Recently, I got a set of data where I try to predict the label (a continuous variable between 1000 - 3500) given 13 feature variables. By applying the kernel density approximation on the label (shown below), I was able to see a bi-modal distribution. I assume that this is because there are two "operating conditions". Each corresponding to each distribution.
After some research, I decided to separate the 2 operating conditions using a clustering technique such as k-means, GMM, DBSCAN, etc. After separating the 2 operating conditions, I was going to build a separate model for each distribution. During live implementation, depending on the distance of the new data to each cluster, I was going to use a mixed model to do the prediction on the output.
My questions are:
1. Is the above a right way to even tackle the problem?
2. What is the theoretical reason behind why one linear model cannot fit a bi-modal distribution. I assumed that by building a well generalized model, it should be able to predict all values within my label with adequate accuracy. And that the density of my labels should not really affect accuracy.