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Date:         Wed, 21 Sep 2005 16:30:13 -0300
Reply-To:     Hector Maletta <hmaletta@fibertel.com.ar>
Sender:       "SPSSX(r) Discussion" <SPSSX-L@LISTSERV.UGA.EDU>
From:         Hector Maletta <hmaletta@fibertel.com.ar>
Subject:      Re: Regresssion Plot in SPSS
Comments: To: Karl Koch <TheRanger@gmx.net>
In-Reply-To:  <10351.1127317343@www11.gmx.net>
Content-Type: text/plain; charset="us-ascii"

Karl, 1. The general equation you write, with an "e" at the end, is the equation giving the observed value of an individual case. This observed value Y(i) is the sum of the predicted value _Y_(i) = a+bX(i)+cZ(i) plus an error e(i) specific to that individual. The term "e" is not a variance, but an individual error. It is by definition a random variable with zero mean, and the least square procedure ensures that the sum of all the e(i) squared is a minimum.

2. Your regression reveals that the variable B is not significant. Its estimated coefficient (-0.028) has a relatively large standard error (0.046) so that there is a large probability (0.534) that the true value is zero. Therefore, B is not to be used in the equation. You should run regression again, excluding variable B.

3. Suppose for a moment that you run the regression again, excluding B, and the value of coefficients for A and C remain the same (this is not likely to happen, but let say so for the sake of this explanation). For every subject, the predicted value of Y should be:

_Yi_ = 4.195 -0.779*Ai - 1.635*Ci.

(Y use underscores for _Y_ instead of the usual hat for convenience here).

For every subject, this prediction incurs an error ei=Yi- (_Yi_).

This equation predicting the value of Y uses the raw coefficients b, with the constant. If the variables are standardized into z-scores, with zero mean and unit standard deviation, the equation is expressed in terms of beta coefficients as follows (assume Yzi, Azi and Czi are the standardized values of the variables):

_Yzi_ = -0.319 * Azi - 0.442*Czi

Again with this equation there is an error (ezi) for each case, i.e. the difference between the observed standardized value Yzi and the predicted standardized value _Yzi_

4. The example you insert at the end of your mail includes the equation

Y = 4.195 - 0.319 * A - 0.442 * C + e

This equation mixes the constant for unstandardized values (4.195) with the coefficients for standardized values, which is erroneous and would produce terribly wrong results. And besides, you should not use the coefficients for A and C in the equation including B, but the coefficients to be found in a new run without including B.

Hector

> -----Original Message----- > From: SPSSX(r) Discussion [mailto:SPSSX-L@LISTSERV.UGA.EDU] > On Behalf Of Karl Koch > Sent: Wednesday, September 21, 2005 12:42 PM > To: SPSSX-L@LISTSERV.UGA.EDU > Subject: Re: Regresssion Plot in SPSS > > Hello, > > I have now the coefficients table that contains > unstandardized coefficients and standardized coefficients. It > looks like this: > > ---------------------------------------------------------------- > Model Unstd. Coeff. Std. Coeff. t Sig. > B Std. Error Beta > ----------------------------------------------------------------- > 1(Constant) 4.195 .070 58.971 .000 > A -.779 .042 -.319 -18.278 .000 > B -.028 .046 -.010 -.618 .534 > C -1.635 .064 -.442 -25.354 .000 > ----------------------------------------------------------------- > > Now, I have one question. In regression theory, the linear > regression equation (for three IVs) is defined as: > > Y = a + b1*X1 + b2*X2 + b3*X3 + e > > where a is a constant (distance on the Y axis) and b1, b2, b3 > the paramters and e the error variance (which is fixed but random). > > Given the fact that I have only two paramters being > significant, is this the correct equation? > > Y = 4.195 - 0.319 * A - 0.442 * C + e > > What would be e in this case? I have standard erros for each > parameter... > > Karl > > > > > Hi Karl, > > I don't know whether this is the optimal way but the > method I use has > > two steps > > 1) For the regression line use the code > > > > CURVEFIT /VARIABLES=dep_var WITH indep_var > > > > /CONSTANT > > > > /MODEL=LINEAR > > > > /PLOT FIT. > > 2) For getting the regression equation use > > > > REGRESSION > > > > /MISSING LISTWISE > > > > /STATISTICS COEFF OUTS R ANOVA > > > > /CRITERIA=PIN(.05) POUT(.10) > > > > /NOORIGIN > > > > /DEPENDENT dep_var > > > > /METHOD=ENTER indep_var . > > Hope this helps. > > Deepak > > > > On 9/21/05, Karl Koch <TheRanger@gmx.net> wrote: > > > > > > Hi all, > > > > > > how can I draw a regression diagram with the independent > variable on > > > the > > X > > > axis and the dependent variable on the Y axis in a plot together > > > with > > the > > > regression equation as a line ? > > > > > > Karl > > > > > > -- > > > GMX DSL = Maximale Leistung zum minimalen Preis! > > > 2000 MB nur 2,99, Flatrate ab 4,99 Euro/Monat: > > > http://www.gmx.net/de/go/dsl > > > > > > > -- > Lust, ein paar Euro nebenbei zu verdienen? Ohne Kosten, ohne Risiko! > Satte Provisionen f|r GMX Partner: http://www.gmx.net/de/go/partner > > __________ Informacisn de NOD32 1.1228 (20050921) __________ > > Este mensaje ha sido analizado con NOD32 Antivirus System > http://www.nod32.com > >


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