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 MAY NOT TRANSLATE TO THE CORRECT SINGLE QUOTES IN MATLAB EDITOR OR IT MAY NOT PASTE HARD RETURNS. ****DOWNLOAD THE MATLAB PROGRAM**** DIRECTLY 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://nm.mathforcollege.com/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 http://autarkaw.wordpress.com')
disp(' ')
disp('MFILE SOURCE')
disp(' http://nm.mathforcollege.com/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://nm.mathforcollege.com, the textbook on Numerical Methods with Applications available from the lulu storefront, and the YouTube video lectures available at http://nm.mathforcollege.com/videos and http://www.youtube.com/numericalmethodsguy

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