Question

question 7 5 pts
two variables are correlated (r = -0.64). what is the coefficient of determination (r²)?
0.86
0.57
0.54
0.41

Explanation:

Step1: Square the correlation coefficient

The formula for the coefficient of determination \(r^{2}\) is simply squaring the given correlation coefficient \(r\). Given \(r=- 0.64\), we calculate \((-0.64)^{2}\).

$$ (-0.64)^{2}=(-0.64)\times(-0.64) $$

Step2: Perform the multiplication

Multiply \(-0.64\) by \(-0.64\). When we multiply two negative numbers, the result is positive. \(0.64\times0.64 = 0.4096\approx0.41\)

Answer:

\(0.41\) (corresponds to the last option)