% Matlab diary from cs111, Oct 31 2007.
%
% This is what I typed in class.  
%
% Type it into Matlab yourself to
% reproduce the output I showed.

diary on
warning on
load censusdata
whos
t
y
plot(t,y,'o')
beta1 = 2
beta2 = -3700
yy = beta1 * t + beta2
hold on
plot(t,yy,'r')
y
n = length(y)
y
t
ones(3,5)
X = [t  ones(n,1)]
y
beta = X \ y
beta(1)
beta(2)
yyy = beta(1) * t + beta(2)
plot(t,yyy,'k')

residJRG = y - X*[beta1;beta2]
residJRG = y - yy
residKFG = y - X * beta
fitJRG = norm(residJRG)
fitKFG = norm(residKFG)
plot(t,yyy,'ko')

clf
plot(t,y,'o')
X
t.^2
X = [ t.^2   t    ones(n,1)]
beta = X \ y
beta(1)
beta(2)
beta(3)
yyyy = X * beta
residual2 = y - yyyy
fit2 = norm(residual2)
fitKFG
plot(t,yyy,'k')
hold on
plot(t,y,'o')
plot(t,yyyy,'r')
X
X = [ t.^3 t.^2 t ones(n,1)]
beta
size(X)
size(y)
beta = X \ y
y
X(:,4)
X(:,3)
X(:,2)
X(:,1)
beta = X \ y
plot(t,X*beta,'g')
beta(1)
fit2 = norm(residual2)
fit3 = norm(X*beta-y)
X = [ t.^ 4 t.^3 t.^2 t ones(n,1)]
beta = X \ y
beta(1)
beta(2)
beta(4)
beta(5)
plot(t,X*beta,'r')
X
cond(X)

X = [ t.^3 t.^2 t ones(n,1)]
cond(X)

diary off