Message-ID: <CAEhWdG7Tn-WPXta316faTBphFYgsDxYzhwMLsb7XSbvhJjAdLw@mail.gmail.com>
Date: 2011-11-23T20:32:02Z
From: Weidong Gu
Subject: How to explain interaction variable in Linear regression?
In-Reply-To: <CAM2SJwT9HhMy7TTB0WpZYA+RedQyODH+j+=bXDv5YUv44j4H+A@mail.gmail.com>
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
<chenxiu.worldwide at googlemail.com> wrote:
> 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
>
> ? ? ? ?[[alternative HTML version deleted]]
>
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