How can Clustering (Unsupervised Learning) be used to improve the accuracy of Linear Regression model (Supervised Learning)
Just an idea:

You may be able to cluster a continuous variable and add the clusters as indicator in a linear regression jointly with an interaction term.

Say your linear model is income (inc) explained by years of job experience (exp)... 

inc = b0 + b1*exp + u. 

Now say you have two groups (low/high skilled workers). If you cluster inc in two groups, and add this as a dummy with interaction term, you may be able to increase the fit of the model.

inc = b0 + b1*exp + b2*indicator + b3*exp*indicator + u.

The idea is that low/high skilled workers will increase income contingent on experience in a different way (different slope). However, this approach requires that you can identify clusters well.

Edit: same strategy may work with clustering the X.