Question

the value of the linear correlation coefficient r to find the coefficient of determination and the percentage of ation that can be explained by the linear relationship between the two variables.
r = 0.188
what is the value of the coefficient of determination?
r² = 0.0353 (round to four decimal places as needed.)
what is the percentage of the total variation that can be explained by the linear relationship between the two variables?
explained variation = □% (round to two decimal places as needed.)

Explanation:

Step1: Recall the formula for explained variation

The percentage of total variation explained by the linear relationship is the coefficient of determination \( r^2 \) multiplied by 100.
We know \( r^2 = 0.0053 \).

Step2: Calculate the explained variation percentage

Multiply \( r^2 \) by 100: \( 0.0053\times100 = 0.53 \).

Answer:

0.53