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
SUMMARY
INTRODUCTION
INPUTS
DISPLAYING INPUTS
THE CODE
DISPLAYING OUTPUTS

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 http://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(' ')

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

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('  ')

  
INPUTS
________________________
     x         y  
________________________
 -340.0000    2.4500
 -280.0000    3.3300
 -200.0000    4.3000
 -120.0000    5.0900
  -40.0000    5.7200
   40.0000    6.2400
   80.0000    6.4700

________________________
   
The x values where you want to predict the y values
  -300
  -100
    20
   125

________________________

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('  ')

  
OUTPUTS
________________________
   xasked   ypredicted  
________________________
 -300.0000    3.1370
 -100.0000    5.0146
   20.0000    6.1411
  125.0000    7.1269

________________________