Question

For a given line of best fit, you computed that $r=0.6501$ using $n=12$ data points and the critical value is $0.576$. Can the line be used for prediction? Why or why not?

Short answer

$r(0.6501)$is greater than positive critical value $(0.576)$. Therefore, $r$ is significant.

Step-by-step solution

introduction

linear regression is a linear methodology for displaying the connection between a scalar reaction and at least one informative factor. The instance of one logical variable is called basic linear regression

Explanation

Given,

The degrees of freedom can be computed as shown below:

$df=n-2$

$=12-2$

$=10$

The critical value associated with degrees of freedom $10$is $0.576$. If $r$is less than the negative critical value or $r$is greater than positive critical value then $r$is significant. Here, $r(0.6501)$is greater than a positive critical value $(0.576)$. Therefore, $r$is significant. The number line is shown below:

Final Answer

$r(0.6501)$is greater than positive critical value $(0.576)$. Therefore, $r$ is significant.