# Interactions Effects in ANOVA using R

I would like to estimate and test interaction effects but I am unable to do so. The data consist of three factors with three levels and one response:

`````` X1 = c("250", "250", "250", "300", "300", "300", "350", "350", "350")
X2 = c("1.5", "3.0", "4.5", "1.5", "3.0", "4.5", "1.5", "3.0", "4.5")
X3 = c("0.24", "0.34", "0.44","0.34", "0.44", "0.24", "0.44", "0.24", "0.34")
Y = c("0.317", "0.377", "0.400", "0.426", "0.513", "0.408", "0.541", "0.444", "0.606")

df = data.frame(X1, X2, X3, stringsAsFactors = TRUE)
df\$Y= as.numeric(Y)
``````

Performing an ANOVA analysis we find out there is no significant effect of the factors to the response.

``````anova(lm(Y ~ X1+ X2+ X3, data = df))

Response: Y
Df   Sum Sq   Mean Sq F value Pr(>F)
X1         2 0.041173 0.0205863  8.6594 0.1035
X2         2 0.002867 0.0014333  0.6029 0.6239
X3         2 0.015650 0.0078250  3.2915 0.2330
Residuals  2 0.004755 0.0023773
``````

If I try to look at interactions I get a warning message.

``````anova(lm(Y ~ X1+ X2+ X3 + X1*X2 + X1*X3 + X2*X3, data = df))

Warning message:
In anova.lm(lm(Y ~ X1 + X2 + X3 + X1 * X2 + X1 * X3 + X2 * X3, data = df)) :
ANOVA F-tests on an essentially perfect fit are unreliable
``````

Can anybody help me to estimate and test interactions?

Thanks!