Multiple Regression with four variables? Also in MATLAB

[KingNothing]

I am not sure if Multiple regression is what I want. I essentially have a function Y that is a function of three independent variables. I have a collection of points which have given Y-outputs.

So when given the inputs (1, 30, 60), Y = 5.
When given (1, 30, 210), Y=8.
When given (2, 70, 210), Y=30.

I need to write a function (I understand it will be piecewise) that does a linear interpolation with the inputs >> For example, I would like to model from the values above what Y is when given (1.5, 40, 85).

The trick is that my regressions MUST hit the given values. So when you plug (1, 30, 60) into my regression, it MUST give an output of 5. Can anyone tell me in words what exactly I am looking for here (mathematically)? Is multiple regression what I want?

 

[KingNothing]

In other words, in any given scenario, I will have 16 given points, (each specified by four variables) and I need a regression which will fit the data exactly. I get the feeling that this would be a fourth-order polynomial multiple regression.