Question

Annual Amount Spent on Organic Food = α + b₁Age + b₂AnnualIncome
+ b₃Number of People in Household + b₄Gender

After you have reviewed the results from the estimation, write a report to your boss that interprets the results that you obtained. Please include the following in your report:

1. The regression output you generated in Excel.
2. Your interpretation of the coefficient of determination (r-squared).
3. Your interpretation of the global test for statistical significance (the F-test).
4. Your interpretation of the coefficient estimates for all the independent variables.
5. Your interpretation of the statistical significance of the coefficient estimates for all the independent variables.
6. The regression equation with estimates substituted into the equation. (Note: Once the estimates are substituted into the regression equation, it should take a form similar to this: y = 10 +2x₁ +1x₂ +4x₃ +0.9x₄)
7. An estimate of “Annual Amount Spent on Organic Food” for the average consumer. (Note: You will need to substitute the averages for all the independent variables into the regression equation for x, the intercept for α, and solve for y.)
8. A discussion of whether or not the coefficient estimate on the Age variable in this estimation is different than it was in the simple linear regression model from Module 3 Case. Be sure to explain why it did/did not change.
9. You decide you want to generate an elasticity coefficient, so you log the following variables in Excel: Annual Amount Spent on Organic Food, Annual Income.
10. Using Excel, generate regression estimates for the following model:

Log(Annual Amount Spent on Organic Food) = α +b₁Age + b₂Log(AnnualIncome)
+ b₃Number of People in Household + b₄Gender

11. Your interpretation of the coefficient estimate for Log(AnnualIncome).
12. Your interpretation of the coefficient of determination (r-squared) for this new model.

Annual Amount Spent on Organic Food	Age	Annual Income	Number of People in Household	Gender (0 = Male; 1 = Female)
7348	77	109688	3	1
11598	47	109981	5	1
9224	23	112139	4	1
12991	38	113420	5	1
16556	58	114101	5	0
11515	44	115100	5	0
10469	34	116330	5	0
17933	75	116339	6	0
18173	32	117907	7	0
12305	39	119071	5	1
9080	65	58603	5	1
9113	48	58623	4	1
6185	48	61579	2	1
6470	49	62180	2	0
6000	57	62202	5	1

Answer 1

Regression output:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.88600362
R Square	0.785002414
Adjusted R Square	0.699003379
Standard Error	2220.834832
Observations	15
ANOVA
	df	SS	MS	F	Significance F
Regression	4	180081843.8	45020461	9.128038	0.00226243
Residual	10	49321073.5	4932107
Total	14	229402917.3
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-1325.95133	3947.374868	-0.33591	0.743882	-10121.25064	7469.34798
Age	26.09987382	39.91641113	0.653863	0.527949	-62.83943265	115.03918
Annual Income	0.050854676	0.027956731	1.819049	0.09893	-0.011436802	0.11314615
Number of People in Household	1626.800994	522.0201163	3.116357	0.010942	463.6676912	2789.9343
Gender	-2058.955049	1258.720488	-1.63575	0.132936	-4863.559072	745.648973

Annual Amount Spent on Organic Food = -1325.9513 + 26.0999 Age + 0.0509 AnnualIncome
+ 1626.8010 Number of People in Household -2058.9550 Gender

coefficient of determination =0.7850 i.e. 78.50% of total variation in the sample of Annual Amount Spent on Organic Food is explained by this regression equation.

Interpretation of the global test for statistical significance: Since p-value of ANOVA test= 0.0023<0.05 so overall regression equation is significant.

When Age is increased by one unit and other independent variables are kept fixed then estimated Annual Amount Spent on Organic Food is increased by 26.0999 units.

When Annual Income is increased by one unit and other independent variables are kept fixed then estimated Annual Amount Spent on Organic Food is increased by 0.0509 units.

When Number of People in Household is increased by one unit and other independent variables are kept fixed then estimated Annual Amount Spent on Organic Food is increased by 1626.8010 units.

When it is Female and other independent variables are kept fixed then estimated Annual Amount Spent on Organic Food is -1325.9513-2058.9550=-3384.906 units.

When it is Male and other independent variables are kept fixed then estimated Annual Amount Spent on Organic Food is -1325.9513 units.

Since p-values corresponding Age, Annual income, Gender>0.05 so there are insignificantly present in this regression model whereas p-value corresponding Number of People in Household?<0.05 so Number of People in Household is significantly present in this model.