Question

Compare the coefficients of determination (r-squared values) from the three linear regressions: simple linear regression from Module 3 Case, multivariate regression from Module 4 Case, and the second multivariate regression with the logged values from Module 4 Case. Which model had the “best fit”? Calculate the residual for the first observation from the simple linear regression model. Recall, the Residual = Observed value - Predicted value or e = y – ŷ. What happens to the overall distance between the best fit line and the coordinates in the scatterplot when the residuals shrink? What happens to the coefficient of determination when the residuals shrink? Consider the r-squared from the linear regression model and the r-squared from the first multivariate regression model. Why did the coefficient of determination change when more variables were added to the model? Annual Amount Spent on Organic Food Age Annual Income 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

Answer 1