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I am sorry if this is duplicate - I couldn't find exactly what I was looking for anywhere else and have not used multiple regression in quite some time.

I have a data set with one dummy variable using '0' and '1' as the two levels. I only have one other predictor, which I have chosen to input as an interacting factor. The dummy variable indicates a within-subjects condition, and the other predictor is rate of responding (I work with rats). I believe that the rate of responding should be interacting with the condition so that in one condition (dummy variable = 0), the predictor should significantly predict the response variable, while in the other condition (dummy = 1) the numeric predictor should not have a relationship to the response variable. I will show my code for visual reference - I am using R:

reg <- lm(response ~ condition*rate, data = regData)
summary(reg)

My output shows that I have a significant intercept and that the numerical predictor's slope is also significant. The interaction factor is not significant. What does the significant intercept value mean in this case? Does it mean that the dummy variable '0' condition is significantly impacting the response variable, while dummy variable '1' does not? Since the interaction is also not significant, should that mean that the dummy and numerical predictors do not interact with each other? I will show output for visual reference:

Call:
lm(formula = response ~ condition * rate, data = regData)

Residuals:
    Min      1Q  Median      3Q     Max 
-20.982  -8.933  -1.464   6.245  31.196 

Coefficients:
                Estimate Std. Error t value Pr(>|t|)   
(Intercept)       30.543      9.548   3.199  0.00451 **
condition       -13.086     14.246  -0.919  0.36929   
rate              12.095      4.628   2.614  0.01663 * 
condition:rate   27.724     15.815   1.753  0.09491 . 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 15.3 on 20 degrees of freedom
Multiple R-squared:  0.4488,    Adjusted R-squared:  0.3661 
F-statistic: 5.428 on 3 and 20 DF,  p-value: 0.006762

I apologize I am not the best with regression; thank you in advance for your time. Please let me know if I should clarify anything above.

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When you fit an interaction, the choice of center and scale for the first order effects suddenly matters. You can, for instance, change them to have mean 0, and the regression will show a non-significant result for those values even though it doesn't affect the overall fitted values at all. That's because the interpretation of "condition" is an expected difference in response for groups differing by one unit in condition assuming rate=0.

If you were, in this case, interested in testing the hypothesis of whether the effect of condition were 0, you would also have to set the interaction term coefficient to 0. The "null" model would be a "rate" only effect.

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  • $\begingroup$ (+1) Nicely explained :) $\endgroup$ May 20 at 20:07
  • $\begingroup$ @AdamO thank you this is starting to make a lot more sense to me; would you suggest that I switch my condition levels so that the one I believe has the effect is set to '1' and the one which is currently '1' is set to '0' so it's assumed there is no effect? Should that fix my current model's interaction term as well? $\endgroup$
    – mbeasle2
    May 20 at 20:27
  • $\begingroup$ @mbeasle2 no I don't think you need to change anything about the model. The point is that the test output that is returned by default doesn't make sense. $\endgroup$
    – AdamO
    May 20 at 21:32

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