Re: Adjusted R2 (R Bar Squared)

From: Jeff Sauro (jeff_sauro_at_despammed.com)
Date: 11/30/04 

Date: Tue, 30 Nov 2004 18:55:55 +0000 (UTC)

The adjusted r-square cannot be negative by definition since any
number squared is positive. The r, or Pearson Product Moment
Correlation can be negative and can take the values anywhere from -1
to +1. You might be confusing the two. Since r can only take values
between –1 and +1, it’s square also by definition cannot be greater
than one (two decimals squared always make a smaller number).

Adjusted r-square and r are related. Once you have the correlation
between two variables say -.5, squaring this value (.25) provides you
with r-squared. You were correct in that the values for r-square and
adjusted r-square range from 0 to 1. The value is usually presented
as a percentage (25%) and is usually described as one variable
explains 25% of the variation in the other variable. It is also called
the coefficient of determination and when you are only describing a
relationship between two variables, then it’s simply Pearson’s r-
squared.

Adjusted r-square is a slight modification on the r-square that takes
into account the strength of the correlation and the sample size.
Also, recall the a correlation has two components, one describes the
strength of the relationship (that’s the –1 to 1) and the other
describes the significance of the relationship and is described using
the familiar p-value (unfortunately a lot of people leave off the
significance when reporting correlations.) A correlation can be
strong but not significant or weak but significant. A weak but
significant correlation for example would be (e.g. r = .12, p < .01).
The significance is derived using the sample size and the value of r.
With two variables it is evaluated against the t-distribution with n-2
degrees of freedom.

Jeff

On 29 Nov 04 07:09:38 -0500 (EST), Ingvar wrote:
>Hi
>
>I have a question regarding the adjusted R2 number.
>
>I thought that this number have to be between 0-1? but can this
number
>also be negative? or be above 1?
>
>
>/Ingvar

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