Analysis Interpretation

Data

SUMMARY OUTPUT

SUMMARY OUTPUT (Log)

Interpretation

Using Excel, generate regression estimates for the following model: 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. (SUMMARY OUTPUT Sheet)) 2. Your interpretation of the coefficient of determination (r-squared). Coefficient of determination =0.690 i.e. 69% of total variation in the sample of Annual Amount Spent on Organic Food is explained by this regression equation. 3. Your interpretation of the global test for statistical significance (the F-test). Interpretation of the global test for statistical significance: Since p-value of ANOVA test= 0.00 <0.05 so overall regression equation is significant. 4. Your interpretation of the coefficient estimates for all the independent variables. 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 14.12 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 0.02 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 2222.51 units. When it is Female and other independent variables are kept fixed then estimated Annual Amount Spent on Organic Food is -1932.11+40=-1891.61 units. When it is Male and other independent variables are kept fixed then estimated Annual Amount Spent on Organic Food is -1932.11 units. 5. Your interpretation of the statistical significance of the coefficient estimates for all the independent variables. Since p-values corresponding Age and Gender>0.05 so there are insignificantly present in this regression model whereas p-value corresponding Number of People in Household and annula 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) Annual Amount Spent on Organic Food = -1932.11 + 14.12* Age + 0.02*AnnualIncome + 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.) Aveg(Annual Amount Spent on Organic Food) = -1932.11 + 48.23* Age + 161006.62 *AnnualIncome + 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 becaue in the linear regression we are looking for linear relatioship but the average dosent 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(AnnualIncome) + b3Number of People in Household + b4Gender Log(Annual Amount Spent on Organic Food) =2.092 +0.0004Age + 0.289Log(AnnualIncome) + 0.095Number of People in Household + 0.008Gender 11. Your interpretation of the coefficient estimate for Log(AnnualIncome). 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.