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Re: statistics questions
*To*: mathgroup at smc.vnet.net
*Subject*: [mg62378] Re: statistics questions
*From*: Bill Rowe <readnewsciv at earthlink.net>
*Date*: Tue, 22 Nov 2005 04:42:28 -0500 (EST)
*Sender*: owner-wri-mathgroup at wolfram.com
On 11/21/05 at 5:25 AM, chris.chiasson at gmail.com (Chris Chiasson)
wrote:
>I guess what I mean by "mean response" is that regression generates
>a least squares fit function for y, which then has a confidence
>interval associated with it: regression function + or -
>t[v,ci]*sqrt(variance/n)
Hmmm... I assume in the above formula "variance" is intended to be the variance of y? If so, this will not provide what is usually meant by a confidence interval for any of your data.
There are two sources of variability that need to be considered. First, there is the variation in the response variable at a fixed set of input conditions. Second, there is the variation in response caused by a variation of input conditions. So, if you want a confidence interval for the predicted response at a given set of input conditions both factors need to be addressed.
>I think if y is supposed to be a constant value, then least squares
>regression is equivalent to the mean of the data.
More or less true. If y is constant (independent of x) then fitting a linear model mx+b with m = 0 will cause b to be the mean of y. But when m is not forced to 0, b will only be close to the mean of y.
>Anywho, does anyone know of a way to obtain the regression function
>plus its confidence interval directly?
Simply put, I cannot make sense of this. Regression functions don't have confidence intervals. There are confidence intervals for the estimated parameters of a regression function and there are confidence intervals for any of the data points (either predicted or observed) but not the regression function itself.
>Am I just using statistics incorrectly here?
I don't know. You do seem to be using terminology in what appears to be a non-standard way which makes it difficult to know how to answer your question. Perhaps referring to a good text on regression would be helpful?
A couple of texts I like are
Applied Linear Regression by Sanford Weisberg
and
Fitting Equations to Data by Cuthbert Daniel & Fred S. Wood.
Of these two, I like the presentation in Weisberg better. But I think Daniel & Wood is referenced more frequently and in fact, is referenced by Weisberg.
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