MATLAB Multiple Regression with four variables? Also in MATLAB

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The discussion centers on the need for a mathematical function to model a dependent variable Y based on three independent variables, with the requirement that the function must exactly match specified output values for given input combinations. The user seeks a method to perform linear interpolation between these points to predict Y for new inputs, such as (1.5, 40, 85). There is a consideration of using multiple regression, but the user expresses uncertainty about whether this is the correct approach. The key requirement is that the regression must fit the data precisely, suggesting that a fourth-order polynomial multiple regression may be necessary to achieve this exact fit across the 16 specified data points. The discussion highlights the need for a piecewise function that can interpolate between these values while ensuring accuracy at the defined points.
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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?
 
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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.
 

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