Random Forests: Question about R^2

-----Original Message-----
From: Dimitri Liakhovitski [mailto:ld7631 at gmail.com] 
Sent: Monday, April 13, 2009 4:35 PM
To: Liaw, Andy
Cc: R-Help List
Subject: Re: [R] Random Forests: Question about R^2

Andy,
thank you very much!
One clarification question:

If MSE = sum(residuals) / n, then
in the formula (1 - mse / Var(y)) - shouldn't one square mse before
dividing by variance?

Dimitri


On Mon, Apr 13, 2009 at 10:52 AM, Liaw, Andy 
<andy_liaw at merck.com> wrote:

MSE is the mean squared residuals. ?For the training data, the OOB
estimate is used (i.e., residual = data - OOB prediction, MSE =
sum(residuals) / n, OOB prediction is the mean of 

predictions from all

trees for which the case is OOB). ?It is _not_ the average 

OOB MSE of

trees in the forest.

I hope there's no question about how the pseudo R^2 is computed on a
test set? ?If you understand how that's done, I assume the 

confusion is

only how the OOB MSE is formed.

Best,
Andy

From: Dimitri Liakhovitski

Dear Random Forests gurus,

I have a question about R^2 provided by randomForest (for 

regression).

I don't succeed in finding this information.

In the help file for randomForest under "Value" it says:

rsq: (regression only) - "pseudo R-squared'': 1 - mse / Var(y).

Could someone please explain in somewhat more detail how 

exactly R^2

is calculated?
Is "mse" mean squared error for prediction?
Is "mse" an average of mse's for all trees run on out-of-bag
holdout samples?
In other words - is this R^2 based on out-of-bag samples?

Thank you very much for clarification!

--
Dimitri Liakhovitski
MarketTools, Inc.
Dimitri.Liakhovitski at markettools.com

Notice: ?This e-mail message, together with any 

attachments, contains

information of Merck & Co., Inc. (One Merck Drive, 

Whitehouse Station,

New Jersey, USA 08889), and/or its affiliates (which may be known
outside the United States as Merck Frosst, Merck Sharp & Dohme or
MSD and in Japan, as Banyu - direct contact information for 

affiliates is

available at http://www.merck.com/contact/contacts.html) that may be
confidential, proprietary copyrighted and/or legally 

privileged. It is

intended solely for the use of the individual or entity 

named on this

message. If you are not the intended recipient, and have 

received this

message in error, please notify us immediately by reply e-mail and
then delete it from your system.

-- 
Dimitri Liakhovitski
MarketTools, Inc.
Dimitri.Liakhovitski at markettools.com