In the article, “Variation in cancer risk among tissues can be explained by the number of stem cell divisions” (Tomasetti and Vogelstein, Science, vol. 47, 2015), the authors stated: “A linear correlation equal to 0.804 suggests that 65% of the differences in cancer risk among different tissues can be explained by the total number of stem cell divisions in those tissues.”
a. How did they get 65%?
b. By how many percentage points does the overall prediction error (as measured by the sum of squares) decrease when using the prediction equation from a linear regression model to predict cancer risk rather than using the sample mean of the observed risks to predict it?