Question

use the value of the linear correlation coefficient r to find the coefficient of determination and the percentage of the total variation that can be explained by the linear relationship between the two variables.
r = 0.066
what is the value of the coefficient of determination?
r² = \boxed{} (round to four decimal places as needed.)

Explanation:

Step1: Recall the formula for coefficient of determination

The coefficient of determination \( r^2 \) is the square of the linear correlation coefficient \( r \). So we use the formula \( r^2=(r)^2 \).

Step2: Substitute the given value of \( r \)

Given \( r = 0.066 \), we calculate \( r^2=(0.066)^2 \).
Calculating \( 0.066\times0.066 = 0.004356 \).

Answer:

\( r^2 = 0.0044 \) (rounded to four decimal places)