Question

the arm span and foot length were both measured (in centimeters) for each of 20 students in a biology class. the computer output displays the regression analysis.
predictor coef se coef t - ratio p
constant - 7.611 2.587 2.943 0.046
arm span 0.184 0.033 5.377 0.000
s = 1.62 r - sq = 63.0% r - sq(adj) = 61.9%
which of the following is the best interpretation of the coefficient of determination r²?
○ about 37% of the variation in arm span is accounted for by the linear relationship formed with the foot length.
○ about 63% of the variation in foot length is accounted for by the linear relationship formed with the arm span.
○ about 63% of the variation in arm span is accounted for by the linear relationship formed with the foot length.
○ about 63% of the variation in foot length is accounted for by the linear relationship formed with the arm span.

Explanation:

The coefficient of determination \( r^{2}\) (here \(R - sq=63.0\%\)) measures the proportion of the variance in the dependent variable that is predictable from the independent variable. In a regression model where foot - length is the dependent variable (response variable) and arm - span is the independent variable (predictor variable), \(r^{2}\) tells us the percentage of the variation in the dependent variable (foot - length) that can be explained by the linear relationship with the independent variable (arm - span).

Answer:

About 63% of the variation in foot length is accounted for by the linear relationship formed with the arm span.