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