What does Multiple R mean in a multiple linear regression? I understand in a simple linear regression with one independent variable multiple R = correlation between the dependent and independent variables. am i right? multiple r = sqroot of R2?
Multiple R is the percentage of variation of the dependent variable explained by the independent variable(s). In a simple linear regression it is equal to: correlation^2
perimel Wrote: ------------------------------------------------------- > Multiple R is the percentage of variation of the > dependent variable explained by the independent > variable(s). I thought that is R2. > > In a simple linear regression it is equal to: > correlation^2 R2 again. R2 = correlation^2
In a multiple regression you do not have a single correlation but many more depending on the number of independent variables. So R2 is a valid measure for a simple linear regression but not for a multiple one. Multiple R is applicable to both cases. R2 only in the simple linear case (where R2 = Multiple R).
perimel, no offense but i suggest you should do problem no #14 on page 334 of book 1. i hope it will be an eye opener to you, as it was to me. i am still unsure what is MULTIPLE R in multiple linear regression?
It gets more fun as you consider what adjusted R2 is!
Pepp, No offense, that is why this forum is invaluable. I checked the Q. You are right. In simple linear regression multiple R is the correlation and R2 is the the percentage of variation of the dependent variable explained by the independent variable(s). Regarding your question however, the multiple R does not appear in Reading 12 which relates to the multiple regression. I did a quick overview of the Reading and saw nowhere the multiple R in an regression output. What is displayed is the multiple R SQUARED. Can you tell me in which point of the Reading the multiple R appears?
Dreary, As you add more and more independent variables to a regression, its likely that it’s R2 will go up, as long the newly added independent variable explains slight of the variation in dependent variable, or in other words is correlated to dependent variable. However, adjusted R2 is that measure that doesn’t get affected by simply additions of new independent variables to the model. While it’s easy to explain adjusted R2, its simply not worth remembering the formula to compute it. Ref pg 368. ouch! I think i’ve forgotten how to compute the Prediction interval. 
(especially the formula to compute the estimated variance of the prediction error. What a B****).
Perimel: Refer Pg 386. I am trying to understand what is Multiple R2 of .7521 means? Anyone can you interpret?
Pepp, No offense, but I do not understand what you cannot understand since the text gives the answer in the second paragraph below: ‘Note also that this regression…Specifically the R^2 from this regression is 0.7521. Thus, approximately 75% of the variation…’ R^2 = Multiple R-squared (multiple regression) R^2 = Multiple R-squared = multiple R ^2 = correlation^2 (simple linear regression).
pepp Wrote: ------------------------------------------------------- > Dreary, > > As you add more and more independent variables to > a regression, its likely that it’s R2 will go up, > as long the newly added independent variable > explains slight of the variation in dependent > variable, or in other words is correlated to > dependent variable. > Yes, I accepted that and moved on…but why would adding another independent variable *necessarily* improves, or at least not reduce the explanatory power? It seems you could add another independent variable which would worsen the model, not improve it!
If you spend some time thinking out the OLS line is derived even for multiple regression models you’d realize why adding a new variable can’t really worsen the model. a) Take 1 independent and 1 dependent variable, the worst you can do is explain 0 variation! b) Add 1 more independent variable to the model, now could you actually go below? you can’t have negative r^2. so the only way to go is up. It’s possible you stay at 0, but if we say you stay at 0, you it implies that this new variable is not correlated anyhow with the dependent variable. hence by adding more and more you could only go up.
got that… so any variable you add will have a correlation with the dependent variable of anywhere from +1 to -1. Only when the correlation is 0 you get no further correlation with the dependent variable. For all other cases, you get more correlation, which explains the bahaviour of the dependent variable further.
yup, pretty much. as long there is some correlation between dependent and the newly added independent variable, you are capable of explaining some of the variation of the dependent variable, hence overall capable of increasing your r2 (total explained variation).
but realize that is precisely why there is the adjusted R --> which accounts for the addition of # of variables by adjusting the R.