Is Coefficient of Determination always R²?

In the CFA text, it says to square the correlation to get the coefficient of determination, which can be used in linear regression with one independent variable.

The way they say it makes it sound like you can’t do this if there are more than 1 independent variable.

Can you do this with more than 1 independent variable?

On a related note, when you have more than 1 independent variables, what is multiple r in the anova table saying?

When you have simple linear regression, r2 = R2 like you said. R2 is also called multiple R.

If you have regression with multiple coefficients, coefficient of determination formula needs to be modified because additional variable(s) artificially increase R2 even though variable`s contribution is marginal. The formula goes like this:

Adjusted R = 1 - [(n-1) / (n - k - 1)] × (1 - R2)

Hope it helps.

That’s better.

Yup, that is right. Thanks.

My pleasure.

Thanks for the replies.

If you have the text, i’m talking about EOC problem 20 in reading 10.

The problem gives you multiple R-squared = 0.36 for a multiple regression problem.

The answer says "correlation between predicted and actual values of the dependent variable is 0.60.

Explanation at back of text says, "The correlation between the predicted and actual values of the dependent variable is the square root of the R-squared or sqrt(0.36) = 0.60

I’ve always understood correlation to be between 2 variables. Is this saying the correlation between the independent variables and dependent variable is 0.60?

No.

Correlation is, indeed, calculated between exactly two variables. In this case, the two variables are the predicted values of the dependent variable (i.e., the values that come from the regression model) and the actual values of the dependent variable.