Categorical variables in Linear Regression I learned that in order to use categorical variables in Linear Regression models, I have to convert them to several binary dummy variables. Binary dummy variables can either be 0 or 1, so they aren't continuuos, too. So why does it work better with binary dummies?
 A: It is all about interpretation.
Suppose you have a variable $X$ that can take three different values: A, B and C. And suppose we are interested only in the realtionship between $X$ and some response variable $Y$. If we do not encode $X$ with the dummy variables, but use $0$, $1$ and $2$ instead, then the model is:
$$ Y = \alpha + \beta X + \epsilon.$$
When we estimate $\beta$ with $\hat{\beta}$, then our interpretation of the model would be something like: "a change in X from group A to group B is associated with $\hat{\beta}$ changes in units of $Y$, whereas a change in X from group A to group C is associated with twice as much change!"
But what if you code the groups differently? For example, you can change $A$ and $B$, and you will get a completely different interpretation. The estimator may even be very close, but the conslusion will be different.
With dummy variables you wouldn't run into these kind of problems.
There are models where it makes sense: for example, if you have $X$ representing age groups. If the categorical variable is ordered and one expects that the difference between A and B is the same as between B and C, then yes, it may make sense to just forget about dummies and use the variables straightforward. But most often, the categorical variables stand for something like race or gender, where there is no ordering. Hence, dummy variables.
