Question

given $r = 0.13$, find the coefficients of determination and nondetermination and explain the meaning of each.

the coefficient of determination is \boxed{}.

\boxed{}% of the variation of $y$ is \text{select} to the variation of $x$.

the coefficient of nondetermination is \boxed{}.

\boxed{}% of the variation of $y$ is \text{select} to the variation of $x$.

Explanation:

Step1: Calculate coefficient of determination

$r^2 = (0.13)^2 = 0.0169$

Step2: Convert to percentage

$0.0169 \times 100 = 1.69\%$

Step3: Calculate coefficient of nondetermination

$1 - r^2 = 1 - 0.0169 = 0.9831$

Step4: Convert to percentage

$0.9831 \times 100 = 98.31\%$

Step5: Interpret meanings

Coefficient of determination: % of y variation explained by x. Coefficient of nondetermination: % of y variation not explained by x.

Answer:

0.0169; 1.69%; explained by; 0.9831; 98.31%; not explained by