# R lm() interaction terms or effect? [duplicate]

I have quick look but I do not seem to find the answer to the following question. Basically, I get the following output when I run lm():

    Call:
lm(formula = y ~ as.factor(x1) * x2, data = data)

Residuals:
Min       1Q   Median       3Q      Max
-13.7237  -3.4391   0.8872   3.7576   8.3555

Coefficients:

Estimate Std. Error t value Pr(>|t|
(Intercept)                  8.448e+01  1.646e+00  51.318   <2e-16 ***
as.factor(x1)2               5.273e-01  2.967e+00   0.178   0.8597
as.factor(x1)3               2.442e+00  2.542e+00   0.961   0.3416
x2                          -3.259e-05  8.820e-05  -0.369   0.7134
as.factor(x1)2:x2           -2.641e-04  2.636e-04  -1.002   0.3215
as.factor(x1)3:x2           -2.728e-04  1.314e-04  -2.076   0.0434 *
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 5.809 on 47 degrees of freedom
(2 observations deleted due to missingness)
Multiple R-squared:  0.207, Adjusted R-squared:  0.1227
F-statistic: 2.454 on 5 and 47 DF,  p-value: 0.04683


The question is what is the interpretation of regression coefficients? More specifically what do the estimates of interaction mean? For example, is -2.728e-04 the interaction term or the effect of x2 on (x1)3?

Thank you very much in advance!

## 1 Answer

For the individuals with x1 equal to the reference value (here 1), an increase of x2 by one unit is associated to an increase of y by -3.259e-5.

For the individuals with x1 equal to 3, an increase of x2 by one unit is associated to an increase of y by -3.259e-5 + (-2.728e-4).