Question

given $r = 0.19$, 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 select to the variation of $x$. the coefficient of nondetermination is \boxed{}. \boxed{}% of the variation of $y$ is select to the variation of $x$.

Explanation:

Step1: Calculate coefficient of determination

The coefficient of determination (\(r^2\)) is the square of the correlation coefficient (\(r\)). Given \(r = 0.19\), we calculate \(r^2\) as follows:
\(r^2=(0.19)^2 = 0.0361\)
To convert this to a percentage, we multiply by 100: \(0.0361\times100 = 3.61\%\). This means 3.61% of the variation of \(y\) is explained by the variation of \(x\).

Step2: Calculate coefficient of nondetermination

The coefficient of nondetermination is \(1 - r^2\). We already know \(r^2 = 0.0361\), so:
\(1 - r^2=1 - 0.0361 = 0.9639\)
Converting this to a percentage, we get \(0.9639\times100 = 96.39\%\). This means 96.39% of the variation of \(y\) is unexplained by the variation of \(x\).

Answer:

The coefficient of determination is \(0.0361\) (or \(3.61\%\)).
\(3.61\%\) of the variation of \(y\) is explained by the variation of \(x\).
The coefficient of nondetermination is \(0.9639\) (or \(96.39\%\)).
\(96.39\%\) of the variation of \(y\) is unexplained by the variation of \(x\).