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:
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?
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?
Can I test contrasts with this linear regression model (e.g. Category1 vs. Category2)?
Should I include interactions?
I'd be glad for any help :-)