How can I fit curve quadratically such that fit goes like in the picture?

I want to fit the curve based on equation

f(x) = b1+b2*x+b3*(x^2)

I got the curve as shown in the fiqure below:

I mean, this is the perfect fit, but I want fit that goes like following figure:

I got this from eqn f(x) = 20+0.1*x+b3*(x^2), by pre-defining b1 and b2 parameters.

Is there a way of curve plotting so that I can get all b1,b2,b3 automatically, such that curve goes in beween from all values?

Answer 1

[Image Analyst]

Try this:

T_b = [.143, .163, .168];
P_b = [87, 107, 123];
plot(T_b, P_b, 'b.', 'MarkerSize', 25);
coefficients = polyfit(T_b, P_b, 2)
x = linspace(min(T_b), max(T_b), 1000);
yFit = polyval(coefficients, x);
hold on;
plot(x, yFit, 'r-', 'LineWidth', 2)
grid on;
xlabel('T_b', 'Interpreter', 'none');
ylabel('P_b', 'Interpreter', 'none');

Answer 2

[John D'Errico]

It appears you have chosen to fit a quadratic polynomial to your data. And you say you want a quadratic polynomial, but you DREW a STRAIGHT line.

So which is it? You fit a quadratic. But then when you got a quadratic, you don't want it.

help polyfit

 POLYFIT Fit polynomial to data.
    P = POLYFIT(X,Y,N) finds the coefficients of a polynomial P(X) of
    degree N that fits the data Y best in a least-squares sense. P is a
    row vector of length N+1 containing the polynomial coefficients in
    descending powers, P(1)*X^N + P(2)*X^(N-1) +...+ P(N)*X + P(N+1).
 
    [P,S] = POLYFIT(X,Y,N) returns the polynomial coefficients P and a
    structure S for use with POLYVAL to obtain error estimates for
    predictions.  S contains these fields:
 
          R  -  Triangular R factor (possibly permuted) from a QR
                decomposition of the Vandermonde matrix of X
         df  -  Degrees of freedom
      normr  -  Norm of the residuals
 
    If the data Y are random, an estimate of the covariance matrix of P is
    (Rinv*Rinv')*normr^2/df, where Rinv is the inverse of R.
 
    [P,S,MU] = POLYFIT(X,Y,N) finds the coefficients of a polynomial in
    XHAT = (X-MU(1))/MU(2) where MU(1) = MEAN(X) and MU(2) = STD(X). This
    centering and scaling transformation improves the numerical properties
    of both the polynomial and the fitting algorithm.
 
    Warning messages result if N is >= length(X), if X has repeated, or
    nearly repeated, points, or if X might need centering and scaling.
 
    Example: simple linear regression with polyfit
 
      % Fit a polynomial p of degree 1 to the (x,y) data:
        x = 1:50;
        y = -0.3*x + 2*randn(1,50);
        p = polyfit(x,y,1);
 
      % Evaluate the fitted polynomial p and plot:
        f = polyval(p,x);
        plot(x,y,'o',x,f,'-')
        legend('data','linear fit')
 
    Class support for inputs X,Y:
       float: double, single
 
    See also POLY, POLYVAL, ROOTS, LSCOV.

    Documentation for polyfit
       doc polyfit

    Other uses of polyfit

       codistributed/polyfit    gpuArray/polyfit    tall/polyfit

Given 3 general data points, there exists a unique quadratic polynomial that passes through the points. That it may not have the shape you wanted is the fault of your data. Only 3 points is not enough to define a curve terribly well. It is sufficient for a quadratic fit, but you are appranelty not happy with it. The faulty is therefore not in the fitting tool, but in your data, or in what you asked of the fitting tool.

So you could have done

p1 = polyfit(x,y,1);

Or, use the curve fitting toollbox, using the 'poly1' fitting method.