Chen Xiu
2011-Nov-23 17:20 UTC
[R] How to explain interaction variable in Linear regression?
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]]
Weidong Gu
2011-Nov-23 20:32 UTC
[R] How to explain interaction variable in Linear regression?
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]] > > ______________________________________________ > R-help at r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. >