
R Square 0.425377
Adjusted R Square 0.400924
Standard Error 0.884571
Observations 50
ANOVA
df SS MS F Significance F
Regression 2 27.2241 13.61205 17.39634 2.22E-06
Residual 47 36.7759 0.782466
Total 49 64
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 1.159216 1.271867 0.911429 0.366721 -1.39945 3.717882 -1.39945 3.717882
Chlorides -9.63315 3.681845 -2.61639 0.011913 -17.0401 -2.22623 -17.0401 -2.22623
Alcohol 0.496247 0.109359 4.537798 3.94E-05 0.276246 0.716248 0.276246 0.716248

FF

Fixed Acidity Volatile Acidity Citric Acid Residual Sugar Chlorides Free Sulfur Dioxide Total Sulfur Dioxide Density pH Sulphates Chlorides Alcohol Quality
11.5 0.3 0.6 2 0.067 12 27 0.9981 3.11 0.97 0.067 10.1 6
7.7 0.715 0.01 2.1 0.064 31 43 0.99371 3.41 0.57 0.064 11.8 6
10.4 0.575 0.61 2.6 0.076 11 24 1 3.16 0.69 0.076 9 5
9.2 0.63 0.21 2.7 0.097 29 65 0.9988 3.28 0.58 0.097 9.6 5
7.9 0.35 0.46 3.6 0.078 15 37 0.9973 3.35 0.86 0.078 12.8 8
8.9 0.745 0.18 2.5 0.077 15 48 0.99739 3.2 0.47 0.077 9.7 6
7.6 0.51 0.24 2.4 0.091 8 38 0.998 3.47 0.66 0.091 9.6 6
10.8 0.5 0.46 2.5 0.073 5 27 1.0001 3.05 0.64 0.073 9.5 5
6.4 0.47 0.4 2.4 0.071 8 19 0.9963 3.56 0.73 0.071 10.6 6
9.9 0.63 0.24 2.4 0.077 6 33 0.9974 3.09 0.57 0.077 9.4 5
6.9 0.685 0 2.5 0.105 22 37 0.9966 3.46 0.57 0.105 10.6 6
7.3 0.45 0.36 5.9 0.074 12 87 0.9978 3.33 0.83 0.074 10.5 5
6.8 0.81 0.05 2 0.07 6 14 0.99562 3.51 0.66 0.07 10.8 6
7.5 0.51 0.02 1.7 0.084 13 31 0.99538 3.36 0.54 0.084 10.5 6
10.4 0.34 0.58 3.7 0.174 6 16 0.997 3.19 0.7 0.174 11.3 6
7.1 0.46 0.14 2.8 0.076 15 37 0.99624 3.36 0.49 0.076 10.7 5
9.1 0.5 0.3 1.9 0.065 8 17 0.99774 3.32 0.71 0.065 10.5 6
7.3 0.69 0.32 2.2 0.069 35 104 0.99632 3.33 0.51 0.069 9.5 5
7.7 0.6 0 2.6 0.055 7 13 0.99639 3.38 0.56 0.055 10.8 5
6.7 0.46 0.24 1.7 0.077 18 34 0.9948 3.39 0.6 0.077 10.6 6
8.6 0.47 0.27 2.3 0.055 14 28 0.99516 3.18 0.8 0.055 11.2 5
8.3 0.65 0.1 2.9 0.089 17 40 0.99803 3.29 0.55 0.089 9.5 5
6 0.31 0.47 3.6 0.067 18 42 0.99549 3.39 0.66 0.067 11 6
8.6 0.49 0.28 1.9 0.11 20 136 0.9972 2.93 1.95 0.11 9.9 6
7.9 0.54 0.34 2.5 0.076 8 17 0.99235 3.2 0.72 0.076 13.1 8
10.2 0.49 0.63 2.9 0.072 10 26 0.9968 3.16 0.78 0.072 12.5 7
8 0.33 0.53 2.5 0.091 18 80 0.9976 3.37 0.8 0.091 9.6 6
7.6 0.39 0.31 2.3 0.082 23 71 0.9982 3.52 0.65 0.082 9.7 5
7.1 0.59 0 2.1 0.091 9 14 0.99488 3.42 0.55 0.091 11.5 7
8.3 0.6 0.13 2.6 0.085 6 24 0.9984 3.31 0.59 0.085 9.2 6
8.8 0.46 0.45 2.6 0.065 7 18 0.9947 3.32 0.79 0.065 14 6
8.5 0.47 0.27 1.9 0.058 18 38 0.99518 3.16 0.85 0.058 11.1 6
10.2 0.645 0.36 1.8 0.053 5 14 0.9982 3.17 0.42 0.053 10 6
11.6 0.32 0.55 2.8 0.081 35 67 1.0002 3.32 0.92 0.081 10.8 7
6.3 0.55 0.15 1.8 0.077 26 35 0.99314 3.32 0.82 0.077 11.6 6
7.5 0.38 0.48 2.6 0.073 22 84 0.9972 3.32 0.7 0.073 9.6 4
9.1 0.765 0.04 1.6 0.078 4 14 0.998 3.29 0.54 0.078 9.7 4
8.4 1.035 0.15 6 0.073 11 54 0.999 3.37 0.49 0.073 9.9 5
6.2 0.56 0.09 1.7 0.053 24 32 0.99402 3.54 0.6 0.053 11.3 5
7.3 0.74 0.08 1.7 0.094 10 45 0.99576 3.24 0.5 0.094 9.8 5
7.8 0.39 0.42 2 0.086 9 21 0.99526 3.39 0.66 0.086 11.6 6
10.4 0.44 0.42 1.5 0.145 34 48 0.99832 3.38 0.86 0.145 9.9 3
11.6 0.47 0.44 1.6 0.147 36 51 0.99836 3.38 0.86 0.147 9.9 4
8.3 0.65 0.1 2.9 0.089 17 40 0.99803 3.29 0.55 0.089 9.5 5
6.3 0.55 0.15 1.8 0.077 26 35 0.99314 3.32 0.82 0.077 11.6 6
6.7 1.04 0.08 2.3 0.067 19 32 0.99648 3.52 0.57 0.067 11 4
7.2 0.33 0.33 1.7 0.061 3 13 0.996 3.23 1.1 0.061 10 8
6.8 0.815 0 1.2 0.267 16 29 0.99471 3.32 0.51 0.267 9.8 3
5.5 0.49 0.03 1.8 0.044 28 87 0.9908 3.5 0.82 0.044 14 8
7.4 0.59 0.08 4.4 0.086 6 29 0.9974 3.38 0.5 0.086 9 4

Step by Step Solution

There are 3 Steps involved in it

Step: 1

blur-text-image

Get Instant Access to Expert-Tailored Solutions

See step-by-step solutions with expert insights and AI powered tools for academic success

Step: 2

blur-text-image

Step: 3

blur-text-image

Ace Your Homework with AI

Get the answers you need in no time with our AI-driven, step-by-step assistance

Get Started

Recommended Textbook for

More Books

Students also viewed these Mathematics questions

Question

Explain the goal of behavior therapy.

Answered: 1 week ago

Question

2. Information that comes most readily to mind (availability).

Answered: 1 week ago

Question

3. An initial value (anchoring).

Answered: 1 week ago

Question

4. Similarity (representativeness).

Answered: 1 week ago