Statistika For Life: 24 new messages in 14 topics

sci.stat.math
http://groups.google.com/group/sci.stat.math?hl=en

sci.stat.math@googlegroups.com

Today's topics:

==============================================================================
TOPIC: MI5 Persecution: Flying Eye (Mar/1999) (3254)
http://groups.google.com/group/sci.stat.math/browse_thread/thread/5e969f787135b51f?hl=en
==============================================================================

== 1 of 1 ==
Date: Sat, Nov 10 2007 9:17 pm
From: MI5Victim@mi5.gov.uk

Jackie King from the Flying Eye 14/3/99

Certainty level: 40%

In early March 1999, Capital Radio alleged they had received some emails,
one of which was forwarded to me. It contained the words, "you know this
bloke, he says we're trying to kill him, we should be done for attempted
manslaughter!" which Chris Tarrant had said in 1994.

Following these emails there was an explosion in abuse activity, both from
Capital Radio, and from MI5 themselves. MI5 followed me around and hurled
abuse at me. The following audio file contains what may be abuse from the
radio station.

Jackie King from the Flying Eye made these remarks on Sunday (14/3/99)
lunchtime 12.24pm; "gas main work being, er, HANDLED if you like (laughs,
embarrassed) outside Madame Tussauds, Euston Road obviously feeling the
backlash of that".

The key word is "handled", which she sounds embarrassed to be saying; to
me it looks like an attempt at a sexual slander. Capital Radio aren't even
pretending not to get at me any more. I asked Chris Tarrant several times
about his remark from 1994, and he has consistently avoided answering.

3254

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==============================================================================
TOPIC: How to obtain Critical Values by Monte Carlo
http://groups.google.com/group/sci.stat.math/browse_thread/thread/fcf9cf5624ababe9?hl=en
==============================================================================

== 1 of 3 ==
Date: Sun, Nov 11 2007 1:22 am
From: "Luis A. Afonso"

How to obtain Critical Values by Monte Carlo

It´s well known that concerning Test of Hypotheses the majority of the usual sample statistics distribution laws are only approximate. This fact leads frequently to errors in the final DECISIONS because the degree of approximation is generally ignored (or simply unknown). Therefore (among other strategies) the use of the Monte Carlo simulative method (MC) is a common practice since the last FOUR DECADES.
The idea behind MC is to synthesise randomly a large amount of the total Sample Space (SS) and then to build the sample statistics in study. From this generally very large set we find out the values (critical values) concerning the cumulative frequencies we want, for example, 0.005, 0.01, 0.025, 0.975, 0.99, 0.995.
From this values we obtain the CONFIDENCE INTERVALS of the two-tailed tests relative to the probabilities 99%, 98%, 95% the parameter be inside.
It worth to be noted that the sample statistics values need not to be ordered (a very time-consuming step): it is sufficient to classify them in very narrow (typically 0.001), classes.
Such an algorithm can be easily be carry out in a common Personal Computer as long as we are able to simulate the samples.

Luis A. Afonso

== 2 of 3 ==
Date: Sun, Nov 11 2007 8:19 am
From: Jack Tomsky

> How to obtain Critical Values by Monte Carlo
>
>
> It´s well known that concerning Test of Hypotheses
> the majority of the usual sample statistics
> distribution laws are only approximate. This fact
> leads frequently to errors in the final DECISIONS
> because the degree of approximation is generally
> ignored (or simply unknown). Therefore (among other
> strategies) the use of the Monte Carlo simulative
> method (MC) is a common practice since the last FOUR
> DECADES.
> The idea behind MC is to synthesise randomly a large
> amount of the total Sample Space (SS) and then to
> build the sample statistics in study. From this
> generally very large set we find out the values
> (critical values) concerning the cumulative
> frequencies we want, for example, 0.005, 0.01, 0.025,
> 0.975, 0.99, 0.995.
> From this values we obtain the CONFIDENCE INTERVALS
> of the two-tailed tests relative to the probabilities
> 99%, 98%, 95% the parameter be inside.
> It worth to be noted that the sample statistics
> values need not to be ordered (a very time-consuming
> step): it is sufficient to classify them in very
> narrow (typically 0.001), classes.
> Such an algorithm can be easily be carry out in a
> common Personal Computer as long as we are able to
> simulate the samples.
>
> Luis A. Afonso

Once again, this shows confusion between sample statistics and parameters. I strongly urge that no one pay any attention to such nonsense.

Jack

== 3 of 3 ==
Date: Sun, Nov 11 2007 9:24 am
From: John Smith

Luis,

How I have missed your ignorance. Your absence deprived me of the joy of pointing out your ignorance.

You write:
"From this values we obtain the CONFIDENCE INTERVALS of the two-tailed tests relative to the probabilities 99%, 98%, 95% the parameter be inside."

Either the parameter is INSIDE or OUTSIDE. The probability that the parameter is inside is either 100% or 0%. Same for the probability that the parameter is outside.

I thank Allah that he put a moron like you on this earth so that I could be amused.

John

==============================================================================
TOPIC: Log-Normal: Means and Variances
http://groups.google.com/group/sci.stat.math/browse_thread/thread/281495749e54b5f8?hl=en
==============================================================================

== 1 of 2 ==
Date: Sun, Nov 11 2007 2:20 am
From: Ray Koopman

On Nov 9, 4:12 pm, "Stratocaster" <sto...@verizon.net> wrote:
> I am posting to ask for help/verification regarding two relatively simple
> questions I have regarding Log Normal Random Variables. I believe my work
> is correct, but I would feel much more confident if someone else (who is
> more experienced with this) would confirm my belief. I am really just
> looking for a "yeah, that looks right" or, "Oh no you didn't". Thanks
>
> I am concerned with calculations of means and variances when either the X or
> Y term are modified by a constant (which I will denote with 'c'). i.e.
>
> X+c = Ln(Y) AND X = Ln(Y + c)
>
> (I suppose it must be said): Where X and Y are Random Variables and X is
> normally distributed with parameters 'mu' and 'sigma'.
>
> When I refer to "the regular expression for the mean/variance", I am
> refering to:
> where X = Ln(Y)
> E(Y) = e^[mu+(sigma^2)/2]
> V(Y) = (e^[2*mu+sigma^2])*([e^sigma^2]-1)
>
> Case I: X+c = Ln(Y)
>
> E(Y) = (e^c)*(regular expression for the mean)
> V(Y) = (e^c^2)*(regular expression for the variance)
>
> Case II: X = Ln(Y+c)
>
> E(Y) = (regular expression for the mean) - c
> V(Y) = (regular expression for the variance)
>
> I would supply my work, but it seems trivial, almost to trivial (which is my
> concern)... I will post it if you feel it is necessary.
> Thanks for taking the time to help me.

I parse e^c^2 as e^(c^2). For the case I variance,
I would write the multiplier as (e^c)^2 = e^(2c).

== 2 of 2 ==
Date: Sun, Nov 11 2007 12:02 pm
From: "Stratocaster"

"Ray Koopman" <koopman@sfu.ca> wrote in message
news:1194776437.255538.70330@t8g2000prg.googlegroups.com...
> On Nov 9, 4:12 pm, "Stratocaster" <sto...@verizon.net> wrote:
> >
> > Case I: X+c = Ln(Y)
> >
> > E(Y) = (e^c)*(regular expression for the mean)
> > V(Y) = (e^c^2)*(regular expression for the variance)
> >
> > Case II: X = Ln(Y+c)
> >
> > E(Y) = (regular expression for the mean) - c
> > V(Y) = (regular expression for the variance)
> >
> > I would supply my work, but it seems trivial, almost to trivial (which
is my
> > concern)... I will post it if you feel it is necessary.
> > Thanks for taking the time to help me.
>
> I parse e^c^2 as e^(c^2). For the case I variance,
> I would write the multiplier as (e^c)^2 = e^(2c).
>

This is another interesting topic to me. I usually interpret (e^c^2) as
(e^c)^2, but will agree that (e^c^2) is ambiguous (after all, you interpret
it differently from me). Regardless, thanks for taking the time to help me.

==============================================================================
TOPIC: MI5 Persecution: Johnny Boy (21/Aug/1998) (5428)
http://groups.google.com/group/sci.stat.math/browse_thread/thread/85a6daa9c0b9b031?hl=en
==============================================================================

== 1 of 1 ==
Date: Sat, Nov 10 2007 10:49 pm
From: MI5Victim@mi5.gov.uk

Virgin Radio-Johnny Boy (21/August/1998)

Certainty level: 60%

On Saturday 15 August 1998 I attended a gathering of contributors to
newsgroup uk.misc at London's Victoria railway station. Also present was
Simon G, who had previously given this description of what he would be
wearing;

At 06:36 AM 13/8/98 GMT, Simon wrote:
>further clarification to aid recognition, i'll be wearing
>a t shirt, a brown suede waistcoat, a brown suede miniskirt,
>& a pair of patchwork leggings (& may have a widebrimmed straw
>hat, too).

It is my belief that my persecutors, who monitor my home telephone line
(and consequently read all modem communications including email),
were aware of this meeting, and may even have observed the "meat" taking
place.

Following the "meat" it seemed to me that one or two attempts were made by
my persecutors to portray me as "gay", on the basis of Simon's suede
miniskirt, which in their inventiveness my persecutors attributed to me,
not Simon. (Just for the record, Simon is hetero, and has agreed to the
above email extract being published.) The following item from Johnny Boy's
Wheels of Steel (between 7pm-11pm, Friday 21/8/98) is one such attempt.

(conversation) (J=Johnny-Boy, H=Hipster)

J: Texas of course part of V98 this weekend enjoy it if you're going. Keep
your eyes out on Sunday in Chelmsford for Hipster, because he's going to
be there. What are you going to be wearing?

H: I'll be wearing my, er, my suede shorts.
(sycophantic laughter)

J: and believe me he ain't joking, he ain't joking. OK coming next at Virgin
on the Wheels of Steel...

Why do I think Hipster's "suede shorts" refers to Simon's mini-skirt?
Because "suede" in both cases (obvious!); because "suede shorts" indicates
"gay" which they were trying to pin on me; because "shorts" = something
short, such as a "mini"-skirt; and because the two DJs both laughed as soon
as Hipster said "suede shorts", they knew what the joke was, they knew that
they were meant (and probably paid) to find it funny.

5428

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==============================================================================
TOPIC: MI5 Persecution: Johnny Boy (19/June/1999) (7602)
http://groups.google.com/group/sci.stat.math/browse_thread/thread/bff97474ccf964e6?hl=en
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== 1 of 1 ==
Date: Sat, Nov 10 2007 11:50 pm
From: MI5Victim@mi5.gov.uk

Virgin Radio-Johnny Boy (19/June/1999)

Certainty level: 30%

I'm not quite sure about this one, so I've given it a one in three chance
of being about me. First the background.... from mid-March 1999 for some
three or four months, every weekend, I bombarded Westminster MPs with
faxes about the terrible, all-encompassing MI5 Persecution. (Jesting aside,
it really is terrible and all-encompassing, in the UK anyway.) Of course
each week some MPs replied; but in June 1999, after I'd been at it some
three months, I started getting "covert" feedback from Virgin Radio.

The first feedback I got was from Danny Baker, on Sunday 13th June. That
weekend I was sending an article which contained biting criticism of the
police inaction in this case. Danny Baker on his Virgin radio show started
an angry rant that "he knows it's rubbish", ie. he was rubbishing what I'd
said in that weekend's faxed article. Unfortunately I wasn't recording this
programme.

The next possible Virgin-Radio feedback was a week later on 19th June 1999.
This is contained in the audio file above, in which Johnny Boy on his
"Wheels of Steel" programme says;

"and if you would like to put a triple play together, ahhh.... because
quite frankly Hipster and me are running out of ideas...."

He goes on to counter Hipster's "how dare you" with a protestation that he
is "only joking".

What I reckon is that my article faxed to MPs that weekend was forwarded
by one of the recipients to Virgin Radio. My article had included the words;

"I am beginning to run out of both new topics and energy to write
these articles."

So what I reckon is that Johnny Boy read the article.... and rephrased
the above line "run out of ... new topics" to "running out of ideas".
I recognise that this is a pretty tenuous inference to make.... but do
listen to the audio file, from the "ahhh...." pause in JB's speech you
can guess he is about to say something "risky" and at someone's expense.
Anyway, I listen to the Wheels of Steel regularly and will continue to do
so, recording it as I always do - so any future funny remarks will get
immortalised on these pages!

7602

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==============================================================================
TOPIC: MI5 Persecution: Brighton 24/9/98 (9776)
http://groups.google.com/group/sci.stat.math/browse_thread/thread/af06ddb3a91f93ef?hl=en
==============================================================================

== 1 of 1 ==
Date: Sun, Nov 11 2007 12:48 am
From: MI5Victim@mi5.gov.uk

Brighton Day Trip - 24/Sept/1998

Certainty level: 5%

On a day trip to Brighton, carrying a minidisc recorder, I managed to
collect several indistinct instances of what I think were people swearing
at me. Between the 0.5 and 1.5 second marks of the above recording is
something that sounds like "nutter". I recorded at least three other much
more obscene sexual words on the same day.

I don't honestly think the "nutter" recorded here is part of the conspiracy
against me. I've been called similar things elsewhere, where it's been
blindingly clear that the insult does form part of the conspiracy - but
not in this case. This illustrates quite a worrying point - as a result of
the many years of abuse "in public", I now sometimes simply don't know
whether somebody is insulting me because they think I look like a dweeb, or
whether the conspiracy is in action. Sometimes, due to background noise
and people talking quietly relative to ambient noise, I can't be sure of
what's being said, even after listening to it again on my minidisc. Or put
another way, I now have a mild form of what I recognise to be occasional
auditory delusions - but these are fuelled by the many years of actual
verbal abuse.

9776

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==============================================================================
TOPIC: MI5 Persecution: POSK 2/2/98 (11950)
http://groups.google.com/group/sci.stat.math/browse_thread/thread/206458f8637474bd?hl=en
==============================================================================

== 1 of 1 ==
Date: Sun, Nov 11 2007 1:47 am
From: MI5Victim@mi5.gov.uk

POSK Cafe - 2/Feb/1998

Here are two independent segments, both of which occurred in London on
the same day, the first at a Polish cafe, the second on the Tube.

Certainty level: 100%

POSK is the Polish Social-Cultural Centre in Hammersmith, London. It has
quite a nice cafe which does pierogi, golabki etc. I went there with my
mother early in 1998. Seated at the window table were three Polish men
talking amongst themselves. One of them let rip with a sexual obscenity
which was clearly directed at me (it's the same one that's been heard
again and again since about November 1995), and which was recorded on my
minidisc walkman. I have not included it in the above excerpt, which shows
the reaction of another of the trio to the first man's swearing - namely,
"jestes swinia jednak" which in English is "nevertheless you're a swine".

Certainty level: 20%

Somewhere on the London Underground. "Psycho" (I think - a little unclear).

11950

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==============================================================================
TOPIC: MI5 Persecution: Leicester Square 9/2/98 (14124)
http://groups.google.com/group/sci.stat.math/browse_thread/thread/aaa5ae0e36f82d1b?hl=en
==============================================================================

== 1 of 1 ==
Date: Sun, Nov 11 2007 2:52 am
From: MI5Victim@mi5.gov.uk

Leicester Square - 9/Feb/1998

In February 1998 I spent some time in Leicester Square, in the West End
of London. This is a very busy area of London, and one which can be relied
on to produce "contacts". Capital Radio's offices and their cafe are
located here, the Trocadero is nearby, and the place is full of cinemas
and entertainment venues.

Certainty level: 100%

A young girl is heard to say, "Alright I'm going to talk to myself" to her
friends, followed by all of them laughing together, as I passed by.

Believe me, I do not look mad in real life, these young people would not
have directed their comments and laughter at me unless they had already
been told by others that I was ill. I am absolutely certain that their
behaviour was directed at me, and this audio file is particularly clear.

Certainty level: 60%

This one was recorded in a cafe in Green Park. Two women are talking to
each other, one of them says to the other, "something wrong with him",
with an emphasis on the "wrong".

The words "something wrong with him" have been repeated at me dozens of
times, at my former workplace in Canada, in England, etc. The words are
quite deliberately chosen to have two meanings; they obviously imply that
I am ill, without forcing the abusers to demean themselves by using
more pejorative terms, although they have shown that they have no
compunction in that area; and secondly, the words "wrong ... him" make
me at fault, and place the guilt for the abusers' wrongdoing on my
shoulders.

Certainty level: 30%

Recorded on a Victoria line tube train leaving Green Park station.
If you listen carefully you can pick up the word "hunchback". The speaker
had emitted a swear word immediately before this excerpt; both the swear
word, and the "hunchback", were (I believe) directed at me.

14124

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==============================================================================
TOPIC: Are there any honest statisticians?
http://groups.google.com/group/sci.stat.math/browse_thread/thread/c29564089afa3de3?hl=en
==============================================================================

== 1 of 2 ==
Date: Sun, Nov 11 2007 7:46 am
From: Ray Johnstone

Are there any honest statisticians?
My reason for asking can be found by looking at some of the
links on my home page. For example:

http://members.iinet.net.au/~ray/WHO.html

Edmund Burke is often credited as saying:

"The only thing necessary for the triumph of evil, is for good men
to do nothing."

Perhaps there are many statisticians, good men, doing nothing.

ray@iinet.com.au
www.iinet.com.au/~ray

== 2 of 2 ==
Date: Sun, Nov 11 2007 10:38 am
From: "Kenneth M. Lin"

I do not see anywhere in the article that they employed statisticians to
analyze their data.

"Ray Johnstone" <ray@iinet.com.au> wrote in message
news:4n8ej3128v6uhsbmk806pe9h6bvmg4h7dq@4ax.com...
> Are there any honest statisticians?
> My reason for asking can be found by looking at some of the
> links on my home page. For example:
>
> http://members.iinet.net.au/~ray/WHO.html
>
> Edmund Burke is often credited as saying:
>
> "The only thing necessary for the triumph of evil, is for good men
> to do nothing."
>
> Perhaps there are many statisticians, good men, doing nothing.
>
> ray@iinet.com.au
> www.iinet.com.au/~ray

==============================================================================
TOPIC: linear regression and multicollinearity
http://groups.google.com/group/sci.stat.math/browse_thread/thread/e22deec37b268ddf?hl=en
==============================================================================

== 1 of 5 ==
Date: Sun, Nov 11 2007 10:55 am
From: hberig@gmail.com

Thanks for answer!

I agree with you and R, in my second message I've tryed to explain
that R shows me the right results.

My difficulties are: understand how multicollinearity affects the
regression analysis and how it's related with a computational problems
(like ill and possed X'X matrix) and statistical problem (like with a
"small" change in predictors data may arrive to very different results
in the model).
I know the definitions eigenvalue, singular matrix and condition
number but I'm trying to understand implications in the statistics
area.
Again, thanks for answer!

On 7 nov, 02:26, David Winsemius <doe_s...@comcast.n0T> wrote:
> Dear DP;
>
> You _should_ get an error when you try to invert a singular matrix. R is
> behaving correctly.
>
> When I run you your data through the function lm() the output contains
> the line:
> "Coefficients: (1 not defined because of singularities)".
> Again R is giving appropriate warnings.
>
> > str(x.df)
>
> 'data.frame': 4 obs. of 4 variables:
> $ V1: num 1 1 1 1
> $ V2: num 2 4 6 8
> $ V3: num 3 6 9 12
> $ y : num 3 6 9 12
>
> > xdf.mdl<-lm(y ~ V2+V3,data=x.df)
> > summary(xdf.mdl)
>
> Call:
> lm(formula = y ~ V2 + V3, data = x.df)
>
> Residuals:
> 1 2 3 4
> 3.680e-16 -6.134e-16 1.227e-16 1.227e-16
>
> Coefficients: (1 not defined because of singularities)
> Estimate Std. Error t value Pr(>|t|)
> (Intercept) 1.110e-15 6.374e-16 1.742e+00 0.224
> V2 1.500e+00 1.164e-16 1.289e+16 <2e-16 ***
> V3 NA NA NA NA
>
> I do not understand what difficulties you are having because you are not
> producing the output that you feel is incorrect. It appears you may need
> to further study the meanings of "singular", "eigenvalue", and
> "condition number".
>
> --
> David Winsemius

== 2 of 5 ==
Date: Sun, Nov 11 2007 10:57 am
From: hberig@gmail.com

I'll look for "Matrix Algebra from a Statistician's Perspective",
thanks!
About your wikipedia links, I'll look for more data examples in
relation with the multicollinearity problem than deeper theory.
Thanks for answer!

On 7 nov, 07:05, "David Jones" <dajx...@ceh.ac.uk> wrote:
> hbe...@gmail.com wrote:
>
> > I appreciate very much your help! I'm trying to understand deeply the
> > essence of the subject, to understand why, in which cases and how much
> > may cause a problem or not (I think is more important than remember
> > rules, and some texts gives only rules without deep explanations, the
> > esscence). Then I'm trying to get and unify concepts from:
> >http://en.wikipedia.org/wiki/Linear_least_squares
> >http://en.wikipedia.org/wiki/Linear_regression
>
> To "understand deeply" you should also consider the approach via the "generalized inverse" or "pseudoinverse"of a matrix: seehttp://en.wikipedia.org/wiki/Generalized_inverse and, in particular the bit under "applications" on the pagehttp://en.wikipedia.org/wiki/Moore-Penrose_pseudoinverse
>
> However, you may do better by finding some appropriate-level text book than relying on wiki., as it looks as if this material is written at a highly technical level. You might try something like "Matrix Algebra from a Statistician's Perspective" by D A Harville (Springer, 1997).
>
> David Jones

== 3 of 5 ==
Date: Sun, Nov 11 2007 11:08 am
From: hberig@gmail.com

On 7 nov, 14:54, Jack Tomsky <jtom...@ix.netcom.com> wrote:
> > Hi,
>
> > I have 2 questions:
>
> > 1)
> > I know that multicollinearity may cause some
> > problems, but may be not?
> > Suppose I've X1, X2 predictors and Y response
> > variable with the
> > following data:
> > X1 X2 Y
> > -----------
> > 1 2 3
> > 2 4 6
> > 3 6 9
> > 4 8 12
>
> > X2 = 2*X1, there exists multicollinearity between X1
> > and X2.
>
> > When I try a least squares regression for Y = b0 +
> > b1*X1 + b2*X2
> > I expect Y =X1 + X2
> > (b0 = 0 and b1= b2 = 1), the unbiased and minimum
> > variance estimator
> > But with a software package, exactly R, I get that
> > the system is
> > singular.
> > It's ok, if I have the X matrix
> > > X
> > [,1] [,2] [,3]
> > [1,] 1 1 2
> > [2,] 1 2 4
> > [3,] 1 3 6
> > [4,] 1 4 8
>
> > X and then R try to invert X' X (in R notation t(X)
> > %*% X) that is not
> > invertible and I get an error.
>
> > Of course is not a real world case problem but, this
> > is an error? is
> > common in other packages than R?
>
> > Thanks!
> > hb
>
> The least-squares solutions in your example are all of the form, b0=0, b1=c, and b2=(3-c)/2, for any specified c.
>
> One way of getting around the multicolinearlity is to reduce the problem to one of estimating two (rather than three) parameters. Restate the model as
>
> Z = b0 + b2*X2,
>
> where Z = Y-c*X1.
>
> Then Zi = (3-c)*i and X2i = 2i.
>
> X'X is a 2 by 2 nonsingular matrix whose first row is (N, Sum(2i)) and whose second row is (Sum(2i), Sum((2i)^2)).
>
> Specifically, the first row is (N, N(N+1)) and the second row is (N(N+1), 2N(N+1)(2N+1)/3).
>
> X'Z is a 2 by 1 vector whose elements are (3-c)N(N+1)/2 and (3-c)N(N+1)(2N+1)/3.
>
> After multiplying X'X^(-1) by X'Z, you end up with b0 = 0 and b2 = (3-c)/2.
>
> Jack

Thanks Jack!
I know about some ways of getting around with the multicollinearity
problem (like eliminating variables or getting principal components of
the predictor variables and use the rotated base). I'm trying to
understand how variations in the data variates the quality of results.
With (1) orthogonal variables we haven't multicollinearity problem,
and (2) a (quasi perfect) linear dependence in predictor variables
(like X4 aprox= 2X1 + 3X2 - X3) we have a strong multicollinearity
problem and a small change in predictors data may cause big changes in
the model (this is the worst problem using multicollinear
predictors?); between the extreme cases (1) and (2) I'm trying to
visualize in some way how the predictors data affects the model.
Again, Thanks for answer!

== 4 of 5 ==
Date: Sun, Nov 11 2007 2:17 pm
From: David Winsemius

hberig@gmail.com wrote in news:1194807316.448951.136200@d55g2000hsg.googlegroups.com:

> I agree with you and R, in my second message I've tryed to explain
> that R shows me the right results.
>
> My difficulties are: understand how multicollinearity affects the
> regression analysis and how it's related with a computational problems
> (like ill and possed X'X matrix) and statistical problem (like with a
> "small" change in predictors data may arrive to very different results
> in the model).
> I know the definitions eigenvalue, singular matrix and condition
> number but I'm trying to understand implications in the statistics
> area.

Short answer following Myers, "Classical and Modern Regression with
Applications". The variance of predictions is proportional to
x_i'*inv(X'X)x_i. Some of the diagonal elements of inv(X'X) will be
large when multicollinearity exists. "Variance inflation factors" (VIF)
are the diagonal elements of the singular decomposition of X'X.

Perhaps reading one of these items (found with a search on VIF and
"condition number") will help:
<http://www.nd.edu/~rwilliam/stats2/l11.pdf>
<http://www.masil.org/documents/multicollinearity.pdf>

Adding CRAN to that search strategy to get r-specific hits produced:
<http://www.sci.usq.edu.au/courses/STA3301/StudyBook.pdf>
..see pages 3.26-3.33

And:
<http://www-personal.umich.edu/~jwbowers/CLASSES/PS532f07/HANDOUTS/handout7.pdf>
..see pages 2 and 14 and any pages in between that catch yur eye.

The condition number is obtained in R with:
kappa(<matrix or model object>)

--
David Winsemius

== 5 of 5 ==
Date: Sun, Nov 11 2007 7:47 pm
From: Richard Ulrich

On Sun, 11 Nov 2007 11:08:10 -0800, hberig@gmail.com wrote:

> On 7 nov, 14:54, Jack Tomsky <jtom...@ix.netcom.com> wrote:
[snip, previous]
>
> Thanks Jack!
> I know about some ways of getting around with the multicollinearity
> problem (like eliminating variables or getting principal components of
> the predictor variables and use the rotated base). I'm trying to
> understand how variations in the data variates the quality of results.
> With (1) orthogonal variables we haven't multicollinearity problem,

right.

> and (2) a (quasi perfect) linear dependence in predictor variables
> (like X4 aprox= 2X1 + 3X2 - X3) we have a strong multicollinearity
> problem and a small change in predictors data may cause big changes in
> the model (this is the worst problem using multicollinear
> predictors?);

Is change of coefficients seen as a problem by you?

If two models give (almost) exactly the same predictions,
then it is fair, by *most* standards, to say that they are the
same model. Or, "The same model can be described in
more than one way."

The "problem" when two models exist with different coefficients
depends on other some other criterion. Does one replicate
or cross-validate better than the other? - either of two solutions
may work as well if the non-independence is mechanical (using B
C, and B/C). Having suppressor variables that are incidental seems
to be a good clue that one particular equation will not be robust.

"Sense" is another sort of criterion. If you have highly correlated
variables, it can be plain silly to pretend that you have coefficients
that are worth "interpreting" for their nominal values. I like to
combine the variables where it makes sense to combine them,
leaving pretty good independence, so that I *can* make sense
of coefficients. But you cannot start out by "making sense" when
you read a set of correlated partial regression coefficients, unless
you are already aware of which outcomes are effectively the same.

> between the extreme cases (1) and (2) I'm trying to
> visualize in some way how the predictors data affects the model.
> Again, Thanks for answer!

--
Rich Ulrich, wpilib@pitt.edu

http://www.pitt.edu/~wpilib/index.html

==============================================================================
TOPIC: The genesis of Critical Values
http://groups.google.com/group/sci.stat.math/browse_thread/thread/34b14065736520a7?hl=en
==============================================================================

== 1 of 2 ==
Date: Sun, Nov 11 2007 12:32 pm
From: "Luis A. Afonso"

The genesis of Critical Values

A pair, or couple, of idiots (that are unable to understand the basis of DECISIONS of Hypotheses Tests) compelled me to open a new thread concerning the same matter.
I apologize Sci. Stat. Math.
Critical Values are a direct consequence of the Test Statistics Distribution Function.
In order to legitimate Monte Carlo two questions are pertinent:
_1) Am I able to simulate a large set of the Sample Space?
_2) Can I attain a set of the Test Statistics Values such that its cumulative frequencies be very close to the theoretical Distribution, difference in absolute value = d? How many values (n) should I to consider?
The answer is YES.
In fact the Dvoretzky-Diefer-Wolfowitz assures us that 2) is surely attained:
________p(d>e)<= 2*EXP(-2*n*e*e)

Suppose that n=1E7 , e=5E(-4)= 0.0005
Then the right side: 2*EXP(-5) = 0.013.
The final prove is that I was able to obtain exactly the Critical Values in the case of known exact theoretical Sample Distributions (namely Normal and Chi-Square).
Furthermore I found the values relative to other known Distributions obtained exactly by Random Simulation.

Only those that didn't read any Bibliography the last 40 years can be surprised before these results.
When reality is uncomfortable something's wrong.

_____
Luis A. Afonso

== 2 of 2 ==
Date: Sun, Nov 11 2007 1:49 pm
From: John Smith

Luis,

"A pair, or couple, of idiots (that are unable to understand the basis of DECISIONS of Hypotheses Tests) compelled me to open a new thread concerning the same matter."

It's obvious why you open a new thread, because your last thread displayed your ignorance.

Before you move on to a new display of your ignorance, let's finish discussing your last one.

On Nov 11, 4:22 am

You wrote:
"From this values we obtain the CONFIDENCE INTERVALS of the two-tailed tests relative to the probabilities 99%, 98%, 95% the parameter be inside."

Either the parameter is INSIDE or OUTSIDE. The probability that the parameter is inside is either 100% or 0%. Same for the probability that the parameter is outside.

Please defend your assertion that there can be a 99% probability that a parameter is inside the interval.

John

==============================================================================
TOPIC: why is probability and statistics a hard subject?
http://groups.google.com/group/sci.stat.math/browse_thread/thread/35284645dd365175?hl=en
==============================================================================

== 1 of 1 ==
Date: Sun, Nov 11 2007 3:37 pm
From: Robert Dodier

Nasser Abbasi wrote:

> I am taking a course in probability and statistics now. It is at
> the level of upper division / first year graduate.
>
> This is the hardest course I have ever taken so far, Yet, I am
> not sure why it is hard.
>
> Looking at the math on its own, it is hard, but manageable,
> upper level calculus I would say. But for some reason, I find the
> whole subject hard to do well at.

Belief and decision analysis is greatly simplified by adopting
Bayesian probability to represent beliefs, and utility theory to
represent values. Combining the two yields what is typically
called decision theory.

Conventional statistical hypothesis testing (either Fisher's or
the Neyman-Pearson variety) is essentially an attempt to formulate
a decision theory without introducing the probability of hypotheses
and without taking value (utility) of actions into consideration.
This leads to quite needless, and quite useless circumlocutions.
Naturally it is very difficult for students.

My advice to you, Nasser, is to drop whatever class you are taking,
and if there are no proper decision theory classes at your school,
then just study on your own. As I was saying, it is quite simple and
a bright person like yourself doesn't need professor to explain it.

FWIW

Robert Dodier

PS. Here are some readings for you. Some of these were
recommended to me but I haven't looked at all of them.

Probability theory: the logic of science, by E.T. Jaynes
(now published, maybe still on the web somewhere)

Probability, frequency, and reasonable expectation, by R.T. Cox
American J. Physics, 14(1):1--13, 1946.
(reprinted in Shafer & Pearl, Readings in Uncertain Reasoning)

Making Hard Decisions, by Robert Clemen

Bayesian Data Analysis, by Gelman, Carlin, Stern, & Rubin

Decision Analysis for Management Judgment
by P. Goodwin, G. Wright

Thinking and Deciding, by J. Baron

Probabilistic Methods for Financial and Marketing Informatics
by Richard Neapolitan

Decision Analysis, by Howard Raiffa

Smart Choices: A Practical Guide to Making Better Decisions
by John Hammond, Ralph Keeney, Howard Raiffa
http://www.amazon.com/Smart-Choices-Practical-Making-Decisions/dp/0767908864

Decision Tree Primer, by Craig Kirkwood
http://www.public.asu.edu/~kirkwood/DAStuff/decisiontrees/index.html

==============================================================================
TOPIC: Solutions
http://groups.google.com/group/sci.stat.math/browse_thread/thread/fb060dd5a91f7056?hl=en
==============================================================================

== 1 of 1 ==
Date: Sun, Nov 11 2007 3:39 pm
From: Kal

Could you please send me the solutions for Fundamentals of
Differential Equations and Boundary Value Problems by Nagle, Saff and
Snider.
Thanks!!
-Kal

==============================================================================
TOPIC: Sample Size
http://groups.google.com/group/sci.stat.math/browse_thread/thread/ff810bbd9cf63993?hl=en
==============================================================================

== 1 of 2 ==
Date: Sun, Nov 11 2007 6:50 pm
From: Mike

In article <TKhZi.3260$pr6.1363@newsfe06.phx>, nma@12000.org says...
>
> "Proginoskes" <CCHeckman@gmail.com> wrote in message
> news:1194677452.756563.73500@v29g2000prd.googlegroups.com...
> > On Nov 9, 1:27 pm, Gregory <> wrote:
> >> I have a bundle of files that I can be assessed as being either YES or
> >> NO.
> >>
> >> Sometimes there are 300.
> >>
> >> Sometimes there are 2000
> >>
> >> Sometimes there are 10000
> >>
> >> How do you work out how many you need to sample to give an assessment
> >> of the lot + or - x% accuracy? Is there a standard calculation? Does
> >> anyone know of any websites that explain all that?
> >
> > You're looking for some kind of statistical method. I suspect this is
> > a basic question. (Cross-posted to sci.stat.math for this reason;
> > someone there can probably give you an answer without having to look
> > it up.)
> >
> > --- Christopher Heckman
> >
>
> I think you can use the confidence interval for population propertion for
> this problem.
>
> The formula is this,
>
> let n=sample size (>=20)
> let p=propertion of YES to NO in the sample picked.
>
> Then the propertion of YES to NO in the population is (with 95%
> confidence) will be within
>
> p +- 1.96 * Sqrt( p*(1-p)/n )
>
> So to make p closer to the true population propertion, make n larger. The
> large n is, the smaller the confidence interval is.
>
> Nasser
>
...and note that the assesment is independant of the population size as long as:
1) the population size is sufficient to supply n samples,
2) the samples can be chosen 'randomly' from the population.

Mike

== 2 of 2 ==
Date: Sun, Nov 11 2007 8:38 pm
From: Allen McIntosh

[I'm directing followups away from alt.math.recreational]

Mike wrote:
> In article <TKhZi.3260$pr6.1363@newsfe06.phx>, nma@12000.org says...
>> let n=sample size (>=20)
>> let p=proportion of YES to NO in the sample picked.
>> Then the propertion of YES to NO in the population is (with 95%
>> confidence) will be within
>> p +- 1.96 * Sqrt( p*(1-p)/n )
>> So to make p closer to the true population propertion, make n larger. The
>> large n is, the smaller the confidence interval is.
> ...and note that the assesment is independent of the population size as long as:
> 1) the population size is sufficient to supply n samples,
> 2) the samples can be chosen 'randomly' from the population.

To elaborate a little on what Mike says, and to mention a few assumptions:

1) The formula 1.96*sqrt(...) uses a Normal approximation that doesn't
work well if n*p is too small

2) All this assumes that the OP is sampling without replacement

3) As Mark points out the OP is sampling from a finite population, so
that 1.96*sqrt(...) should really be multiplied by sqrt(1-n/N) where n
is the sample size and N is the population size. This term matters when
the sample is a significant fraction of the population, and matches the
intuition that when the sample is the entire population, there is no
uncertainty in the result

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