Multiple Regression with four variables? Also in MATLAB

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SUMMARY

The discussion centers on the need for a mathematical model to perform linear interpolation based on multiple independent variables in MATLAB. The user has three independent variables and a dependent variable Y, with specific input-output pairs provided. The goal is to create a regression model that exactly fits the given data points, suggesting the use of a fourth-order polynomial multiple regression. The user seeks clarification on whether multiple regression is the appropriate method for achieving this precise fit.

PREREQUISITES
  • Understanding of multiple regression analysis
  • Familiarity with polynomial regression techniques
  • Proficiency in MATLAB programming
  • Knowledge of linear interpolation methods
NEXT STEPS
  • Explore MATLAB's polyfit function for polynomial regression
  • Learn about piecewise functions in MATLAB
  • Research linear interpolation techniques in multiple dimensions
  • Study the implications of exact fitting in regression analysis
USEFUL FOR

Data scientists, statisticians, and MATLAB users who are involved in modeling complex relationships between multiple variables and require precise fitting of regression models.

KingNothing
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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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