%stat351-kernel.m


%Unempolyement rate
plot(unemployment,'.');
t=[1:252]';
X=[ones(252,1),t,t.^2];

>> X
X =
           1           1           1
           1           2           4
           1           3           9
                .....
                    
           1         251       63001
           1         252       63504

>>a=inv(X'*X)*X'*unemployment
a =
    4.2911
    0.0510
   -0.0002

Y=4.2911 + 0.0510*t-0.0002*t.^2;
hold
plot(t,Y)
   
>>mu_0=mean(unemployment);
mu_0 =
6.6913
Y=unemployment-mu_0;
plot(Y,'.');

%Shape of a Gaussian kernel


x=[-10:0.1:10];
plot(x,normpdf(x,0,1))

x=[-10:1:10];
plot(x,normpdf(x,0,1))

>>normpdf(x,0,4)'
ans =
    0.0044
    0.0079
    0.0135
    0.0216
    0.0324
    0.0457
    0.0605
    0.0753
    0.0880
    0.0967
    0.0997
    0.0967
    0.0880
    0.0753
    0.0605
    0.0457
    0.0324
    0.0216
    0.0135
    0.0079
    0.0044
      
W= [0.0135
    0.0216
    0.0324
    0.0457
    0.0605
    0.0753
    0.0880
    0.0967
    0.0997
    0.0967
    0.0880
    0.0753
    0.0605
    0.0457
    0.0324
    0.0216
    0.0135]
    
mu=convn(Y,W,'same');  
hold on
plot(mu+mu_0,'-')