机器学习基础教程：线性建模fitlinear

Define the data
Change these to use a different dataset

x = [1;3;5];
t = [4.8;11.1;17.2];
N = length(x); % 3

Compute the various averages required

$$\overline x ={1/N}*\sum_{n} x_n$$

m_x = sum(x)/N;

$$\overline t ={1/N}*\sum_n t_n$$

m_t = sum(t)/N;

$$\overline {xt} ={1/N}*\sum_n t_n*x_n$$

m_xt = sum(t.*x)/N;

$$\overline {x^2} ={1/N}*\sum_n x_n^2$$

m_xx = sum(x.*x)/N;

Compute w1 (gradient) (Equation 1-10)

$$\hat w_1=\frac{\overline{xt}-\overline x\overline t}{\overline {x^2}-{\overline x}^2}$$

w_1 = (m_xt - m_x*m_t)/(m_xx - m_x^2);

Compute w0 (intercept) (Equation 1-8)

$$\hat w_0 = \overline t - w_1\overline x$$

w_0  = m_t - w_1*m_x;

Plot the data and linear fit

%% Plot the data and linear fit
figure(1);hold off
plot(x,t,‘bo‘,‘markersize‘,10,‘linewidth‘,2)
xplot = [0 6];
xlim(xplot)
hold on
plot(xplot,w_0+w_1*xplot,‘r‘,‘linewidth‘,2)
xlabel(‘x‘);
ylabel(‘t‘);

关于Machine Learning更多讨论与交流，敬请关注本博客和新浪微博songzi_tea.