Question

For a given line of best fit, you compute that $r=0.5204$ using $n=9$ data points, and the critical value is 0.666. Can the line be used for prediction? Why or why not?

Short answer

The critical value associated with degrees of freedom $7$is $0.666$.Therefore,$r$ is insignificant.

Step-by-step solution

Given Information

$r=0.5204$

$n=9$

$criticalvalue=0.666$.

Explanation

The degrees of freedom can be computed as shown below:

$df=n-2$

$=9-2$$=7$

The critical value associated with degrees of freedom $7$ is $0.666$. If $r$ is less than negative critical value or $r$ is greater than positive critical value then $r$ is significant. Here, $r(0.5204)$ is less than positive critical value $(0.666)$. Therefore, $r$ is insignificant.