# Thread: What does R, R square , Adjusted R square, STD error of estimates helps for ?

1. ## What does R, R square , Adjusted R square, STD error of estimates helps for ?

Hello

After I run out the regression analysis, can someone enlighten me what can I get from R, R square, STD Error estimates and the adjusted r square ?!

P.S: I am not professional in stats, I have only taken one course in university and that was back 4 years ago so I don't have any knowledge about that except watching couple videos in youtube.

2. ## Re: What does R, R square , Adjusted R square, STD error of estimates helps for ?

Well, I'll help you with R. That is, R is the Pearson correlation between the actual values of the dependent variable (Y) and the predicted values of Y (Y-hats) - regardless of the number of predictors (X's) in the regression model. As such, R is an index of the strength of the linear association between Y and Y-hats. Note that R is bounded between 0 and 1.

3. ## The Following User Says Thank You to Dragan For This Useful Post:

bruin (12-06-2014)

4. ## Re: What does R, R square , Adjusted R square, STD error of estimates helps for ?

Originally Posted by Dragan
Note that R is bounded between 0 and 1.
We talking about the same R here?

5. ## Re: What does R, R square , Adjusted R square, STD error of estimates helps for ?

Originally Posted by Dragan
Note that R is bounded between 0 and 1.
Between -1 and 1.

6. ## Re: What does R, R square , Adjusted R square, STD error of estimates helps for ?

Originally Posted by Miner
Between -1 and 1.
Well, no...it is not....rather, the correlation between Y and the Y-hats is bounded between 0 and 1 as I stated above.

7. ## Re: What does R, R square , Adjusted R square, STD error of estimates helps for ?

R^2 is the R value squared, which is bounded between 0 and 1. It is typically interpreted as the amount of variance predicted by a variable (or variables, if there are more than 1 in a model).

8. ## Re: What does R, R square , Adjusted R square, STD error of estimates helps for ?

Based on this...

Originally Posted by Dragan
R is the Pearson correlation between the actual values of the dependent variable (Y) and the predicted values of Y (Y-hats)
...wouldn't a negative R only occur if your regression line had the wrong slope? How could a least-squares line have the wrong slope?

9. ## Re: What does R, R square , Adjusted R square, STD error of estimates helps for ?

Originally Posted by bruin
Based on this...

...wouldn't a negative R only occur if your regression line had the wrong slope? How could a least-squares line have the wrong slope?
Technically speaking, it is conceivable to obtain a negative value of R^2. This (unusual) case can occur when one conducts a regression without an intercept term i.e. regressing through the origin. However, the OLS estimate of the slope coefficient is still unbiased - unless you force the error terms to sum to zero.

10. ## Re: What does R, R square , Adjusted R square, STD error of estimates helps for ?

Bruin,

See the first figure for traditional depictations of correlations:

http://en.wikipedia.org/wiki/Correlation_and_dependence

11. ## Re: What does R, R square , Adjusted R square, STD error of estimates helps for ?

Originally Posted by Dragan
Well, no...it is not....rather, the correlation between Y and the Y-hats is bounded between 0 and 1 as I stated above.
i thought this could be provable so i decided to give it a try. i haven't done one of this in a while so plz point out potential mistakes:

to show that we could show that .

to do this, it is convenient to use , the 'hat matrix' that we know so that:

so since we've established

we can do:

now, we know:

by assumption of independence (or we'd introduce heteroskedasticity and violate the typical assumptions of OLS Regression)

so we substitute that back in:

which is clearly greater than 0 because is positive (it's a variance) and is positive-definite.

so that (i think) shows which i'm sure, when standardized, bounds to be between 0 and 1.