MATLAB实现最小二乘拟合的相关系数 【例】

代码如下所示：

disp('This program performs a leastsquares fit of an ');

disp('input data set to a straight line.');

n_points = input('Enter the number of input [x y] points: ');

% Read the input data

for ii = 1:n_points

string=['Enter the ' int2str(ii) '[x y] pair'];

temp=input(string);

x(ii) = temp(1);                

y(ii) = temp(2);

end

% Accumulate statistics

sum_x = 0;

sum_y = 0;

sum_x2 = 0;

sum_y2 = 0;

sum_xy = 0;

for ii = 1:n_points

sum_x = sum_x + x(ii);

sum_y = sum_y + y(ii);

sum_x2 = sum_x2 + x(ii)^2;

sum_y2 = sum_y2 + y(ii)^2;

sum_xy = sum_xy + x(ii) * y(ii);

end

% Now calculate the slope and intercept.

x_bar = sum_x / n_points;

y_bar = sum_y / n_points;

slope = (sum_xy - sum_x * y_bar) / ( sum_x2 - sum_x * x_bar);

r=(n_points*sum_xy-sum_x*sum_y) / (sqrt(n_points*sum_x2-sum_x^2)*(n_points*sum_y2-sum_y^2));

y_int = y_bar - slope * x_bar;

% Tell user.

disp('Regression coefficients for the leastsquares line:');

fprintf(' Slope (m) = %8.3f\n', slope);

fprintf(' Intercept (b) = %8.3f\n', y_int);

fprintf(' No of points = �\n', n_points);

fprintf('相关系数r=%8.3f\n',r);

% Plot the data points as blue circles with no

% connecting lines.

plot(x,y,'bo');

hold on;

% Create the fitted line

xmin = min(x);

xmax = max(x);

ymin = slope * xmin + y_int;

ymax = slope * xmax + y_int;

% Plot a solid red line with no markers

plot([xmin xmax],[ymin ymax],'r','LineWidth',2);

hold off;

% Add a title and legend

title ('\bfLeastSquaresFit');

xlabel('\bf\itx');

ylabel('\bf\ity');

legend('Input data','Fitted line');

grid on