How can I fit a smooth curve to this data and get the equation of the curve?

I tried lsline but this is for best fit, and doesn't really match this data

How can I fit a smooth curve to this data and get the equation of the curve?

%% current vs power
current = [26, 30, 40, 50, 60, 70, 80];
power = [0.00460174, 0.0475519, 0.214428, 0.441353, 0.712228, 0.91066, 1.05903];

figure;
plot(current,power,'o');

Answer 1

[John D'Errico]

It is a bad idea to name your variables with the same name as an existing and useful MATLAAB function. Power is one such example.

current = [26, 30, 40, 50, 60, 70, 80];
powr = [0.00460174, 0.0475519, 0.214428, 0.441353, 0.712228, 0.91066, 1.05903];

plot(current,powr,'o')

The problwm is, there are infinitely many functions that will fit that data. Any set of data in fact, can be fit by infintely many possible models. However, here a polynomial is probably adequate. The inflection point in the curve suggests a cubic polynomial would be necessary, so I might try it:

p3 = fit(current',powr','poly3')

p3 = 
     Linear model Poly3:
     p3(x) = p1*x^3 + p2*x^2 + p3*x + p4
     Coefficients (with 95% confidence bounds):
       p1 =  -8.102e-06  (-1.117e-05, -5.032e-06)
       p2 =    0.001298  (0.0008073, 0.001788)
       p3 =    -0.04391  (-0.06845, -0.01938)
       p4 =       0.413  (0.03479, 0.7912)

hold on
plot(p3)

legend('Current vs power data','Cubic fit','location','northwest')

a higher order polynomial would not be justified, but the cubic seems adequate here.

[Gucci]

Also I get this error

Undefined function 'fit' for input arguments of type 'double'.

Error in line 10

p3 = fit(current,powr,'poly3')

[Voss]

fit requires the Curve Fitting Toolbox. You can use polyfit and polyval instead.

current = [26, 30, 40, 50, 60, 70, 80];
powr = [0.00460174, 0.0475519, 0.214428, 0.441353, 0.712228, 0.91066, 1.05903];

plot(current,powr,'o')

format long
p3 = polyfit(current',powr',3)

p3 = 1×4

-0.000008101612205 0.001297647238392 -0.043911168056246 0.413001104899347

% ^^^ there are the coefficients of your cubic polynomial
% in order of: x^3, x^2, x, 1 (same as you get from fit)

hold on
more_current = linspace(floor(current(1)/10)*10,ceil(current(end)/10)*10,100);
plot(more_current,polyval(p3,more_current))

legend('Current vs power data','Cubic fit','location','northwest')

[Gucci]

Thank you, this works

How can I now get the equation of this curve? so I can get the Y value of any X value I choose?

[Voss]

p3 is the coefficients of the cubic polynomial (see the comment about coefficients in the code I posted), in order of decreasing powers of x, so the equation would be:

p3(1)*x^3 + p3(2)*x^2 + p3(3)*x + p3(4)

polyval evaluates the polynomial at any x you want. I used polyval to get the values to plot in red.

[Alex Sha]

If prefer to another fitting formula rather than the polynomial, one of will be:

y = p1-p2*Exp(-p3*x^p4);

Sum Squared Error (SSE): 0.000194020813066487
Root of Mean Square Error (RMSE): 0.00526471832195211
Correlation Coef. (R): 0.999908440561234
R-Square: 0.999816889505599

Parameter	Best Estimate
----------	-------------
p1	1.14840232711552
p2	1.22125975267146
p3	1.50816314630436E-6
p4	3.27583408702712