Re: st: about residuals and coefficients

[Joseph Luchman <jluchman@gmail.com>]

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

*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/faqs/resources/statalist-faq/
*   http://www.ats.ucla.edu/stat/stata/