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 = 0.687
what is the value of the coefficient of determination?
r² = \boxed{} (round to four decimal places as needed.)

Explanation:

Step1: Recall formula for \( r^2 \)

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 \( r = 0.687 \)

Substitute \( r = 0.687 \) into the formula: \( r^2=(0.687)^2 \). Calculate \( 0.687\times0.687 \).
\( 0.687\times0.687 = 0.471969 \)

Step3: Round to four decimals

Round \( 0.471969 \) to four decimal places. The fifth decimal is 6, which is greater than 5, so we round up the fourth decimal. \( 0.471969\approx0.4720 \)

Answer:

\( r^2 = 0.4720 \)