Least Square Linear Approximation

Hi,

Based on the least square linear approximation, use this to fit a the function y = aln(x) + bcos(x) + ce^x to the data below. Find a, b, and c.

x=[0.24, 0.65, 0.95, 1.24, 1.73, 2.01, 2.23, 2.52, 2.77, 2.99];
x=x'; %Transposes x%
y=[0.23, -0.26, -1.10, -0.45, 0.27, 0.10, -0.29, 0.24, 0.56, 1.00];
y1=[log(x) cos(x) exp(x)]

When I run this code it gives me a 3x10 matrix, how do I find the value of a, b and c (each one should have one value)?

Thank you so much in advance!

Answer 1

[Star Strider]

You’re almost there! Please let me introduce you to the mldivide,\ (link) function and operator to get you the rest of the way:

The Code —

x=[0.24, 0.65, 0.95, 1.24, 1.73, 2.01, 2.23, 2.52, 2.77, 2.99];
y=[0.23, -0.26, -1.10, -0.45, 0.27, 0.10, -0.29, 0.24, 0.56, 1.00];
DesignMatrix = [log(x(:)) cos(x(:)) exp(x(:))];
Coefficients = DesignMatrix\y(:);
a = Coefficients(1)
b = Coefficients(2)
c = Coefficients(3)

The Results —

a =
         -1.04103221690367

b =
         -1.26131878469978

c =
         0.030734825739463

The colon index reference (:) creates column vectors out of whatever they reference, from vectors to multi-dimensional matrices. That also eliminates ambiguities such as having to know if a vector is a row or column vector before transposing it.

[(Unknown)]

Thank you so much Star Strider!!!!!!

How do you become proficient in MATLAB? Any suggestions?

[Star Strider]

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