Question: What percentage of the variation in percent growth in wealth is explained by the regression in problem?
Problem: An article in the Journal of Monetary Economics assesses the relationship between percentage growth in wealth over a decade and a half of savings for baby boomers of age 40 to 55 with these people's income quartiles. The article presents a table showing five income quartiles, and for each quartile there is a reported percentage growth in wealth. The data are as follows.
Income quartile: 1 2 3 4 5
Wealth growth (%): 17.3 23.6 40.2 45.8 56.8
Run a simple linear regression of these five pairs of numbers and estimate a linear relationship between income and percentage growth in wealth.