Clarifying collinearity

#1
I am trying to run a regression model where the Y is concentration and predictors are stove type (e.g., stove1, stove 2, stove 3) and fuel type (e.g., wood, crop waste, LPG). Stove 3 uses only the fuel type LPG, while Stove 1 and Stove 2 use wood and crop waste. When conducting the multiple linear regression, the fuel type LPG gives me a coefficient of "NA" (I am using R statistical software). I am not really clear as to why this is coming up as NA, other than to say something along the lines of because Stove 3 only uses 1 fuel type, LPG, it is returning NA for the regression results. Is this an example of collinearity and if not what is it and can I still use the regression model as I have set it up?
Thanks.
 
#2
Is your stove variable in fact 3 different binomial variables, such as stove_LPG (yes/no), stove_wood (yes/no), and stove_cropwaste (yes/no)?

If that's the case, you have to have one of those removed, because you otherwise get into a situation called linear dependency, which is a form of collinearity. In short, if you have a "yes" for one variable, the other 2 variables have to be a "no". Thus, the three variables are perfectly related to each other.
 
#3
No, there is one variable called "stove type" and it can be one of three choices - stove 1, stove 2, and stove 3. It seems that Stove 3 and the fuel type LPG are actually characterizing the same thing. Though I am not certain, given that, if I can still use the regression results as is.
 
#4
Well, for starters you can't place a categorical variable as an independent variable in your model.

Think about it this way: if LPG is coded as 1 and wood is coded as 2, the software, who doesn't know any better, assumes that wood > LPG. But of course there is no true direction there. So you first need to manipulate your data into a set of binomial variables where the stove is LPG (1 if yes, 0 if no), the stove is wood (1 if yes, 0 if no), etc.