优秀例题——用最小二乘法画噪声数据的近似曲线 - 数学建模社区-数学中国

<p>% Script file: lsqfit.m
% Purpose:
% To perform a leastsquares fit of an input data set
% to a straight line, and print out the resulting slope
% and intercept values. The input data for this fit
% comes from a userspecified input data file.
%
% Record of revisions:
% Date Programmer Description of change
% ==== ========== =====================
% 01/03/99 S. J. Chapman Original code
%
% Define variables:
% ii Loop index
% n_points Number in input [x y] points
% slope Slope of the line
% sum_x Sum of all input x values
% sum_x2 Sum of all input x values squared
% sum_xy Sum of all input x*y yalues
% sum_y Sum of all input y values
% temp Variable to read user input
% x Array of x values
% x_bar Average x value
% y Array of y values
% y_bar Average y value
% y_int yaxis intercept of the line
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
temp = input('Enter [x y] pair: ');
x(ii) = temp(1);
y(ii) = temp(2);
end
% Accumulate statistics
sum_x = 0;
sum_y = 0;
sum_x2 = 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_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);
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 = %8d\n', n_points);
% 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
</p>

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