MATLAB: Fit a first,second,and third degree polynomial, and determine the respective regression co-efficients.

and third degree polynomialfirstregression co-efficientssecond

i am new to matlab and just need an example to follow, please help Please see attached. thanx

i attempted the first part, plz help with regression…

Time = [1,2,3,4,5,6,7,8,9,10];
Pressure = [26.1,27.0,28.2,29.0,29.8,30.6,31.1,31.3,31.0,30.05];
New_Time = 0:0.5:10;
newf1 = polyval(polyfit(Time,Pressure,1),New_Time);
newf2 = polyval(polyfit(Time,Pressure,2),New_Time);
newf3 = polyval(polyfit(Time,Pressure,3),New_Time);
plot(Time,Pressure,'o',New_Time,newf1,New_Time,newf2,New_Time,newf3)
title('Fit of Pressure Samples')
xlabel('Sample Interval,sec')
ylabel('Pressure, PSI')
legend('Data','Linear Fit','Quadratic Fit','Cubic Fit') % linear is first order, quadratic is second order and cubic is third order

Best Answer

R3 = polyfit(Time,Pressure,3) ;

Gives the coefficients of the polynomial. In this case coefficients of third degree polynomial.

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MATLAB: Which is the best degree of the polynomial

I think orders 2 and 3 fit better.

T = table([0;10;15;20;32;59;62;125],[0;56.40;97.23;136.25;226.16;403.86;440.44;1265.23]);
T.Properties.VariableNames = {'Time' 'Velocity'}
v=T.Velocity;
t=T.Time;
plot(t, v, 'b*-', 'LineWidth', 3, 'MarkerSize', 18);
grid on;
tFit = linspace(min(t), max(t), 500);
hold on;
for order = 1 : 4
  coefficients = polyfit(t, v, order);
  vFit = polyval(coefficients, tFit);
  plot(tFit, vFit, '-', 'LineWidth', 1);
end
% Enlarge figure to full screen.
set(gcf, 'Units', 'Normalized', 'OuterPosition', [0, 0.04, 1, 0.96]);

You don't want to do over fitting. It can lead to really bad values in between the training points. Look how much the 4th order curve varies from "reasonable" between 90 and 110.

MATLAB: Obtaining slope from fitlm results

Oh, it's a tangled web TMW has weaved, fer shure...what with all the different mechanisms to do the same thing in different toolboxen plus the base product, and nary the doubled twain shall meet...

Anyhoo, fitlm in Statistics Toolbox returns an object of the Linear Model class. There's a page documenting properties and methods for it you can get to by clicking on the Output Arguments section link mdl or the 'See Also' section for more details.

In short, the coefficients are obtainable by referencing the field Estimate in the table returned by Coefficients property. So, given

lm=fitlm(x,y,'poly1');             % a linear model
betahat=lm.Coefficients.Estimate;  % the coefficients

NB: These are case-sensitive names, btw...and must be spelled-out in their entirety, none of this "first n characters stuff" here (not that that's any different than for other dot addressing, just noting it).

BTW, the order of these are intercept first which is in direct conflict with the venerable polyfit/polyval pair.

To just evaluate the fit to draw the regression line, use predict method that will get the coefficients for you given just the model object and x vector.

Best Answer

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MATLAB: Which is the best degree of the polynomial

MATLAB: Obtaining slope from fitlm results

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