Question

A regression equation is obtained for a collection of paired data. It is found that the total variation is 20.711, the explained variation is 18.592, and the unexplained variation is 2.119. Find the coefficient of determination.

Answer 1

Answer: $R^{2}$ = 0.89

Step-by-step explanation:

Coefficient of determination is represented by $R^{2}$. This tells us that how much of the variation in the dependent variable is explained by the independent variable.

It is the ratio of explained variation by the independent variables to the total variation in the dependent variable.

Hence,

Coefficient of determination = $\frac{Explained\ Variation}{Total\ Variation}$

= $\frac{18.592}{20.711}$

$R^{2}$= 0.89

∴ 89% of the variation in the dependent variable is explained by the independent variables.