% Matlab diary from cs111, Nov 7 2007.
%
% This is what I typed in class.  
%
% Type it into Matlab yourself to
% reproduce the output I showed.

load censusdata
whos
plot(t,y,'o')
X = [ t.^2 t ones(11,1)]
y
beta = X \ y
hold on
plot(t, X*beta, 'r')
warning on
n = length(y)
X
format long
X
X(:,7)
clc
format short
size(X)
beta = X \ y
rank(X)
hold on
plot(t, X*beta, 'k')
X
t
s = (t - 1950)
s = (t - 1950) / 50
X = [s.^6 s.^5 s.^4 s.^3 s.^2 s ones(11,1)]
rank(X)
beta = X \ y
plot(t, X*beta, 'r')

censusgui

X = [ t ones(n,1) ]
y
logy = log(y)
beta = X \ log(y)
lambda = beta(1)
k = exp(beta(2))
plot(t,y,'o')
hold on
plot(t, k * exp(lambda * t))


X = [ 1 2 ; 3 4 ; 5 6]
y = [1 ; 2 ; 4]
beta = X \ y

% This is how I plotted the three lines
t = -1:.1:3
s1 = (y(1)-X(1,1)*t)/X(1,2);
s2 = (y(2)-X(2,1)*t)/X(2,2);
s3 = (y(3)-X(3,1)*t)/X(3,2);
plot(t,s1);hold on;
plot(t,s2,'r')
plot(t,s3,'k')

y
X
[Q,R] = qr(X)

Q'
Q * Q'
Q' * Q
cond(Q)

diary off