Beyond Common Core
Problem 13 of 45s12-013
For 40 used cars, the correlation between age in years and price is . What percent of the variation in price is explained by the linear relationship with age?
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Solution walkthrough1:37
- The coefficient of determination, , is the fraction of the variation in price that the line with age explains.
- Square the correlation from the question: . A negative times a negative is positive.
- As a percent, . The linear relationship with age explains of the variation in price.
- The other is scatter around the line, from things other than age.
- Traps: forgot to square, kept the minus sign, and is the part not explained.