Multivariable time dependent regression

I'm trying to solve the following equation using multivariate regression. I have a target in 2 dimensions (gridcell,time) and four predictors in the same dimensions. The equation is below.

 A(t,i) = a(i) + b(i)*B(t,i) + c(i)*C(t,i) + d(i)*D(t,i) + e(i)*E(t,i)

Where, A, B, C, D, E are known, t and i are indices and I wish to find the values for a, b, c, d and e which minimise the difference between existing value of A and the predicted value of A.

t = 1:30 and i ~ 1:250000

Using the mvregress tool I'd need to build the inputs X and Y. I think Y in mvregress equals my A matrix but I cannot think how to make X.