Question

question #1
when running a regression consisting of 25 data points, the linear regression coefficient was r = .471. does there appear to be a relationship? use α = 0.01.

critical values of the pearson
correlation coefficient r
chart with n, α=.05, α=.01 columns and values

○ no, because .471 < .505.
○ yes, because .471 < .505.
○ no, because .471 < .254.
○ yes, because .471 < .254.

Explanation:

Step1: Determine degrees of freedom or sample size

The number of data points \( n = 25 \). We need to find the critical value for \( \alpha = 0.01 \) (since the table has columns for \( \alpha = 0.05 \) and \( \alpha = 0.01 \), and we use \( \alpha = 0.01 \)) and \( n = 25 \). Looking at the table, for \( n = 25 \) and \( \alpha = 0.01 \), the critical value is \( 0.505 \) (from the table, the row for \( n = 25 \) and column \( \alpha = 0.01 \) gives \( 0.505 \)).

Step2: Compare correlation coefficient with critical value

The linear regression coefficient (Pearson's \( r \)) is \( r = 0.471 \). To determine if there is a significant linear relationship, we compare \( |r| \) with the critical value. If \( |r| \) is less than the critical value, we fail to reject the null hypothesis (no relationship). Here, \( 0.471 < 0.505 \), so we conclude there is no significant relationship.

Answer:

A. No, because.471 <.505.