The standard regression model is not for independent inputs: no assumption is made about dependence between input variables. However, if there is an interaction effect, you might find that simply adding an interaction term into the regression model improves results: with this, your model becomes:
y = a + b1.x1 + b2.x2 + b2.x1.x2
I'm not sure what the state of SVR is, and whether you can put this option in directly; you can certainly fake it by adding that feature to the input, or use a regression method which directly supports it.
Another potential hazard is how you're representing time, as I can easily see this going wrong. What does your time input look like?