Wavelenth vs Absorbance plot in MATLAB - matlab

Question

I have a number of wavelengths and their corresponding absorbances.
First I entered the x and y values
x = [400 425 450 475 500 505 510 525];
y = [.24 .382 .486 .574 .608 .608 .602 .508];
To plot the points
plot(x, y, 'o')
Then I want to fit the data.
I'm not sure what degree of polynomial to choose, but since it's a plot of Wavelength vs Absorbtion, wont there already be a mathematical formula? Like how you know a plot of Kinetic energy vs Velocity will be degree 2 because KE = 1/2mv^2?

Answer 1

Alright so here is a solution that works fine with your data, using polyfit and polyval to evaluate a polynomial that passes through your data points.
In the doc for polyfit (here), it states that
In general, for n points, you can fit a polynomial of degree n-1 to
exactly pass through the points.
Since you have 8 data points, we can try using a polynomial of degree 7 and see what it givesL
clear
clc
x = [400 425 450 475 500 505 510 525];
y = [.24 .382 .486 .574 .608 .608 .602 .508];
%// Get polynomial coefficients to fit the data
p = polyfit(x,y,7)
%// Create polynomial to plot
fFit = polyval(p,x);
plot(x,y,'o')
hold on
plot(x,fFit,'r--')
hold off
axis([400 525 0 .7]);
legend({'Data points' 'Fitted curve'},'Location','NorthWest')
gives this:
So it does look to work very well! If we look at the coefficients given by polyfit:
p =
1.0e+05 *
Columns 1 through 6
0.0000 -0.0000 0.0000 -0.0000 0.0000 -0.0003
Columns 7 through 8
0.0401 -2.7206
Maybe the degree 7 was a bit overkill since the first 5 coefficients are 0 ( or about 0), but anyhow it fits very well!
Hope that helps!