Question

66. Can a coefficient of determination be negative? Why or why not?

Short answer

A coefficient of determination cannot be negative.

Step-by-step solution

Given information

A coefficient of determination can be negative or not.

Explanation

A Coefficient of finding $R^2$ is the linear equation utilized for prediction. The coefficient of a conclusion is estimated as follows:
$\begin{array}{r}{R}^2=1-\frac{S{S}_{\text{res}}}{S{S}_{\text{tot}}}\end{array}$

$S{S}_{\text{res}}=\sum _{i=1}^n e_i^2$

$S{S}_{\text{tot}}=\sum _{i=1}^n {\left(y_i-\overline{y}\right)}^2$

where $S{S}_{\text{res}},S{S}_{\text{tot}}$sum of residuals and the total sum of squares, respectively. Since, $r$ nearer to $1$ is that the standard is better.
From the earlier, the coefficient of the conclusion can't be negative. It has values between 0 and 1 . And if the$R^2$ is small, the model used for prediction is not appropriate and requires fixing because it received the wrong predicted values.