# interpretation of dummy coded linear regression

I'm struggling with the interpretation of a regression model where a categorial variable (5 levels) is dummy coded. Here is the result of my calculation in R:

Call:
lm(formula = DV ~ Age + Gender + factor(Categorial) +
Continuous 1 + Continuous 2 + Continuous 3,
data = dat)

Residuals:
Min       1Q   Median       3Q      Max
-1.30058 -0.25326  0.00349  0.28123  1.49877

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept)           -0.42367    0.30694  -1.380  0.16842
Age                   -0.05949    0.02026  -2.936  0.00356 **
Gender                -0.01800    0.04828  -0.373  0.70952
factor(Categorial)2   -0.30625    0.12645  -2.422  0.01596 *
factor(Categorial)3   -0.03441    0.07752  -0.444  0.65736
factor(Categorial)4   -0.12603    0.09914  -1.271  0.20453
factor(Categorial)5   -0.08417    0.13269  -0.634  0.52630
Continuous 1           0.12080    0.04346   2.779  0.00575 **
Continuous 2          -0.06592    0.04383  -1.504  0.13354
Continuous 3          -0.06230    0.03475  -1.793  0.07392 .
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.4259 on 336 degrees of freedom
(6 observations deleted due to missingness)
Multiple R-squared:  0.1315,    Adjusted R-squared:  0.1057
F-statistic: 5.089 on 10 and 336 DF,  p-value: 6.353e-07


Ok. Age, Factor 2 of the categorial variable and the first continuous variable are significant predictors of the dependent variable. so far so good.

What I'm not understanding is:

1. The reference category of the dummy coded categorial variable is the intercept and the first category of the categorial variable. right? How do I interpret this?

2. When doing an anova with the categorial variable as a independent variable, this factor is a significant predictor. With the results of the linear model, one could conclude that this is only due to category 2, right?

3. Can I test contrasts with this linear regression model (e.g. Category1 vs. Category2)?

4. Should I include interactions?

I'd be glad for any help :-)

• It seems that you get confused by the difference between "variable" and "value of a variable". Here it seems that age and gender are recognised as scale variables (probably gender is 0 and 1?). The p value in variables age, gender and the 3 continuous mean that they are significant predictors. But the p value of factor 2 means that it is significantly different than the base line which is factor 1, in the presence of the other variables. Factor 2 it self can't be significant predictor as it is part of a variable. It doesn't make sense to say that. – AntoniosK Aug 9 '15 at 20:45