Question

given $r = 0.19$, find the coefficients of determination and nondetermination and explain the meaning of each.

the coefficient of determination is \\(\square\\).
\\(\square\\%\\) of the variation of $y$ is \\(\text{select}\\) to the variation of $x$.

the coefficient of nondetermination is \\(\square\\).
\\(\square\\%\\) of the variation of $y$ is \\(\text{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 \(r^2=(0.19)^2 = 0.0361\). 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 \(1 - r^2\). So we calculate \(1 - 0.0361 = 0.9639\). Converting to a percentage, we get \(0.9639\times100 = 96.39\%\). This means 96.39% of the variation of \(y\) is not explained by the variation of \(x\).

Answer:

The coefficient of determination is \(0.0361\) (or \(3.61\%\) of the variation of \(y\) is explained to the variation of \(x\)).
The coefficient of nondetermination is \(0.9639\) (or \(96.39\%\) of the variation of \(y\) is not explained to the variation of \(x\)).