Coefficient of determiniation - multi variable regression

In simple linear regression coefficient of determination is equal to R2.

Is this the same case for the other types of regression models?

How would we have to know all this for the level 2 exam?


In a simple regression, _R_² is the square of the correlation coefficient:

_R_² = _ρ_²

In a multiple regression, _R_² is the square of multiple R.

In both cases, _R_² describes the percentage of the variability of the dependent variable explained by the variability of the independent variable(s).

Yes, in the simple linear regression model, the correlation coefficient squared (r2) = coefficient of determination (R2).

No, this isn’t the case for more general regression models.

You only need to know what the learning outcome statements (LOS) ask you to. If it isn’t covered in the LOS and the curriculum, it isn’t examinable.

And Magician enlightens us again. I really think he is like Yoda in Star Wars or Ali in Boxing :slight_smile:

To S2000, is the multiple r and the correlation coefficient the same thing in a simple regression model?

From the learning outcome statement:

"calculate and interpret the standard error of estimate, the coefficient of determination, and a confidence interval for a regression coefficient;"

Not sure if that includes multi variate regression models


Multiple R = |ρ|

I would clarify that and point out that multiple R is really something referring to a correlation in a multiple regression-- that is the correlation between the actual and predicted values of Y, although it’s not that helpful. In a simple linear regression, the (positive) square root of R-squared is the absolute value of the correlation between the two variables involved (really, you’d pick pos or negative root based on the sign of the estimated beta coefficient or by looking at a scatter plot of the data).

Only a small point of terminology: multivariate refers to multiple outcome variables (DVs) in the same model whereas multivariable refers to multiple explanatory variables (independent variables) in a model such as in a multiple linear regression.

What I meant is that does this LOS mean we have to know what the coefficient of determination would be in a multiple regression model (with multiple x variables) as supposed to a simple regression model?

I understood what you intended. My point was to make a distinction between the word you chose (multivariate) and the word intended (multivariable); it can become confusing (and often is confused) if you’re thumbing through research or another source and see one of the terms (which look awfully similar).

To answer your question: yes. You can calculate it the same in either type of model, though (by using sums of squares). I would remember the trick of squaring the correlation coefficient to calculate r-squared for simple linear regression, as I can see them giving you a question like that.

Sounds good. So absolute value of the correlation coefficient equals the multiple R in simple regression as well as multiple regression model?

I am guessing that is the case based upon what you have said?

Thanks again!

There isn’t really a “multiple r” for a simple linear regression model (only one independent variable) since it just turns into the bivariate correlation (represented by “r”).

People really like correlation coefficients, so they said “I can square the correlation ® between X&Y and end up with R-squared in SLR, maybe there is a similar relationship in MLR.”

They took the positive root of (multiple) R-squared and got “multiple R”-- which is the correlation between the actual and predicted Y-values (you can’t get R-squared in MLR by squaring the individual correlations of Y with each X). It doesn’t really have much utility.

Thanks for the health conversation, it’s very helpful for me. I also try to learn how to determine how to calculate the Coefficient for multivariable regression. But it is very confusing for me. So when I start browsing online to find the solution. But unfortunate not find anything. So please help me in finding any free tool or software to find the solution.