# [R] Interpreting coefficients in linear models with interaction terms

Rolf Turner rolf.turner at xtra.co.nz
Sat Jan 12 23:33:11 CET 2013

```We don't do people's homework for them.

But since you seem to have put in at least a little bit of your
own effort .....  It is perfectly possible for there to be an interaction
without there being main effects.

Consider two factors A and B each with two levels.  Let mu_11 be
the population mean when A is at level 1 and B is at level 1, and so
on.

Suppose mu_11 = 1, mu_12 = -1, mu_21 = -1, and mu_22 = 1.

Then there are no main effects; A averages to 0, as does B.

But there is an elephant-ful of interaction.

cheers,

Rolf Turner

cheers,

Rolf Turner

On 01/13/2013 10:56 AM, theundergrad wrote:
> Hi,
>
> I am trying to interpret the coefficients in the model: RateOfMotorPlay ~
> TestNumber + Sex + TestNumber * Sex where there are thee different tests and
> Sex is (obviously) binary. My results are: Residuals:
>     Min     1Q Median     3Q    Max
> -86.90 -26.28  -7.68  22.52 123.74
>
> Coefficients:
>                   Estimate Std. Error t value Pr(>|t|)
> (Intercept)        29.430      6.248   4.710 4.80e-06 ***
> TestNumber2        56.231      8.837   6.364 1.47e-09 ***
> TestNumber3        75.972     10.061   7.551 1.82e-12 ***
> SexM                7.101      9.845   0.721    0.472
> TestNumber2:SexM  -16.483     13.854  -1.190    0.236
> TestNumber3:SexM  -24.571     15.343  -1.601    0.111
> ---
> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>
> Residual standard error: 40.97 on 188 degrees of freedom
> Multiple R-squared: 0.3288,	Adjusted R-squared: 0.3109
> F-statistic: 18.42 on 5 and 188 DF,  p-value: 7.231e-15
>
> I am looking for one number that will represent the significance of the
> interaction term. I was thinking of doing an F test comparing this model to
> one without the interaction. When I do this, I get a highly significant
> result. I am not exactly sure how to interpret this. In particular, it seems
> strange to me to have a significant interaction term without both
> independent variables being significant. Any advice would be highly
> appreciated.

```