Re: Simple ? on standardized regression coeff.
d.u. wrote: I now think that the betas would have to be within [-1,+1]. Just for fun, regress Y on the 3 Xs. x1 x2 x3y 19.5 43.1 29.1 11.9 24.7 49.8 28.2 22.8 30.7 51.9 37.0 18.7 29.8 54.3 31.1 20.1 19.1 42.2 30.9 12.9 25.6 53.9 23.7 21.7 31.4 58.5 27.6 27.1 27.9 52.1 30.6 25.4 22.1 49.9 23.2 21.3 25.5 53.5 24.8 19.3 31.1 56.6 30.0 25.4 30.4 56.7 28.3 27.2 18.7 46.5 23.0 11.7 19.7 44.2 28.6 17.8 14.6 42.7 21.3 12.8 29.5 54.4 30.1 23.9 27.7 55.3 25.7 22.6 30.2 58.6 24.6 25.4 22.7 48.2 27.1 14.8 25.2 51.0 27.5 21.1 = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: Simple ? on standardized regression coeff.
In sci.stat.consult d.u. [EMAIL PROTECTED] wrote: : I now think that the betas would have to be within [-1,+1]. Suppose you do a : standarized regression with response Y, and have p variables (X matrix) already in. you're wrong; 1 varb = r sy/sx = r between -1 and 1 but for 2 var everything is partialed and while partial r is betwee -1 and 1, partial sigmas are not see kendall and stuart I think this is a counter example y x1 x2 2 1 1 -1 0 -1 -1 -1 0 = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: Simple ? on standardized regression coeff.
I now think that the betas would have to be within [-1,+1]. Suppose you do a standarized regression with response Y, and have p variables (X matrix) already in. Call the estimates for the current X matrix is beta_hat. Then by induction thru the standard two-step least-squares betas should be [-1,+1]: In the case p=1, beta_hat is [-1,+1]. If it's true for a certain p, then if you add in another variable Z, beta_hat for this new varible (gamma_hat)=inv(Z'RZ)Z'RY. This must also be [-1,+1]. When Z is added in, beta_hat for X becomes inv(X'X)X'(Y-Z*gamma_hat), which are again [-1,+1]. Then it's clear that beta-hats will be [-1,+1]. Hi, thanks for the reply. But is beta really just b/SD_b? In the standardized case, the X and Y variables are centered and scaled. If Rxx is the corr matrix [ ... ] = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: Simple ? on standardized regression coeff.
On Tue, 17 Apr 2001 16:32:06 -0500, "d.u." [EMAIL PROTECTED] wrote: Hi, thanks for the reply. But is beta really just b/SD_b? In the standardized case, the X and Y variables are centered and scaled. If Rxx is the corr matrix [ ... ] No. b/SD_b is the t-test. Beta is b, after it is scaled by the SD of X and the SD of Y. Yes, beta is the b if X and Y are 'scaled' to unit normal. -- Rich Ulrich, [EMAIL PROTECTED] http://www.pitt.edu/~wpilib/index.html = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: Simple ? on standardized regression coeff.
On Mon, 16 Apr 2001 20:24:10 -0500, "d.u." [EMAIL PROTECTED] wrote: Hi everyone. In the case of standardized regression coefficients (beta), do they have a range that's like a correlation coefficient's? In other words, must they be within (-1,+1)? And why if they do? Thanks! There is no limit on the raw coefficient, b, so there is no limit on beta= b/SD. In practice, b gets large when there is a suppressor relationship, so that the x1-x2 difference is what matters, e.g., (10x1-9x2). Beta is about the size of the univariate correlation when the co-predictors balance out in their effects. I usually want to consider a different equation if any beta is greater than 1 or has the opposite sign from its corresponding, initial r -- for instance, I might combine (X1, X2) in a rational way. -- Rich Ulrich, [EMAIL PROTECTED] http://www.pitt.edu/~wpilib/index.html = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: Simple ? on standardized regression coeff.
In sci.stat.consult d.u. [EMAIL PROTECTED] wrote: : Hi everyone. In the case of standardized regression coefficients (beta), : do they have a range that's like a correlation coefficient's? In other : words, must they be within (-1,+1)? And why if they do? Thanks! Only for 1 x variable where it is r. In othere cases it can be anything = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: Simple ? on standardized regression coeff.
Thanks. But how about when you have a X'X matrix that's diagonal after the transformation, then wouldn't you have -1?1 betas also? Elliot Cramer wrote: In sci.stat.consult d.u. [EMAIL PROTECTED] wrote: : Hi everyone. In the case of standardized regression coefficients (beta), : do they have a range that's like a correlation coefficient's? In other : words, must they be within (-1,+1)? And why if they do? Thanks! Only for 1 x variable where it is r. In othere cases it can be anything = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Simple ? on standardized regression coeff.
Hi everyone. In the case of standardized regression coefficients (beta), do they have a range that's like a correlation coefficient's? In other words, must they be within (-1,+1)? And why if they do? Thanks! = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
