I'm using the concept of Hedonic regression in order to model the prices for real estates. I'm having some trouble with my approach.
What I have and what I do
- my data consists out of real estates with following charcteristics:
price | livingArea | propertyArea | condoFloorNumber | roomCount | elevator | garage | quiet | etc.
- I run a robust regression without intercept
lmRob(price ~ . -1)
What I want
- a model with which I can predict the price of real estates, but which are not in the used data set
- also it would be nice to have some constraints on the coefficients
- very often I get bad values for the coefficients
ex: bathroomCount = -80000. it's not possible that with a additive bathroom , the price of the house will sink with
also I tried to use the function
pclsin order to put some constraints on the coefficients, but this method gave very bad results. In the plot
Y = priceand
X = livingArea. as you can see, the regression line isn't correct.
- another thought was to transform the regression problem into a maximization or minimization problem, but didn't managed to do it
- also I tried to use different regression methods
lm, lmrob, ltsReg, MARS, but they also give me bad coefficients. (sometimes this bad coefficients make a good price estimation)
- I think that the big number of dummy variables damages a little bit the regression
Is my approach false?
Does someone have some hints, tricks for me? (I'm not a statistician)
This is how the plotted data looks like. LivingArea is the only non-dummy variable.
y = bX means y = b_0*X_0 + b_1*X_1 + ... + b_k*X_k which is an equation system like this: y = b_0*X_0 + b_1*X_1 + ... + b_k*X_k . . . y[n] = b_0*X_0[n] + b_1*X_1[n] + ... + b_k*X_k[n]
Did I got it right?
If so, isn't possible to add some inequality constraints equation to it. example:
b_0 >= 2000 b_2 <= b_0/2
I'm running the regression without intercept, because if all the characteristics of a real estate = 0, then of course it'S price = 0. Nobody would pay for an apartment with 0m². but it seems that the regression line where it was used an intercept (blue) looks far more better than the regression line without intercept (green). I can't understand why it is so. and why doesn't the regression line without intercept start at the point (0,0)?