[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.
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