A researcher's results are shown below using Femlab (labor force participation rate among females) to try to predict Cancer (death rate per 100,000 population due to cancer) in the 50 U.S. states. $$\begin{array} { l c r c c } \hline \text { Source of variation } & d f & { \text { SS } } & M S & F \ \hline \text { Regression } & 1 & 5377.836 & 5377.836 & 5.228879 \ \text { Residual } & 48 & 49367.389 & 1028.487 & \ \text { Total } & 49 & 54745.225 & & \ \hline \end{array}$$ What is the R² for this regression? A).9018 B).0982 C).8395 D).1605

Question

Quizplus · Accepted Answer

The R², commonly referred to as the coefficient of determination or R-squared (R^2), measures the proportion of the variance in the dependent variable that is predictable from the independent variable(s). It is calculated as 1 - (SS_Residual / SS_Total). From the table, SS_Residual = 49367.389 and SS_Total = 54745.225. Thus, R^2 = 1 - (49367.389 / 54745.225) = 1 - 0.9018 = 0.0982.

A Researcher's Results Are Shown Below Using Femlab (Labor Force