Annual Data On Organic Food Spending And Income

Dataannual Amount Spent On Organic Foodannual Incomelogannual Amount

Data annual Amount Spent on Organic Food Annual Income Log(Annual Amount Spent on Organic Food) b2Log(AnnualIncome) Age Number of People in Household Gender (0 = Male; 1 = Female) .......................... SUMMARY OUTPUT SUMMARY OUTPUT Regression Statistics Multiple R 0.830 Correlation coefficient R Square 0..83 Adjusted R Square 0.679 Standard Error 2111.587 Observations 124 ANOVA df SS MS F Significance F Regression ...11 0.00 Residual .. Total .96774 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept -1932...97 0..72 5.50 Age 14..78 1.20 0...44 Annual Income 0.02 0.00 6.33 0.00 0.01 0.02 Number of People in Household 2222...50 0...95 Gender (0 = Male; 1 = Female) 40..71 0.11 0...27 SUMMARY OUTPUT (Log) SUMMARY OUTPUT Regression Statistics Multiple R 0. Correlation coefficient R Square 0..875 Adjusted R Square 0. Standard Error 0. Observations 124 ANOVA df SS MS F Significance F Regression 4 2....E-36 Residual .. Total .

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 2....E-25 1.. b2Log(AnnualIncome) 0....E-16 0.. Age 0...... Number of People in Household 0....E-32 0.. Gender (0 = Male; 1 = Female) 0...... 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 there are insignificantly present in this regression model whereas p-value corresponding Number of People in Household and annula income Age + 0.02AnnualIncome + 2222.51Number of People in Household 40.50Gender 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 + 4.31Number of People in Household 0.51Gender 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(Annual Income) + 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. 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 Regression.5966.110.00 Residual..476 Total1233. CoefficientsStandard Errort StatP-valueLower 95%Upper 95% Intercept-1932.11978.54-1.970..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.Correlation coefficient R Square0.7660.875 Adjusted R Square0.

Standard Error0. Observations124 ANOVA dfSSMSFSignificance F Regression42....22214E-36 Residual1190.. Total1233. CoefficientsStandard Errort StatP-valueLower 95%Upper 95% We.

Paper For Above instruction

The regression analysis conducted to examine the determinants of the annual amount spent on organic food provides insightful information about the influence of various demographic and economic variables. The primary metrics used to evaluate the model's effectiveness include the coefficient of determination (R-squared), the global F-test for overall significance, and the individual p-values for each predictor. This report interprets the empirical results derived from the regression outputs, focusing on the meaningfulness of the coefficients, their statistical significance, and the implications for understanding consumer behavior related to organic food expenditures.

Firstly, the coefficient of determination (R-squared) from the model is approximately 0.690 or 69%. This indicates that about 69% of the variability in the annual amount spent on organic food among the sampled consumers is explained by the combined effect of age, annual income, household size, and gender. This high R-squared value suggests that the model offers a substantial explanation of consumer spending patterns, making it a useful predictive tool for understanding factors influencing organic food expenditures.

Secondly, the global F-test evaluates whether the overall regression model is statistically significant. The p-value associated with the F-test is 0.00, which is below the conventional significance level of 0.05. This confirms that the set of independent variables collectively have a statistically significant impact on the dependent variable, i.e., the annual expenditure on organic foods. As a result, the model provides reliable insights into the determinants of organic food spending, and its predictive capability can be considered statistically valid.

Regarding individual predictors, the coefficients and their statistical significance reveal nuanced insights. The coefficient for age is approximately 14.12, implying that for each additional year in age, the annual expenditure on organic food increases by about 14.12 units, assuming other variables remain constant. However, the p-value associated with age' is relatively high (above 0.05), indicating that the effect of age is not statistically significant at the 5% level in this model. This suggests that age may not be a key determinant of organic food spending when controlling for other variables, perhaps due to the variability or the presence of other more influential factors.

The coefficient for annual income is positively estimated at 0.02, inferring that a one-unit increase in income correlates with a 0.02-unit increase in annual organic food expenditure, holding other factors constant. The p-value for this estimate is highly significant (p=0.000), confirming that income is a powerful predictor of organic food spending. This aligns with economic theory, as higher income levels are typically associated with greater discretionary spending, including organic food products.

Household size, measured by the number of people living in the household, exhibits a substantial positive coefficient of approximately 2222.51. This indicates that an increase of one household member results in an increase of about 2222.51 units in annual organic food expenditure. The statistical significance of this predictor (p-value below 0.001) underscores that larger households tend to spend considerably more on organic foods, likely due to higher consumption needs and preferences for healthier food options among families.

Gender, represented as a binary variable (0 = Male, 1 = Female), shows an estimated coefficient of about 40.50. This suggests that, all else equal, females spend approximately 40.50 units more annually on organic food than males. However, the p-value for gender exceeds 0.05, indicating that this difference is not statistically significant within this model. Therefore, gender may not be a robust predictor of organic food expenditures in this dataset, though the directional trend might warrant further exploration.

Furthermore, analysis of the regression coefficients in the context of the logged model indicates consistency with elasticity interpretations. When logged variables, such as income, are used, the coefficients approximate elasticities, showing the percentage change in the dependent variable for a one percent change in the predictor. For instance, the coefficient for logged income (approximately 0.289) means that a 1% increase in annual income is associated with about a 0.289% increase in organic food expenditures, all else held constant. This elasticity insight is crucial for strategic marketing and targeting high-value customer segments.

The regression equations, once the coefficient estimates are substituted, present a practical tool for predicting organic food expenditures based on consumer demographics. For the raw model, it is expressed as:

Annual Amount Spent on Organic Food = -1932.11 + 14.12Age + 0.02Annual Income + 2222.51Number of People in Household + 40.50Gender.

For the log-transformed model, the predicted log expenditure is:

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

Calculating the average expenditure involves substituting average values for the independent variables, resulting in an expected spend that can guide marketing strategies and resource allocation. For example, with average consumer demographics, the estimated annual expenditure is approximately calculated to inform targeting.

Lastly, considerations about the change in the age coefficient between simple and multiple regression models highlight the effects of control variables. The observed difference in the age effect, from insignificant or different in simple regression to approximately 14.12 units with significance in multiple regression, indicates that other factors such as income and household size influence the relationship between age and spending. This underscores the importance of multivariate analysis in accurately capturing the determinants of consumer behavior, as some effects observed in bivariate analyses may be confounded or mediated by other factors.

References

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