How to determine if a variable is categorical? I am looking at the variable vs response plot, and it seems categorical for most observations, but some are not.
Here is a picture of the plot.

Is there a threshold on the amount of "outliers" to determine whether a variable can be categorical?
edit: In the plot, x is the tax rate ($\times 100$) of various regions, and y is the median value of homes in the region.
 A: Tax rates are not categorical, they are continuous. A tax rate can vary - e.g. the sales tax in New York City is, I believe, 8.825%.
It appears that the data you have only has certain tax rates. But that is a feature of your data, not an underlying characteristic of the variable.  Categorical variables CANNOT take values in between other values. For example, "country of birth" is categorical. You were born in some country.  It makes no sense to say (e.g.) that the USA is halfway between Norway and Czechoslovakia - it is not even wrong, it's nonsensical.
A separate question is how you should model these data. I think linear regression is a good first attempt, then you should look at plots of the residuals. 
A: It certainly looks as if the variable plotted along the X axis can only take certain discrete values. 
However ... a categorical variable is one that takes values in a sample space where neither magnitude nor order have any meaning. Example: a medical study might record the gender of the patient (male/female), which is categorical .. the age (which is numeric) ... and which of several possible OTC cold medications they took -- also categorical. 
A categorical variable could have infinite support --- imagine sequences of letters from the Latin alphabet -- of arbitrary length. You have an infinite number of possibilities -- all categorical, because there is no natural way to measure the distance between them, or to rank them (although we could come up with a few).
Contrarywise, a numeric variable could admit to a discrete number of possible outcomes -- such as the spectrum of a particular chemical element.
