Principle of least square method and matlab code implementation

Incomplete sorting , It's just a note for you to read .

One 、 Some of the problems

1. Least square method , The sum of the distance between the predicted value and the real value is the smallest , The principle is minimum mean square error .

2. Why square ？

• The square is positive or negative , It's a distance
• The square is equivalent to a weighting

 

Two 、 computational procedure

1. Calculate the mean value of the input sequence
2. Calculation x Variance and x,y The covariance （ Covariance reflects the variable x,y Whether the change trend of is the same ）
3. Calculate slope and intercept  

3、 ... and 、Matlab Code implementation

function [a, b] = LeastSquaresFitting(X,Y)
% The least square method is used to fit the straight line 
%    Input ： Fitting data X,Y
%    Output ：y=ax+b
if (length(X) ~= length(Y))
    error('Length of input vectors must be equal.');
end
    

%%  First step ： O, respectively, x,y mean value 
x_avg = sum(X(:))/length(X);
y_avg = sum(Y(:))/length(Y);

%%  The second step ： seek x,y Covariance and x The variance of 
xy_cov = 0;
x_var = 0;
for i = 1:length(X)
   xy_cov = xy_cov + (X(i)-x_avg)*(Y(i)-y_avg);
   x_var = x_var + (X(i)-x_avg)^2;
end

%%  The third step ： Find the slope a Distance and intercept b
a = xy_cov/x_var;
b = y_avg - a*x_avg;

end