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 = 0.907, where x = distance in miles and y = fare in dollars... what is the value of the coefficient of determination? the coefficient of determination is \boxed{}. (round to four decimal places as needed.)

Explanation:

Step1: Recall 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 \(r^2=(r)\times(r)\).

Step2: Substitute \(r = 0.907\) into the formula

Calculate \(r^2=(0.907)^2\).
\(0.907\times0.907 = 0.822649\).

Step3: Round to four decimal places

Rounding \(0.822649\) to four decimal places gives \(0.8226\).

Answer:

\(0.8226\)