Re: adjusted r-square
In short, you don't. If the number of terms in the model equals the number of observations you have much bigger problems than not being able to compute adjusted R^2. It should always be the case that the number of observations exceed the number of terms in the model otherwise you cannot calculate any of the standard regression diagnostics (F-stats, t-stats etc). My advice is get more data or remove terms from the model. If neither of these is an option you are stuck. Atul [EMAIL PROTECTED] wrote in message [EMAIL PROTECTED]">news:[EMAIL PROTECTED]... I have a doubt regarding adjusted r-square How do we calculate the adjusted r-square when the error degrees of freedom are zero ? (or in other words, number of samples is equal to the number of regression terms including the constant) Such a situation leads to a zero in the denominator in the expression for calculating adjusted r-square. Your help is highly appreciated. Thanks Atul = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: adjusted r-square
In sci.stat.consult Graeme Byrne [EMAIL PROTECTED] wrote: In short, you don't. If the number of terms in the model equals the number of observations you have much bigger problems than not being able to compute adjusted R^2. It should always be the case that the number of observations exceed the number of terms in the model otherwise you cannot calculate any of the standard regression diagnostics (F-stats, t-stats etc). My advice is get more data or remove terms from the model. If neither of these is an option you are stuck. It's worse than not being able to calculate regression diagnostics. You can't make *any* inferences beyond your observed data. Consider the degenerate case of trying to fit a bivariate regression line when you have only two observations. You'll *always* get a perfect fit because two points mathematically define a line. But that perfect fit will tell you absolutely nothing about the underlying relationship between the two variables. It's consistent with *any* possible relationship, including complete independence. You can't tell how far off your model is from the observations because there simply isn't any room for it to be off (room for the model to be off otherwise being known as degrees of freedom). A model with as many parameters as observations is equivalent to the observations themselves, and therefore testing such a model against the observations is the same thing as asking if the observations are equal to themselves, which is circular reasoning. = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: adjusted r-square
If the least-squares regression algorithm does not REQUIRE THE NUMBER OF OBSERVATIONS TO EXCEED THE NUMBER OF PREDICTORS, THEN THE REGRESSION ALGORITHM COULD BE USED TO SOLVE A SYSTEM OF SIMULTANEOUS EQUATIONS THAT WOULD HAVE NO ERRORS. Another interesting characteristic of Excel Regression is that it requires the number of observations to exceed the number of predictors. Fortunately, Colin Bell is working with the Excel folks at Microsoft to improve the numerous interesting characteristics of Statistics in Excel. -- Joe *** Joe H. Ward, Jr. *** 167 East Arrowhead Dr. *** San Antonio, TX 78228-2402 *** Phone: 210-433-6575 *** Fax: 210-433-2828 *** Email: [EMAIL PROTECTED] *** http://www.ijoa.org/resumes/ward.html *** --- *** Health Careers High School *** 4646 Hamilton-Wolfe *** San Antonio, TX 78229 * - Original Message - From: Graeme Byrne [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Wednesday, August 22, 2001 4:42 AM Subject: Re: adjusted r-square In short, you don't. If the number of terms in the model equals the number of observations you have much bigger problems than not being able to compute adjusted R^2. It should always be the case that the number of observations exceed the number of terms in the model otherwise you cannot calculate any of the standard regression diagnostics (F-stats, t-stats etc). My advice is get more data or remove terms from the model. If neither of these is an option you are stuck. Atul [EMAIL PROTECTED] wrote in message [EMAIL PROTECTED]">news:[EMAIL PROTECTED]... I have a doubt regarding adjusted r-square How do we calculate the adjusted r-square when the error degrees of freedom are zero ? (or in other words, number of samples is equal to the number of regression terms including the constant) Such a situation leads to a zero in the denominator in the expression for calculating adjusted r-square. Your help is highly appreciated. Thanks Atul = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ = = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: adjusted r-square
In sci.stat.consult Atul [EMAIL PROTECTED] wrote: : I have a doubt regarding adjusted r-square : How do we calculate the adjusted r-square when the error degrees of : freedom are zero ? You don't. you will have perfect prediction even for random numbers. = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: adjusted r-square
I would like to say, 'on the contrary,' but I'm not contradicting Eric
and the others' comments RE: "you don't calculate r^2 with insufficient
data."
If the number of observations equals the number of terms in the (regression)
model you do have a perfect fit, with no df, etc. This data is, nonetheless,
information. To use the Baysian terminology, you must have prior
information (i.e., strong belief) that the statistical error (variance)
is smaller than some of the observed effects. Then you can use a
few techniques, such as probability plots or raw rank selection, to select
out the larger effects. Where possible, one can then go back, run
some confirmation trials and establish if these effects are 'real.'
Where confirmation trials are not possible the accepted approach
:) is to assert loudly which effects you believe in, and go with them.
You did the study to make a prediction and pick a path to give you an
advantage, yes? Believing the large effects is the way to bet.
What odds you give this path depends in part on how much data you have.
One qualifier to the above: I do most of my work with designed
experiments - near orthogonal arrays. If you have significant confounding
in your design, you need to be aware of what it is so that you are not
led down the traditional garden path by your own data.
Jay
Eric Bohlman wrote:
In sci.stat.consult Graeme Byrne [EMAIL PROTECTED]>
wrote:
> In short, you don't. If the number of terms in the model equals the
number
> of observations you have much bigger problems than not being able
to compute
> adjusted R^2. It should always be the case that the number of observations
> exceed the number of terms in the model otherwise you cannot calculate
any
> of the standard regression diagnostics (F-stats, t-stats etc). My
advice is
> get more data or remove terms from the model. If neither of these
is an
> option you are stuck.
It's worse than not being able to calculate regression diagnostics.
You
can't make *any* inferences beyond your observed data. Consider
the
degenerate case of trying to fit a bivariate regression line when you
have
only two observations. You'll *always* get a perfect fit because
two
points mathematically define a line. But that perfect fit will
tell you
absolutely nothing about the underlying relationship between the two
variables. It's consistent with *any* possible relationship,
including
complete independence. You can't tell how far off your model
is from the
observations because there simply isn't any room for it to be off ("room
for the model to be off" otherwise being known as "degrees of freedom").
A model with as many parameters as observations is equivalent to the
observations themselves, and therefore testing such a model against
the
observations is the same thing as asking if the observations are equal
to
themselves, which is circular reasoning.
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USA
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adjusted r-square
I have a doubt regarding adjusted r-square How do we calculate the adjusted r-square when the error degrees of freedom are zero ? (or in other words, number of samples is equal to the number of regression terms including the constant) Such a situation leads to a zero in the denominator in the expression for calculating adjusted r-square. Your help is highly appreciated. Thanks Atul = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: adjusted r-square
On 21 Aug 2001, Atul wrote: How do we calculate the adjusted r-square when the error degrees of freedom are zero ? (Or in other words, number of samples is equal to the number of regression terms including the constant.) Such a situation leads to a zero in the denominator in the expression for calculating adjusted r-square. Depends in part on the expression you use, but in any case you also get a zero in the numerator. Cf. Draper Smith, Eq. (2.6.11b): the right-hand expression indeed contains (n-p) in the denominator, but it also includes (1-R^2) in the numerator, which produces the indeterminate quotient 0/0. In the middle expression of that equation, the quotient (residual SS)/(n-p) appears, which is also 0/0. All of which only emphasizes that the result of any analysis for which the error d.f. = 0 is meaningless: whether r-square, or regression coefficients, or error mean square, ... . Statistical conclusions cannot, in general, be drawn from such an analysis. Donald F. Burrill [EMAIL PROTECTED] 184 Nashua Road, Bedford, NH 03110 603-471-7128 = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
