We are the happy birthday forum!!

You know something Adam I just watched back to future about two weeks ago. I should have known so forgive me forgive me for my transgression.  But I am old, I can't see well anymore and I know Brian (Traindiesel) . He likes to point out my very rare mistakes. Btw Brian I'm not taking the blame for this!!!!!

Dave

I think it is rude when celebrate some members birthday but not others, I have seen it on a certain other forum. 

The turbo encabulator is one of my favorites.  Another one from that book is the paper which is also the book's title - A Stress Analysis of a Strapless Evening Gown...and, of course, if they really want technical what follows should adequately address their concerns.


From Applied Regression Analysis 2nd Edition – Draper and Smith pages 8-24

Section 1.2 – Linear Regression: Fitting a Straight Line – pp 8-17

Section 1.3 – The Precision of the Estimated Regression – pp 17-22

Section 1.4 – Examining the Regression Equation pp 22-24



In the first two sections the authors describe and illustrate the method of least squares regression. At the beginning of Section 1.4 they state:

“Up to this point we have made no assumptions at all that involve probability distributions. A number of specified algebraic calculations have been made and that is all. We now make the basic assumptions that in the model



Yi = β0 + β1X1 + εi I = 1,2,3,….n



1. εi is a random variable with mean zero and variance σ2 (unknown) that is E(εi ) = 0, V(εi ) = σ2

2. εi and εj are uncorrelated, i ≠ j so that cov(εi , εj ) = 0

3. εi is a normally distributed random variable with mean zero and variance σ2 by(1)”



These assumptions relate only to the residuals. There are no other assumptions concerning any other aspect of least squares regression which means there are no assumptions concerning the distributions of either the Y’s or the X’s.



The fact that it is the behavior of the residuals alone that informs the correctness of the Y’s and X’s used in a regression analysis is one that is widely misunderstood. As a result one can find websites, peer reviewed articles in almost every branch of science, and even some textbooks which state the need for assessing the distributions of the Y’s and the X’s before running a least squares regression. Some of them go so far as to suggest that both Y and X must be normally distributed and must be continuous. In light of the description of the mechanics of least squares regression, and the assumptions about the residuals as outlined in Draper and Smith, statements concerning the need for prior distribution testing of the X’s or the Y’s are without merit.


The focus on the residual behavior is necessary because it is the residuals that are used to assess model term significance. The tests used for this purpose are the t-test and the F test. Both of these tests require approximate normality in the data. Since both tests are robust with respect to non-normality the question becomes one of defining “approximate normality”.


There are many tests one can employ to test for distribution normality. Some of the more popular are Shapiro-Wilk, Kolmogorov-Smirnov, Cramer-von Misis and Anderson-Darling. The problem with these tests is that they are very sensitive to non-normality. So much so that it is possible to take data from a random number generator where the underlying distribution is normal and have that data fail one or more of these tests.


...and no, I didn't have to type this in - it is just a copy/paste of a rebuttal to some false statements made by a referee about a paper on which I was a co-author.