Question

If the coefficient of correlation is .8, then the percentage of variation in the dependent variable explained by the estimated regression equation is _____.

Answer 1

The percentage of variation in the dependent variable explained by the estimated regression equation is 64%.

Step-by-step explanation:

When the coefficient of correlation is 0.8, the percentage of variation in the dependent variable explained by the estimated regression equation is 64%.

To determine this, we use the formula for the coefficient of determination, which is the square of the correlation coefficient. So, (0.8)^2 = 0.64. This means that 64% of the variation in the dependent variable can be explained by the variation in the independent variable using the regression equation.

Answer 2

64%

Step-by-step explanation:

The percentage of variation in the dependent variable explained by the estimated regression is calculated with the coefficient of correlation as follows:

First, square the coefficient of correlation: 0.8^2 = 0.64

And then, multiply this result by 100, so that, it is expressed as a percentage: 0.64*100 = 64%