Analysis Interpretation

Final Report

To further analyze and understand the motives of Loving Organic Foods customer purchasing habits and expenditures, Diligent Consulting Group was requested to complete a final report. The first three reports provided an improved comprehension of customers purchasing habits by simple linear regression analysis. This final report further enhances Loving Organic Foods’ goal by interpreting additional information such as independent variables to explain the motives of their customers.

Based on Regression Statistics, the following interpretation can be gathered. The coefficient of determination (r-squared) is equal to 69% of total variation in the sample of Annual Amount Spent on Organic Food. Furthermore, reviewing the ANOVA analysis, the global test for statistical significance Interpretation reflects a p-value of equal to 0.00 and is less than the 0.05 so overall regression equation is significant.

4. Your interpretation of the coefficient estimates for all the independent variables.

Analyzing the coefficient estimate, identifies that when the age increases by one unit and other independent variables are kept fixed then estimated Annual Amount Spent on Organic Food is increased by 14.12 units. Additionally, when Annual Income increases by one unit and other independent variables are kept fixed then estimated Annual Amount Spent on Organic Food increased by 0.02 units. Furthermore, the 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 2222.51 units. When Female customers and other independent variables are kept fixed then estimated Annual Amount Spent on Organic Food equals negative 1892 units. In contrast, when Male customers and other independent variables are kept fixed then estimated Annual Amount Spent on Organic Food is negative 1932 units.

5. Your interpretation of the statistical significance of the coefficient estimates for all the independent variables.

Since the P-Values correspond to Age and Gender is greater than 0.05, this can suggest the insignificant presence in this regression model whereas p-value corresponding Number of People in Household and annual income <0.05 so Number of People in Household and annual income is significantly present in this model.

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)

Another request from Loving Organic Foods is the regression equations with estimates substituted into the equation. This equation is expressed as: Annual Amount Spent on Organic Food = -1932.11 + 14.12* Age + 0.02*Annual Income + 2222.51*Number of People in Household 40.50*Gender.

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.)

Avg(Annual Amount Spent on Organic Food) = -1932.11 + 48.23* Age + 161006.62 *Annual Income + 4.31*Number of People in Household 0.51*Gender

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.

Yes, it is different because in the linear regression we are looking for linear relationship but the average doesn’t reveal any relation

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. (SUMMARY OUTPUT (Log) Sheet)

10. Using Excel, generate regression estimates for the following model:

Log(Annual Amount Spent on Organic Food) = α +b1Age + b2Log(Annual Income) + b3Number of People in Household + b4Gender Log(Annual Amount Spent on Organic Food) =2.092 +0.0004Age + 0.289Log(Annual Income) + 0.095Number of People in Household + 0.008Gender.

11. Your interpretation of the coefficient estimate for Log (Annual Income).

When log 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 0.289 units.

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

Coefficient of determination =0.766 i.e. 76.6% of total variation in the sample of log Annual Amount Spent on Organic Food is explained by this regression equation.

Addendum

Attachment A

Attachment B

SUMMARY OUTPUT

Regression Statistics

Multiple R0.830Correlation coefficient

R Square0.6900.83

Adjusted R Square0.679

Standard Error2111.587

Observations124

ANOVA

dfSSMSFSignificance F

Regression41179155134294788783.5966.110.00

Residual119530597256.64458800.476

Total1231709752391

CoefficientsStandard Errort StatP-valueLower 95%Upper 95%

Intercept-1932.11978.54-1.970.05-3869.725.50

Age14.1211.781.200.23-9.2037.44

Annual Income0.020.006.330.000.010.02

Number of People in Household2222.51153.2514.500.001919.062525.95

Gender (0 = Male; 1 = Female)40.50384.710.110.92-721.27802.27

SUMMARY OUTPUT

Regression Statistics

Multiple R0.875470796Correlation coefficient

R Square0.7660.875

Adjusted R Square0.758598665

Standard Error0.079392842

Observations124

ANOVA

dfSSMSFSignificance F

Regression42.4615659240.61539148197.631234021.22214E-36

Residual1190.7500835870.006303223

Total1233.211649512

CoefficientsStandard Errort StatP-valueLower 95%Upper 95%

Intercept2.0920.15777592213.260646453.36765E-251.7797986332.404622799

b2Log(AnnualIncome)0.2890.030854759.3805656775.49173E-160.2283395210.350530493

Age0.00040.000444480.7988415940.425973762-0.0005250460.001235183

Number of People in Household0.0950.00577063116.498156431.54342E-320.0837783530.106631206

Gender (0 = Male; 1 = Female)0.0080.0144699570.5537776630.580770084-0.0206388210.036665099