MATLAB: How can ı solve without curve fitting

polynomial

Consider the given xy-data. x=0:5; y=[15, 10, 9, 6, 2, 0];. Write the necessary commands to obtain the equation of a 4th order polynomial (y = a0 + a1 x + a2 x 2 + a 3 x 3 + a 4 x 4 ) that can be fitted to these data. Note that the polynomial should pass trough the data points…. I solve this question with matlab curve fitiing function but ıs there any other way to solve?

Best Answer

Read about polyfit.

x=0:5; 
y=[15, 10, 9, 6, 2, 0];
p = polyfit(x,y,4) ;
xi = 0:0.1:5 ;
plot(x,y,'or',xi,polyval(p,xi))

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MATLAB: How to find value on a curve for different x

% 

y=[0.13 0.31 0.45 0.59 0.70 0.79 0.85 0.92 0.97 1];
x=0.1:0.1:1;
plot(x,y,'-')
% xlim([0 1]);
% 
% ylim([0 1]);
xi =0.01 ;
yi = interp1(x,y,xi,'spline') ;
hold on
plot(xi,yi,'*r')

Read about interp1

MATLAB: Save error R² of an interpolation curve in variable

You misunderstand the idea of interpolation, confusing it with approximation.

R^2 is identically 1 for an interpolation, since interpolation is defined so that it always predicts the original data. So an interpolating spline has always zero residuals in theory, therefore, R^2 == 1.

Anyway, just read the help for fit!!!!!!!

x = rand(10,1);
y = randn(size(x));
[mdl,G] = fit(x,y,'poly2')
y = randn(size(x));
[mdl,G] = fit(x,y,'poly2')
mdl = 
     Linear model Poly2:
     mdl(x) = p1*x^2 + p2*x + p3
     Coefficients (with 95% confidence bounds):
       p1 =       1.399  (-3.992, 6.791)
       p2 =     -0.1758  (-5.699, 5.347)
       p3 =     -0.4521  (-1.34, 0.4359)
G = 
  struct with fields:
           sse: 2.72060725180258
       rsquare: 0.468192584870819
           dfe: 7
    adjrsquare: 0.316247609119625
          rmse: 0.623424557447764

As you can see, G has fields that answer your question: G.rsquare, and G.adjrsquare.

Best Answer

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MATLAB: How to find value on a curve for different x

MATLAB: Save error R² of an interpolation curve in variable

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