Hello , I am dealing with linear least square regression

.I successfully found the coefficients for the quadratic function as follows.

function [a2,a1,a0] = QuadraticRegression (x,y)

x=[10 15 25 40 50 55];
y=[94 116 147 183 215 220];

n = length (x)
sx = sum(x)
sy = sum(y)
sx2 = sum(x.^2)
sx3 = sum(x.^3)
sx4 = sum(x.^4)
sxy = sum(x.*y)
sx2y= sum(x.*x.*y)

A = [ n sx sx2; sx sx2 sx3;sx2 sx3 sx4]
b = [sy;sxy;sx2y]

w= A\b

a2 = w(3)
a1 = w(2)
a0 = w(1)
    % code
  end*

func(y) = -0.0170 x.^2 + 3.8870 x + 59.0062

now i'm suppose to fit the above data into a power function as follows : y = Q (x.^M) Where Q and M are coefficients.

I went through the book https://books.google.com/books/about/Numerical_Methods_for_Engineers_and_Scie.html?id=gMrMBQAAQBAJ&printsec=frontcover&source=kp_read_button#v=onepage&q&f=false

and went through Youtube and google before i posted my question here. I see no method mentions in the any of the resources. Please give me some clues. Thanks

[David Goodmanson]

Hi Charitha,

try taking the logarithm of both sides and using the rule for log(C*x^m) in terms of log(C), m and log(x). That should give you an equation you can fit for two new arrays, logy = log(y) vs. logx = log(x).

Answer 1

[Torsten]

y = Q*x^M  => log(y) = log(Q) + M*log(x)

Thus take "log" of your x- and y-data and fit them by a linear function

y~ = a+b*x~

where

y~=log(y) and x~=log(x).

Once you have determined a and b, Q=exp(a) and M=b.

Another possibility is to use "lsqcurevfit" directly on the nonlinear function y = Q*x^M.

This will give slightly different fit parameters for Q and M because taking the log of x and y and making a linear fit as suggested above somehow distorts the data.

Best wishes

Torsten.

[Charitha Heshan]

Thank you sir