improved on statistics

statistics/code/correlations.m

@@ -1,14 +1,18 @@
-n = 1000
-x = randn( n, 1 );
-y = randn( n, 1 ) + 0.2*x;
-r = corr(x,y)
-
-  nsamples = 500;
-  rs = zeros( nsamples, 1 );
-for i = 1:nsamples
-	  xs = x(randi(n,n,1));
-ys = x(randi(n,n,1));
-	  rs(i) = corr(xs,ys);
+n = 200;
+corrs = [ 1.0, 0.6, 0.0, -0.9 ];
+for k = [1:length(corrs)]
+    r = corrs(k);
+    x = randn(n, 1);
+    y = r*x; % linear dependence of y on x
+    % add noise to destroy perfect correlations:
+    y = y + sqrt(1.0-r*r)*randn(n, 1);
+    % compute correlation coefficient of data:
+    rho = corr(x, y);
+    subplot(2, 2, k)
+    scatter( x, y )
+    text( -2, 2.5, sprintf('r=%.1f', rho) )
+    xlabel('x')
+    ylabel('y')
+    xlim([-3.0, 3.0])
+    ylim([-3.0, 3.0])
 end
-
-hist( rs, 20 )