fitolympic

fitolympic.m
Load the Olympic data
Extract the male 100m data
Compute the various averages required
Compute w1 (gradient) (Equation 1.10)
Compute w0 (intercept) (Equation 1.8)
Plot the data and linear fit

fitolympic.m

From A First Course in Machine Learning, Chapter 1. Simon Rogers, 31/10/11 [simon.rogers@glasgow.ac.uk]

clear all;close all;

Load the Olympic data

load ../data/olympics

Extract the male 100m data

x = male100(:,1); % Olympic years
t = male100(:,2); % Winning times

% Change the preceeding lines for different data.  e.g.
% x = male400(:,1); % Olympic years
% t = male400(:,2); % Winning times
% for the mens 400m event.

N = length(x); % 27

Compute the various averages required

$\frac{1}{N}\sum_n x_n$

m_x = sum(x)/N;

$\frac{1}{N}\sum_n t_n$

m_t = sum(t)/N;

$\frac{1}{N}\sum_n t_n x_n$

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

$\frac{1}{N}\sum_n x_n^2$

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

Compute w1 (gradient) (Equation 1.10)

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

Compute w0 (intercept) (Equation 1.8)

w_0 = m_t - w_1*m_x;

Plot the data and linear fit

figure(1);hold off
plot(x,t,'bo','markersize',10,'linewidth',2)
xplot = [min(x)-4 max(x)+4];
xlim(xplot);
hold on
plot(xplot,w_0+w_1*xplot,'r','linewidth',2)
xlabel('Olympic year');
ylabel('Winning time');