How do I do polynomial regression in MATLAB?


Many students ask me how do I do this or that in MATLAB.  So I thought why not have a small series of my next few blogs do that.  In this blog, I show you how to do polynomial regression.

  • The MATLAB program link is here.
  • The HTML version of the MATLAB program is here.
  • DO NOT COPY AND PASTE THE PROGRAM BELOW BECAUSE THE SINGLE QUOTES DO NOT TRANSLATE TO THE CORRECT SINGLE QUOTES IN MATLAB EDITOR.  DOWNLOAD THE MATLAB PROGRAM INSTEAD

%% HOW DO I DO THAT IN MATLAB SERIES?
% In this series, I am answering questions that students have asked
% me about MATLAB.  Most of the questions relate to a mathematical
% procedure.

%% TOPIC
% How do I do polynomial regression?

%% SUMMARY

% Language : Matlab 2008a;
% Authors : Autar Kaw;
% Mfile available at
% http://numericalmethods.eng.usf.edu/blog/regression_polynomial.m;
% Last Revised : August 3, 2009;
% Abstract: This program shows you how to do polynomial regression?
%           .
clc
clear all
clf

%% INTRODUCTION

disp(‘ABSTRACT’)
disp(‘   This program shows you how to do polynomial regression’)
disp(‘ ‘)
disp(‘AUTHOR’)
disp(‘   Autar K Kaw of https://autarkaw.wordpress.com’)
disp(‘ ‘)
disp(‘MFILE SOURCE’)
disp(‘   http://numericalmethods.eng.usf.edu/blog/regression_polynomial.m’)
disp(‘ ‘)
disp(‘LAST REVISED’)
disp(‘   August 3, 2009’)
disp(‘ ‘)

%% INPUTS
% y vs x data to regress
% x data
x=[-340  -280  -200  -120  -40  40  80];
% ydata
y=[2.45  3.33  4.30   5.09  5.72  6.24  6.47];
% Where do you want to find the values at
xin=[-300 -100 20  125];
%% DISPLAYING INPUTS
disp(‘  ‘)
disp(‘INPUTS’)
disp(‘________________________’)
disp(‘     x         y  ‘)
disp(‘________________________’)
dataval=[x;y]’;
disp(dataval)
disp(‘________________________’)
disp(‘   ‘)
disp(‘The x values where you want to predict the y values’)
dataval=[xin]’;
disp(dataval)
disp(‘________________________’)
disp(‘  ‘)

%% THE CODE
% Using polyfit to conduct polynomial regression to a polynomial of order 1
pp=polyfit(x,y,1);
% Predicting values at given x values
yin=polyval(pp,xin);
% This is only for plotting the regression model
% Find the number of data points
n=length(x);
xplot=x(1):(x(n)-x(1))/10000:x(n);
yplot=polyval(pp,xplot);
%% DISPLAYING OUTPUTS
disp(‘  ‘)
disp(‘OUTPUTS’)
disp(‘________________________’)
disp(‘   xasked   ypredicted  ‘)
disp(‘________________________’)
dataval=[xin;yin]’;
disp(dataval)
disp(‘________________________’)

xlabel(‘x’);
ylabel(‘y’);
title(‘y vs x ‘);
plot(x,y,’o’,’MarkerSize’,5,’MarkerEdgeColor’,’b’,’MarkerFaceColor’,’b’)
hold on
plot(xin,yin,’o’,’MarkerSize’,5,’MarkerEdgeColor’,’r’,’MarkerFaceColor’,’r’)
hold on
plot(xplot,yplot,’LineWidth’,2)
legend(‘Points given’,’Points found’,’Regression Curve’,’Location’,’East’)
hold off
disp(‘  ‘)

This post is brought to you by Holistic Numerical Methods: Numerical Methods for the STEM undergraduate at http://numericalmethods.eng.usf.edu, the textbook on Numerical Methods with Applications available from the lulu storefront, and the YouTube video lectures available at http://numericalmethods.eng.usf.edu/videos and http://www.youtube.com/numericalmethodsguy

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Autar Kaw

Autar Kaw (http://autarkaw.com) is a Professor of Mechanical Engineering at the University of South Florida. He has been at USF since 1987, the same year in which he received his Ph. D. in Engineering Mechanics from Clemson University. He is a recipient of the 2012 U.S. Professor of the Year Award. With major funding from NSF, he is the principal and managing contributor in developing the multiple award-winning online open courseware for an undergraduate course in Numerical Methods. The OpenCourseWare (nm.MathForCollege.com) annually receives 1,000,000+ page views, 1,000,000+ views of the YouTube audiovisual lectures, and 150,000+ page views at the NumericalMethodsGuy blog. His current research interests include engineering education research methods, adaptive learning, open courseware, massive open online courses, flipped classrooms, and learning strategies. He has written four textbooks and 80 refereed technical papers, and his opinion editorials have appeared in the St. Petersburg Times and Tampa Tribune.

2 thoughts on “How do I do polynomial regression in MATLAB?”

  1. I want to use a method for leveling a magnetic data which it’s name is “differential polynomial fitting” how I do it and what is the good matlab code for it?
    The technique is based on polynomial fitting of data points in 1D and 2D sliding windows
    A polynomial is fitted to data points in a 2D circular
    window that contains at least three flight lines. Then the same
    procedure is done inside a 1D window placed at the center of
    the 2D window. The leveling error is the difference between
    1D and 2D polynomial fitted data at the center of the windows

    Like

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