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Re: st: theory reg vs. qreg


From   Yuval Arbel <yuval.arbel@gmail.com>
To   statalist <statalist@hsphsun2.harvard.edu>
Subject   Re: st: theory reg vs. qreg
Date   Mon, 29 Apr 2013 23:46:53 -0700

Roman,

The feature you are referring to is the fact that the regression line
passes via the sample mean.

This is the reason why the projected Y for mean(X) is mean(Y).

This outcome emanates from the derivation of the OLS formula, where we
minimize the RSS (Residual Sum of Squares).

As for qreg: it refers to a procedure where we minimize the absolute
sum of deviation from  the regression line. It is also called median
regression.

The answer to your question is therefore depends on whether the
distribution of the error term is symmetrical (in which case the
median equals the mean) or skewed to the right or left.

You should also take a look at the following textbook:

William H. Greene: Econometric Analysis, Seventh Edition, p. 248-249.
Greene describes his own research, which compares between estimates
obtained from the median and OLS regressions

On Mon, Apr 29, 2013 at 10:23 PM, Kasal Roman <kasalroman@gmail.com> wrote:
> be a little constructive and don't talk about some mud, its obvious that:
>
> <<
>>>sysuse auto
>>>reg price weight length
> you get the equation: Y1=a1*x1+a2*x2+b1
>>>reg price
> you get Y2=b2=mean(price)
>
> then (you can simply prove):
>
> Y1 = mean(weight)*a1+mean(length)*a2+b1 = b2 = Y2 = mean(price) = 6165.2
>
>
> theory shows the same
>
>
> On Mon, Apr 29, 2013 at 2:19 PM, William Buchanan
> <william@williambuchanan.net> wrote:
>> If the editor of the Stata journal and a colleague of John Tukey are questioning your claims, I would venture to say:
>>
>> 1. What you claim is clear is about as transparent as mud.
>> 2. Your notational conventions convey information in a way that is known only to you.
>> 3. You want help but are unwilling to provide anyone with enough information to help you.
>>
>> The members on the Statalist come from a variety of disciplinary backgrounds and different countries, so what may seem clear as day to you can be clear as mud to others.  If numerous people respond to you with the same general line of thought (e.g., the way you are explaining things is unclear), then it is extremely likely that the problem is the way you are describing your problem.  You could help yourself quite a bit if you provided more explicit and detailed information like listserv members continue to request.  In the meantime, you may benefit from reading the Statalist FAQ and follow some of the guidance regarding how to develop questions that are likely to yield responses.
>>
>> Billy
>>
>> Sent from my iPhone
>>
>> On Apr 29, 2013, at 5:08, Kasal Roman <kasalroman@gmail.com> wrote:
>>
>>> Later I will put it here more detailed but its quite clear that on the
>>> same dataset with a simple regression we get:
>>>
>>> Y1=Y2 when replaced "a2" for "mean(x)" in the equation
>>>
>>> thx
>>>
>>> r
>>>
>>>
>>> On Mon, Apr 29, 2013 at 1:54 PM, David Hoaglin <dchoaglin@gmail.com> wrote:
>>>> Roman,
>>>>
>>>> What is the fact?  How is Y1 related to Y2?  Apparently, you have
>>>> tried something with a -reg- command.  Please show us the command and
>>>> the output.
>>>>
>>>> David Hoaglin
>>>>
>>>> On Mon, Apr 29, 2013 at 7:49 AM, Kasal Roman <kasalroman@gmail.com> wrote:
>>>>> but this is a fact, just try it with the simple "reg" command:
>>>>>
>>>>> A) Y1 = b1
>>>>> B) Y2 = a2*X + b2
>>>>>
>>>>> on the same data
>>>>> then MUST be:
>>>>>
>>>>> Y2 = mean(x)*X + b2 = b1 = Y1
>>>>>
>>>>> and I'd like to know if there is something like this possible with the
>>>>> "qreg" command.
>>>>>
>>>>> thx
>>>>>
>>>>> roman
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-- 
Dr. Yuval Arbel
School of Business
Carmel Academic Center
4 Shaar Palmer Street,
Haifa 33031, Israel
e-mail1: yuval.arbel@carmel.ac.il
e-mail2: yuval.arbel@gmail.com

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