Multiple Regression with four variables? Also in MATLAB

In summary, the speaker is seeking a regression model that accurately predicts the output of a function based on given inputs. They have a collection of data points and need a function that will fit the data exactly. They believe a fourth-order polynomial multiple regression may be the solution.
  • #1
KingNothing
882
4
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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  • #2
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.
 

1. What is multiple regression with four variables?

Multiple regression with four variables is a statistical method used to analyze the relationship between a dependent variable and four independent variables. It allows for the identification of the strength and direction of the relationships between the variables, as well as the ability to make predictions based on the data.

2. How do I perform multiple regression with four variables in MATLAB?

To perform multiple regression with four variables in MATLAB, you can use the 'fitlm' function. This function takes in the dependent variable and the four independent variables as inputs, and outputs a linear regression model that can be used to analyze the data and make predictions.

3. What are the assumptions for multiple regression with four variables?

The main assumptions for multiple regression with four variables are linearity, independence of errors, homoscedasticity, and normally distributed errors. This means that the relationships between the variables should be linear, the errors should be independent and have equal variance, and the errors should follow a normal distribution.

4. How do I interpret the results of multiple regression with four variables?

The results of multiple regression with four variables can be interpreted by looking at the coefficients and p-values for each variable. The coefficient represents the direction and strength of the relationship, while the p-value tells us if the relationship is statistically significant. Additionally, the overall model fit can be assessed using metrics such as R-squared and adjusted R-squared.

5. What are some common pitfalls to avoid when using multiple regression with four variables?

Some common pitfalls to avoid when using multiple regression with four variables include multicollinearity, overfitting the model, and failing to meet the assumptions of the analysis. Multicollinearity occurs when two or more independent variables are highly correlated, which can lead to unreliable results. Overfitting the model can occur when there are too many variables or interactions included, which can lead to a model that does not generalize well to new data. It is important to check for and address these issues before drawing conclusions from the analysis.

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