r^2 vs. r

Can anyone explain the difference?

R - Correlation R Squared - Correlation squared. “Goodness of fit” How well your model explains the outcome.

R^2 = (RSS/k)/(TSS/n-k-1) where k=# of independent variables.

But the meaning… Correlation describes the strength of a relationship r^2 describes how well the independent variable explains the dependent variable is that right?

r^2 is how well variations in the independent variable explains variations in the dependent variable. But this is true only for a simple regression. In a multiple regression - that’s why you need to get to the adjusted r^2 adj r^2 = 1 - {[(n-1)*(1-r^2)]/(n-k-1)}

Correlation explains the strength of two variables moving in the same direction. Goes from -1 to +1 (u knew that right?) R^2 is the coefficient of determination and it tells you how well the regression equation explains the expected outcome.

got it

Yes. Correlation describes a standardized strength (unlike covariance) of a relationship. R^2 (coefficient of determination) is how well the independent variable describes the dependent variable. ie SP 500 explains SPY