# Regression technique for data comprised of categorical explanatory variables & a continuous response variable

i suppose one way to characterize data is by a combination of the variable types that comprises it:

Continuous/Continuous  |  Continuous/Discrete
-----------------------|---------------------
Discrete/Discrete      |  Discrete/Continuous

Each of the four cells comprising the 2x2 table just above is comprised of two descriptors, one for the Explanatory Variables (EV), which we'll assume are all of the same type, and one for the Response Variable (RV):

Explanatory Variable Type / Response Variable Type

The columns represent the EV type; the rows, the CV type.

Nearly all of the data i see can be placed in either of the two cells that comprise the first row.

So for instance, OLS Regression is a suitable model type for data in row1/col1; and for data in row1/col2, Logistic Regression is an appropriate model choice.

It's the second row, and in particular row2/col2, that my Question is directed to.

I'm aware of a few regression techniques like ordinal regression which handle a particular type of discrete variables (ordinary or rank, 1st, 2nd, 3rd,....) but i am interested in techniques for handling discrete data more generally, given that most categorical variables do not have an implicit ordinal relationship among the values that comprise them.

For instance:

Sex | City_of_Residence | Car_Make&Model | Married? | DUI? | Prior_3P_Claims?
F  |   Cleveland       |  Chevy Camaro  |   No     |  No  |   Yes

And the Response Variable is continuous--e.g., building a model to predict the quotes offered by major auto insurers--a price.

• I suspect this question is answered many times over in the threads you will find by searching our site – whuber May 24 '12 at 21:38

Of course, OLS makes assumptions beyond the idea that the dependent variable is continuous (or nearly so). e.g. it assumes that the residuals are independent and $\sim{N(0,1)}$
• @macro is right I mean $N(0,\sigma^2)$ and also about the errors, not the residuals, but we don't know the errors, only the residuals. – Peter Flom - Reinstate Monica May 25 '12 at 14:42