MATLAB: Linear Regression Code Formula

Question

function [p_UDF] = LinReg(x, fx)

n = length(x)

sum_x = 0;

sum_x2 = 0;

sum_x3 = 0;

sum_x4 = 0;

sum_y = 0;

sum_xy = 0;

sum_x2y = 0;

for ii = 1:n

sum_x = sum_x + x(ii);

sum_x2 = sum_x2 + (x(ii)^2);

sum_x3 = sum_x3 + (x(ii)^3);

sum_x4 = sum_x4 + (x(ii)^4);

sum_y = sum_y + fx(ii);

sum_xy = (x(ii)*fx(ii));

sum_x2y = (x(ii)^2)*(fx(ii));

end

A = [n sum_x sum_x2;sum_x sum_x2 sum_x3;sum_x sum_x2 sum_x3 sum_x4]

Y = [sum_y;sum_xy;sum_x2y];

p_UDF = A\Y

% Script

x = 0:10

y = [%enter y-values]

p_UDF = LinReg(x,y)

p_FIT = polyfit(x,y)

myFIT = polyval(p_UDF,x)

plot(x,y,'or',x,myFIT)

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Can someone just please explain to me the difference between polyfit and polyval? I'm struggling a lot with figuring out the difference and how this code uses it

Answer 1

The polyfit function creates a least-squares fit of the data to a polynomial, given the independent and dependent variable data, and the desired polynomial degree.

The polyval function uses the polynomial coefficients returned by polyfit, and the desired independent variable vector, and calculates the value of the fitted polynomial at the values of the independent variable supplied to it.