Tutorial · Intermediate · 12 min

Fitting data for a paper

Simulate measurements, fit a model, show uncertainty and residuals, and report the numbers.

1. Reproducible "measurements"

   rng(seed) makes random numbers repeatable, so your figure is the same every time.

   rng(42)
   x = linspace(0, 5, 20);
   y = 1.8*x + 0.5 + 0.7*randn(size(x));
   scatter(x, y, 40, 'filled')
   title('measurements')

   Try it ↗

2. Fit a straight line

   polyfit(x, y, 1) returns slope and intercept; polyval evaluates the fitted line.

   rng(42)
   x = linspace(0, 5, 20);
   y = 1.8*x + 0.5 + 0.7*randn(size(x));
   p = polyfit(x, y, 1);
   scatter(x, y, 40, 'filled'), hold on
   plot(x, polyval(p, x), 'LineWidth', 2), hold off
   legend('data', sprintf('fit: %.2f x + %.2f', p(1), p(2)))

   Try it ↗

3. Error bars and residuals

   errorbar shows uncertainty; a second subplot shows what the model misses.

   rng(42)
   x = linspace(0, 5, 20);
   y = 1.8*x + 0.5 + 0.7*randn(size(x));
   p = polyfit(x, y, 1);
   subplot(2, 1, 1)
   errorbar(x, y, 0.7*ones(size(x)), 'o'), hold on
   plot(x, polyval(p, x), 'LineWidth', 2), hold off
   title('linear fit ± 1σ')
   subplot(2, 1, 2)
   stem(x, y - polyval(p, x)), yline(0, 'k:')
   title('residuals')

   Try it ↗

4. Report the numbers

   Compute statistics and print them with fprintf. Then export the figure as SVG and the data as CSV.

   rng(42)
   x = linspace(0, 5, 20);
   y = 1.8*x + 0.5 + 0.7*randn(size(x));
   p = polyfit(x, y, 1);
   r = y - polyval(p, x);
   R = corrcoef(x, y);
   fprintf('slope      %.3f\n', p(1))
   fprintf('intercept  %.3f\n', p(2))
   fprintf('RMS error  %.3f\n', sqrt(mean(r.^2)))
   fprintf('r          %.4f\n', R(1, 2))

   Try it ↗

   slope      2.040
   intercept  -0.218
   RMS error  0.871
   r          0.9626