Re: st: opposite sign of one of the independent variables

[David Hoaglin <dchoaglin@gmail.com>]

Hi, Deepti.

It may be helpful to look at the "added variable plot" (also known as
the "partial regression plot") for the predictor variable whose sign
is opposite to what you expected.  In that plot, the vertical
coordinate is residual from regressing the dependent variable on all
the predictor variables except that one, and the horizontal coordinate
is the residual from regressing that one predictor variable on all the
other predictors.  A line fitted through the origin of the plot would
have slope equal to the coefficient of the one predictor in the
multiple regression.  Importantly, the plot would show whether the
relationship is nonlinear, and whether some data points are unduly
influential.

More generally, one often has little intuition for the sign or
magnitude of the coefficients in a multiple regression.  The
interpretation often given for an estimated regression coefficient in
a multiple regression is that it is summarizes the change in the
dependent variable corresponding to a change of 1 unit in the
predictor variable when all the other predictors are held fixed.  That
interpretation is too simple, and it is often simply incorrect.  In
general, the appropriate interpretation is that the estimated
regression coefficient summarizes the change in the dependent variable
corresponding to a change of 1 unit in the predictor variable AFTER
ADJUSTING FOR SIMULTANEOUS CHANGE IN THE OTHER PREDICTORS IN THE MODEL
(in the data at hand).  This is more complicated, but multiple
regression is not simple!  If the data have not been collected in a
way that held the other variables fixed, one cannot make broad
statements about holding them fixed, though it is usually satisfactory
to make predictions with them fixed in the region covered by the data
(i.e., one must be cautious about extrapolating beyond the data).

David Hoaglin

On Fri, Nov 11, 2011 at 2:05 AM, Deepti Garg <deeptigarg78@yahoo.com> wrote:
>
>
> Hi list,
>
> I have been working on the panel data in Stata. There are some variables in the data. When I run the regression, the sign of the coefficient I am getting on one of the variables is the opposite of what I am considering in my research. The sign is as expected if I delete one of the independent variables included in the regression model. However, the correlation coefficient does not show any correlation between the two variables. Could someone please guide me on that?
>
> Many many thanks in advance!
> Deepti

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