>> t = (1900:10:1990)';
>> y = [75.995 91.972 105.711 123.203 131.669 ...
150.697 179.323 203.212 226.505 249.633]';
>> X=[t ones(10,1)]
X = 1900 1
1910 1
1920 1
1930 1
1940 1
1950 1
1960 1
1970 1
1980 1
1990 1
>> bhat=X\p
bhat = 1.93
-3594.01
>>yhat=polyval(bhat,t);
>>[polyval(bhat,t) y]
ans = 67.08 76.00
86.35 91.97
105.62 105.71
124.89 123.20
144.16 131.67
163.43 150.70
182.70 179.32
201.96 203.21
221.23 226.50
240.50 249.63
>> norm(yhat-y)
ans =
23.5794
>> [Q,RC]=qr([X y]);
RC =
-6151.30 -3.16 -488.86
0 -0.05 167.82
0 0 23.58
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
>> R1=RC(1:2,1:2)
R1 = -6151.30 -3.16
0 -0.05
>> C1=RC(1:2,3)
C1 = -488.8643
167.8181
>> R1\C1
ans = 1.93
-3594.01
>> C2=RC(3,3)
C2 = 23.5794
>>[Q*[C1;zeros(8,1)] yhat]
ans 67.08 67.08
86.35 86.35
105.62 105.62
124.89 124.89
144.16 144.16
163.43 163.43
182.70 182.70
201.96 201.96
221.23 221.23
240.50 240.50