Question regarding the calling of cfit coefficients

I have used the 'fit' function to apply a power2 curve fit to some data. The cfit object is called fitobject. Shown below:

fitobject = fit(xdata, ydata, 'power2')

As a result I get three coefficients in the form y = ax^b + c.

I know the correct way to call the coefficients in a script is:

a = fitobject.a; b = fitobject.b; c = fitobject.c;

But if I call the following:

a = fitobject(1); b = fitobject(2); c = fitobject(3);

I get slightly different values of the coefficients. Could someone please explain where the values above come from, and thus why they differ. E.g why fitobject.a is not equal to fitobject(1) etc?

I have been scouring the internet and cannot find an explanation. I suspect it's something to do with the confidence bounds?

Many thanks!

Answer 1

[Steven Lord]

The way you gave, asking for the a, b, and c properties of the cfit object named fitobject, is one way to get the coefficients. This documentation page lists another: use the coeffvalues function. You'd probably also want to call the coeffnames function as well.

The second syntax you gave does not extract any coefficients at all. It evaluates the fit for x = 1, x = 2, and x = 3 respectively. Adapting the example on that documentation page:

load census
curvefit = fit(cdate,pop,'poly3','normalize','on')

curvefit = 
     Linear model Poly3:
     curvefit(x) = p1*x^3 + p2*x^2 + p3*x + p4
       where x is normalized by mean 1890 and std 62.05
     Coefficients (with 95% confidence bounds):
       p1 =       0.921  (-0.9743, 2.816)
       p2 =       25.18  (23.57, 26.79)
       p3 =       73.86  (70.33, 77.39)
       p4 =       61.74  (59.69, 63.8)

Let's get one of the coefficients.

curvefit.p1

ans = 0.9210

Let's get all the coefficients and display them as a table.

N = coeffnames(curvefit)

N = 4×1 cell array
    {'p1'}
    {'p2'}
    {'p3'}
    {'p4'}

V = coeffvalues(curvefit)

V = 1×4

0.9210 25.1834 73.8598 61.7444

results = table(N, V.', 'VariableNames', ["Coefficient names", "Coefficient values"])

results = 4×2 table
    Coefficient names    Coefficient values
    _________________    __________________

         {'p1'}               0.92102      
         {'p2'}                25.183      
         {'p3'}                 73.86      
         {'p4'}                61.744      

What's the value of the fitted curve for the year 1925?

pop1925 = curvefit(1925)

pop1925 = 111.5852

Does this look right compared to the fitted curve and the data?

plot(curvefit)
hold on
plot(cdate, pop, 'ko', 1925, pop1925, 'bd')

[TPazz]

Brilliant, thanks!