Question

65. Explain what it means when a correlation has an$r^2$ of $0.72$.

Short answer

A correlation has an $r^2$of $0.72$, it means that the $72\%$ of the dependent variable can be justified by the independent variable utilizing the regression line.

Step-by-step solution

Given information

A correlation has an $r^2$of $0.72$. Correlation is a statistical estimation that represents how two variables are linearly connected.

Explanation

The ratio of explained variation to total variation in the model is known as the coefficient of determination. The coefficient of determination, abbreviated as $r^2$, is a metric for determining the regression line's quality of fit. It's the correlation coefficient squared.

Here, it is delivered that $r^2=0.72$, which indicates that the $72\%$of variation in the dependent variable can be clarified by the independent variable utilizing the regression line.