Regression using two dependent variables

Question

I have some data for time series prediction. variable 1 is speed and variable 2 is time of the day the vehicle is starting. The output is time taken for the vehicle to reach destination. I used both variable 1 and variable 2 as inputs for svr using libsvm but later found out that variable 1 and variable 2 are dependent since speed of the vehicle depends on time of the day.

Can we do regression using two dependent variables as inputs? As I know the regression model y = a + b1.x1 + b2.x2 + ....+ e is for independent variables.

Answer 1

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?