Question

when running a regression consisting of 9 data points, the linear regression coefficient was r =.829. does there appear to be a relationship? use a = 0.01.
critical values of the pearson
correlation coefficient r

no, because.829 >.666
yes, because.829 >.666
yes, because 829 >.798
no, because 829 >.798

Explanation:

Step1: Determine the critical value

For \(n = 9\) and \(\alpha=0.01\), from the table of critical values of the Pearson correlation coefficient \(r\), the critical value is \(0.798\).

Step2: Compare the calculated \(r\) value with the critical value

We are given \(r = 0.829\). Since \(0.829>0.798\) (i.e., \(|r|>r_{\text{critical}}\)), we reject the null hypothesis of no linear relationship.

Answer:

Yes, because \(0.829 > 0.798\) (i.e., the third option: Yes, because \(829>798\))