Use the value of the linear correlation coefficient to calcu

Use the value of the linear correlation coefficient to calculate the coefficient of determination. What does this tell you about the explained variation of the data about the regression line? About the unexplained variation? r=-0.683

Solution

The coefficient of determination of a simple linear regression is nothing but the squared value of the linear correlation between the dependent and the independent variable.

So, if linear correlation coefficient = r = -0.683,

then the coefficient of determination = r² = (-0.683)² = 0.466489.

Coefficient of determination tells us about the amount of variation explained by the linear regression model. This tells us about the variation in the dependent variable that can be explained by the independent variable from the given data . So in this case about 46.65% of the variation is explained by the regression line.