Question

The coefficient of determination in a simple linear regression model is 64%. What is the correlation level between the dependent and independent variables, assuming a negative relationship between them

Answer 1

Answer: -0.64

Step-by-step explanation:

We know that the coefficient of determination  in a simple linear regression model is denoted by $r^2$, which gives the proportion of the variance in the dependent variable that is predictable from the independent variable.

Given, the coefficient of determination in a simple linear regression model is 64%.

i.e.

$r^2= 0.64\\\\\Rightarrow\ r=\sqrt{0.64}=\pm 0.64$

As there is negative relation between the dependent and independent variables.

Then, the correlation coefficient = -0.64