Higher order polynomial regression

I have to run a regression of order 5. My X matrix is

   102.1750
    108.0515
    102.1785
    100.9413
    102.6634

My Y matrix is

         0
      5.4810
      7.6267
     24.7082
      7.7284

Both X and Y are approxiately 20x1, I just wanted to give an idea how they look like.

I have tried the following:

1. Beta=pinv(X'*X)*(X'*Y);
2. Beta=(X'*X)\(X'*Y);
3. Beta=(X*Y);
4. Beta=polyfit(X,Y,5); 
   Expected=polyval(Beta,X);

The results are very different. Additionally polyfit/polyval shows the following warning:"Warning: Polynomial is not unique; degree >= number of data points"

Any ideas or suggestions of what am I doing wrong or how or what else can I try? What is the correct way to do it?

Answer 1

[Star Strider]

Give polyfit your entire (20x1) X and Y arrays, not simply the first five values.

Do that, then only use these lines to do your regression:

Beta=polyfit(X,Y,5); 
Expected=polyval(Beta,X);

That should work.

[Marina]

I still get this warning "Polynomial is not unique; degree >= number of data points. " Is there any other way?

[Image Analyst]

You're not passing in all 20 points. You're just passing in 5 of them!!! Prove it by doing this

whos X
whos Y

Answer 2

[Image Analyst]

coefficients = polyfit(x, y, 5);
% Put training points back in
yFitted = polyfit(coefficients, x);
plot(x,y, 'bs');
hold on
plot(x, yfitted, 'rd-', 'LineWidth', 3);
grid on;