Compare the coefficients of determination (r-squared values)from the three linear regressions: simple linear regression fromModule 3 Case, multivariate regression from Module 4 Case, and thesecond multivariate regression with the logged values from Module 4Case. Which model had the “best fit”? Calculate the residual forthe first observation from the simple linear regression model.Recall, the Residual = Observed value - Predicted value or e = y –?. What happens to the overall distance between the best fit lineand the coordinates in the scatterplot when the residuals shrink?What happens to the coefficient of determination when the residualsshrink? Consider the r-squared from the linear regression model andthe r-squared from the first multivariate regression model. Why didthe coefficient of determination change when more variables wereadded to the model? Annual Amount Spent on Organic Food Age AnnualIncome Number of People in Household Gender
Module 4
| 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 |
Module 3
| Annual Amount Spent on Organic Food | Age |
| 7348 | 77 |
| 11598 | 47 |
| 9224 | 23 |
| 12991 | 38 |
| 16556 | 58 |
| 11515 | 44 |
| 10469 | 34 |
| 17933 | 75 |
| 18173 | 32 |
| 12305 | 39 |
| 9080 | 65 |
| 9113 | 48 |
| 6185 | 48 |
| 6470 | 49 |
| 6000 | 57 |
