How to explain interaction variable in Linear regression?

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Hi,

The significant interaction between A (continous) and B (categorical)
means that the slopes of Y in relation to A are different for classes
of B. Since your categorical B was binary, the default reference class
(B2) was intecept, and the slope of A for (B2) was 0.0017799. However,
the slope of A for another class (B1) was 0.0017799+0.0059008. The
test shows that the slopes were significantly different.

HTH

Weidong

On Wed, Nov 23, 2011 at 12:20 PM, Chen Xiu
Hello everyone,

Recently, I faced a problem on explanatory of *Interaction variable* in
Linear Regression, could anyone give me some help on how to explain that?

the response variable Y is significantly correlated with *Interaction
variable X* which is consisted of Continuous predictor A and Categorical
predictor B. The Categorical predictor B has two factors B1 (value=1) and
B2 (value=0). The result is as follows:

Call:
lm(formula = Y ~ ... + *A:B*, data = ..., na.action = na.omit)

Residuals:
? ? Min ? ? ? 1Q ? Median ? ? ? 3Q ? ? ?Max
-0.84267 -0.29877 ?0.01961 ?0.32187 ?0.98519
Coefficients:
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Estimate ? ? Std. Error ? ? ?t value
Pr(>|t|)
(Intercept) ? ? ? ? ? ? ? ?0.7699265 ? ?0.5129588 ? ? 1.501 ? ? 0.1408
BB1 ? ? ? ? ? ? ? ? ? ? ? ? ?-0.6657700 ? 0.2668956 ? ?-2.494 ? ? 0.0166 *
A ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?0.0017799 ? 0.0007569 ? ? 2.352 ? ? 0.0235 *
... ? ? ? ? ? ? ? ? ? ? ? ? ? ? 0.2393929 ? 0.2334615 ? ? 1.025 ? ? 0.3110
... ? ? ? ? ? ? ? ? ? ? ? ? ? ?-0.3877065 ? 0.2317213 ? ? -1.673 ? ?0.1017
*BB1:A ? ? ? ? ? ? ? ? ? ? ?0.0059008 ?0.0025522 ? 2.312 ? 0.0257 **
---
Signif. codes: ?0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.4379 on 42 degrees of freedom
Multiple R-squared: 0.2813, ? ?Adjusted R-squared: 0.1958
F-statistic: 3.288 on 5 and 42 DF, ?p-value: 0.01354

*My questions:*

? 1. *How to explain the result of BB1:A correlated with Y? since BB1 is
? only one factor of B, and if it is combined with A, how does the
? combination mean?*
? 2. *Can I ?believe the significance of either single BB1 or A? Why?*

Thank you in advance for any possible help!

Chen,

a beginner in R and statistics

?--
Chen Xiu

Guest Fellow/ PhD Student
Department of Conservation Biology
UFZ - Helmholtz Centre for Environmental Research
Permoserstr. 15
D-04318 Leipzig
Germany

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