RE: st: about residuals and coefficients

[Kayla Bridge <kayla.bridge@outlook.com>]

Thanks a lot, Daljit. The document you recommended is really helpful. And thank you all for all the suggestions. 

Best,
Kayla

----------------------------------------
> Date: Tue, 3 Sep 2013 19:32:04 -0700
> Subject: Re: st: about residuals and coefficients
> From: ddhadwal@gmail.com
> To: statalist@hsphsun2.harvard.edu
>
> Another Stata command/article that may be helpful to you in
> understanding/explaining the coefficients in the multiple regression
> equation is the following: Regression anatomy, revealed by Valerio
> Filoso in the Stata Journal (Volume 13 Number 1: pp. 92-106). If you
> don’t have access to the Stata journal, there’s an older version of
> the article here:
> http://works.bepress.com/cgi/viewcontent.cgi?article=1010&context=valerio_filoso
>
> Information on the command is available through: ssc des reganat
>
> Daljit Dhadwal
>
> On Tue, Sep 3, 2013 at 8:47 AM, John Antonakis <John.Antonakis@unil.ch> wrote:
>> Right....dominance analysis will do the trick.
>>
>> See also -shapely- (by Stas Kolenikov), available from ssc:
>>
>> ssc des shapley
>>
>> Best
>> J.
>>
>> __________________________________________
>>
>> John Antonakis
>> Professor of Organizational Behavior
>> Director, Ph.D. Program in Management
>>
>> Faculty of Business and Economics
>> University of Lausanne
>> Internef #618
>> CH-1015 Lausanne-Dorigny
>> Switzerland
>> Tel ++41 (0)21 692-3438
>> Fax ++41 (0)21 692-3305
>> http://www.hec.unil.ch/people/jantonakis
>>
>> Associate Editor:
>> The Leadership Quarterly
>> Organizational Research Methods
>> __________________________________________
>>
>>
>> On 03.09.2013 16:08, Joseph Luchman wrote:
>>> Hi Kayla,
>>>
>>> I might also mention that your interest seems to move toward
>>> evaluating the relative importance of the predictors in terms of how
>>> they reduce prediction error, which gets into how much of an overall
>>> metric such as the R^2 can be ascribed to a predictor.
>>>
>>> As David mentioned there's no way to separate how much of the R^2 is
>>> ascribed solely to one variable or the other unless they're orthogonal
>>> - but relative importance methods do something similar to that and can
>>> be interpreted along those lines. One such method is available
>>> through the - domin - (SSC) program I wrote in which the uncertainty
>>> in ascribing R^2 to a predictor is resolved by averaging (giving both
>>> predictors a portion).
>>>
>>> There are some other metrics available in that module too - take a
>>> look at - domin -'s help file, it may be of use to you for what you're
>>> trying to do.
>>>
>>> - joe
>>>
>>> Joseph Nicholas Luchman, M.A.
>>> ----
>>> Behavioral Statistics Lead | Fors Marsh Group
>>> Email: jluchman@forsmarshgroup.com
>>> forsmarshgroup.com
>>> ----
>>> Doctoral Candidate
>>> Industrial Organizational Psychology
>>> George Mason University
>>> https://www.researchgate.net/profile/Joseph_Luchman/
>>>
>>> On Mon, Sep 2, 2013 at 09:18 AM; Robson Glasscock <glasscockrc@vcu.edu>
>>> wrote:
>>>
>>>> A log-level model specification allows one to directly interpret the
>>>> percentage change in y per change in xi.
>>>
>>> On Mon, Sep 2, 2013 at 8:25 AM, David Hoaglin <dchoaglin@gmail.com> wrote:
>>>> Hi, Kayla.
>>>>
>>>> Your questions seem to be fairly basic ones about multiple regression.
>>>>
>>>> I hope you have looked at the three scatterplots (y vs. x1, y vs. x2,
>>>> and x2 vs. x1) to see how the data behave.
>>>>
>>>> R^2 provides information equivalent to
>>>> [sum(residual^2)]/[sum((y-ybar)^2)], often abbreviated as SSE/SST.
>>>> R^2 = 1 - (SSE/SST) is the percentage of the (squared) variation in y
>>>> that is accounted for by the regression model (i.e., by x1 and x2
>>>> together).
>>>>
>>>> In general, it is not possible to express R^2 as the sum of a
>>>> percentage accounted for by x1 and a percentage accounted for by x2.
>>>> The obstacle is correlation (in the data) between x1 and x2. Thus,
>>>> you can say how much variation x2 accounts for after adjustment for
>>>> x1, and you can say how much variation x1 accounts for after
>>>> adjustment for x2. To get those percentages, you can fit the simple
>>>> regressions involving only x1 and only x2 and subtract the values of
>>>> R^2 for those regressions from the value of R^2 for the regression
>>>> involving both x1 and x2. If x1 and x2 are uncorrelated (technically,
>>>> orthogonal), usually by design, it is possible to express the R^2 of
>>>> the two-variable model as the sum of the contributions of x1 and x2.
>>>>
>>>> I hope this discussion helps.
>>>>
>>>> David Hoaglin
>>>>
>>>> On Mon, Sep 2, 2013 at 5:57 AM, Kayla Bridge <kayla.bridge@outlook.com>
>>>> wrote:
>>>>> Dear all,
>>>>> I am currently running a simple regression, and try to explain the
>>>>> coefficients. The model and estimation results are the following.
>>>>> y=5.41+1.24*x1+.28*x2, R2=0.7, N=20
>>>>> (0.58) (3.4) (2.56)
>>>>> The t-stats are in parentheses.
>>>>> I'd like to know how much (in terms of percentage) of the change in y is
>>>>> accounted for by change in x1, and how much change in y by change in x2.
>>>>> Another question is: can I use [sum(residual^2)]/[sum((y-ybar)^2)],
>>>>> where ybar is the mean value of the dependent variable, to say something
>>>>> about percentage of residual, like smaller percentage of residuals implies
>>>>> that x1 and x2 are good explanatory factors for y?
>>>>> Any suggestion is greatly appreciated.
>>>>> Best,
>>>>> Kayla
>>>
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