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# Re: st: interpretation for negative and positive slope combination of interaction term

 From David Crow To statalist@hsphsun2.harvard.edu Subject Re: st: interpretation for negative and positive slope combination of interaction term Date Thu, 9 May 2013 13:36:58 -0500

```Dear Nahla-

You're on the right track, but not quite right.  I find that it's
helpful to think of the meaning of each coefficient.  Let's boil your
model down to just the two variables (Market Value, MV, and
Overconfident Managers, OC), their interaction, and an intercept:

y = B0 + B1*(MV) + B2*(OC) + B3*(MV*OC) + u
and yhat = B0 + B1*(MV) + B2*(OC) + B3*(MV*OC)

Since OC is an indicator variable (overconfident = 1), when OC=0--that
is, for non-overconfident, or "realistic" managers", yhat is simply B0
+ B1*(MV) and the effect of market value is given by B1.  However,
when OC=1--that is, for overconfident managers--yhat is
B0+B1*MV+B2*OC+B3*MV*OC. Since OC=1, this simplifies to
B0+B1*MV+B2+B3*MV and the effect of MV is given by B1+B2+B3

Your calculation (-0.0566241 + 0.0596146= 0.003) leaves out the term
B2, the coefficient for OC.  So, the correct slopes are:

OC=0:  -0.0566241
OC=1:  -0.0566241 + -.1040174 + 0.0596146 = -.1010269.

In this case, the effects of market value appear to attenuate the
effects of overconfidence.

Hope this helps.

Best,
David

On Thu, May 9, 2013 at 8:20 AM, Nahla Betelmal <nahlaib@gmail.com> wrote:
>
> Dear Statalist,
>
>
> As you can see below, I have a interaction term between OC (dummy =1
> for overconfidence) and MV (continuous variable for market value). The
> interaction term is positive and significant. I want to calculate the
> slope against MB for overconfident managers which should be the
> coefficient of MV plus the coefficient of OC*MV.
> I am confused how to get this figure because MV is negative and OC*MV
> is positive. So, Should it be -0.0566241 + 0.0596146= 0.003? if this
> is true how can I interpret how many times the effect of MV is larger
> for overconfident managers??  0.003/0.0566.
>
> I am really confused and I highly appreciate your help please
>
>
>
>
> Linear regression                                      Number of obs =      49
>                                                        F( 10,    38) =    3.23
>                                                        Prob > F      =  0.0043
>                                                        R-squared     =  0.4385
>                                                        Root MSE      =  .08529
>
> ------------------------------------------------------------------------------
>              |               Robust
> earnings managment|      Coef.   Std. Err.      t    P>|t|     [95%
> Conf. Interval]
> -------------+----------------------------------------------------------------
> var1 |   .0081153   .0058432     1.39   0.173    -.0037137    .0199443
> MV |  -.0566241   .0353602    -1.60   0.118     -.128207    .0149588
>   var3|   .1992782    .093338     2.14   0.039     .0103252    .3882312
>  var4 |  -.0040891   .0109331    -0.37   0.710    -.0262219    .0180437
>    var5 |   .0817256   .1169071     0.70   0.489    -.1549405    .3183917
>   var6 |   .0291373    .026944     1.08   0.286    -.0254079    .0836825
> var7 |  -.0646094   .0320074    -2.02   0.051     -.129405    .0001863
> var8 |  -.0867868   .0311875    -2.78   0.008    -.1499227   -.0236509
>         OC|  -.1040174   .0556577    -1.87   0.069    -.2166906    .0086558
>  OC*MV |   .0596146   .0324333     1.84   0.074    -.0060433    .1252724
>        _cons |   .1643745   .0994735     1.65   0.107    -.0369991     .365748
>
>
> many Thanks
>
> Nahla Betelmal
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