Question

when running a linear regression with 32 data points, the r value was found to be -.473. describe the r - value. critical values of the pearson correlation coefficient r
positive and significant
positive and not significant
negative and not significant.
negative and significant

Explanation:

• The sign of \( r = - 0.473 \) is negative, so we can eliminate the positive - related options (first two options).
• For \( n=32 \) data points, in the table of critical values of the Pearson correlation coefficient \( r \), when \( n = 30 \), the critical value for \( \alpha=0.05 \) is \( 0.361 \), and when \( n = 35 \), the critical value for \( \alpha = 0.05 \) is \( 0.335 \). Using linear - interpolation (or just comparing the magnitude), \(|r|=0.473\). Since \(|r| = 0.473>0.361\) (approximate critical value for \(n = 32\) at \(\alpha = 0.05\)), the correlation is significant.

Answer:

Negative and significant.