Question

Questions: A nutritionist wants to understand the influence of income and healthy food on the incidence of smoking. He collects 2009 data on the percentage of smokers in each state in the U.S. and the corresponding median income and the percentage of the population that regularly eats fruits and vegetables. A portion of the data is shown in the accompanying table.

State	Smoke	Fruits/ Vegetables	Income	State	Smoke	Fruits/ Vegetables	Income	State	Smoke	Fruits/ Vegetables	Income
AK	14.6	23.3	61,604	KY	20.5	21	42,664	NY	12	26.7	50,216
AL	16.4	20.3	39,980	LA	16.4	16.9	45,433	OH	15.6	21	45,879
AR	15.5	20.4	36,538	MA	10.9	26.2	59,373	OK	18.8	14.5	45,878
AZ	11	24.1	45,739	MD	10.3	27.6	47,502	OR	13.1	26.3	49,098
CA	8.1	27.7	56,134	ME	12.5	27.9	64,186	PA	15.1	24.1	48,172
CO	12	24.7	55,930	MI	13.6	22.5	45,994	RI	10.2	26.1	51,634
CT	10.7	28.3	64,851	MN	11.2	21.8	56,090	SC	14.6	17.4	41,101
DC	9	31.4	53,141	MO	18.2	19.8	48,769	SD	12.4	15.7	45,826
DE	13.2	25	52,114	MS	17	16.8	35,078	TN	17.6	23.3	40,517
FL	13.9	24.5	45,631	MT	12.2	25.7	40,437	TX	11.7	23.8	47,475
GA	12.6	24.5	43,340	NC	14.4	20.6	41,906	UT	6.9	23.3	58,491
HI	10.3	23.5	55,649	ND	13.3	22.5	50,075	VA	13.8	27.3	52,318
IA	13.4	18.4	50,721	NE	12.9	20.9	49,595	VT	12.5	29.3	60,501
ID	12.2	24.6	46,778	NH	11.3	27.9	64,131	WA	10.7	25	60,392
IL	12	22.4	52,870	NJ	10	26.3	64,777	WI	12.6	22.7	51,237
IN	17.1	20.6	44,305	NM	11.2	23.1	43,542	WV	20.6	16.1	40,490
KS	13.2	18.6	44,717	NV	15.7	23.7	51,434	WY	15.2	23.3	52,470

SOURCE: Centers for Disease Control and Prevention and U.S. Census Bureau.

Excel Output

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.679166174
R Square	0.461266693
Adjusted R Square	0.438819471
Standard Error	2.194088021
Observations	51
ANOVA
	df	SS	MS	F	Significance F
Regression	2	197.846148	98.923074	20.54894411	3.5725E-07
Residual	48	231.0730677	4.814022243
Total	50	428.9192157
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	27.4116378	2.251057177	12.17722858	2.7396E-16	22.885584	31.9376916
Fruits/Vegetables	-0.354692848	0.103351606	-3.431904577	0.00124267	-0.562495178	-0.146890518
Income	-0.000117775	5.17082E-05	-2.27768364	0.027239308	-0.000221741	-1.38086E-05

Question 1: What is the estimated regression model? Interpret the coefficients.

Question 2: What’s the coefficient of determination? Interpret the coefficient of determination.

Question 3: What’s the p value for each coefficient? Interpret the result/conclusion of each p value.

Question 4: What’s the p value for the joint hypothesis? Interpret the result/conclusion of the p value.

*SHOW STEPS

Answer 1

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.679166174
R Square	0.461266693
Adjusted R Square	0.438819471
Standard Error	2.194088021
Observations	51
ANOVA
	df	SS	MS	F	Significance F
Regression	2	197.846148	98.923074	20.54894411	3.5725E-07
Residual	48	231.0730677	4.814022243
Total	50	428.9192157
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	27.4116378	2.251057177	12.17722858	2.7396E-16	22.885584	31.9376916
Fruits/Vegetables	-0.354692848	0.103351606	-3.431904577	0.00124267	-0.562495178	-0.146890518
Income	-0.000117775	5.17082E-05	-2.27768364	0.027239308	-0.000221741	-1.38086E-05

Ans 1: the estimated regression model is

Smoking = 27.412-0.355 *Fruits/Vegetables -0.00012 *Income

Interpretation of coefficient of Fruit/Vegetables: For every one-unit increase in the healthy food there is the corresponding decrease the smoking by 0.355 units

Interpretation of coefficient of Income: For every one-doller increase in the income there is the corresponding decrease the smoking by0.00012

Ans 2: the coefficient of determination is 0.4613

Interpretation of the coefficient of determination :About 46.13 % variation in Smoking can be explained by the Healthy food and income through given model

Ans 3: the p value for Fruits/Vegetables is 0.0012 , since p value is less than 0.05 so we conclude that Fruits/Vegetables is a significant variable for predicted the smoking

the p value for Income is 0.0272 , since p value is less than 0.05 so we conclude that Income is a significant variable for predicted the smoking

Ans 4: the p value for the joint hypothesis is 0.0000 which is less than 0.05 so we conclude that model significant to use