y 26.2241386 1.98276181 34.2005614 2.57062484 1.98993353 44.8538976 3.18464712 16.0275651 36.3739272 6.96650419 6.59195558 25.2003237 47.5479969 2.91695666 10.8364237 1.99047589 11.1212135 4.62875627 7.18882824 23.4438035 1.95254163 1.97133851 12.8782943 35.953215 9.44059754 1.97268607 2.00520138 18.596781 32.283961 12.8469173 2.33307082 1.9449117
x 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 7.26737266 0.01525926 8.33033235 1.39805292 0.08575701 9.56083865 1.88207648 5.60563982 8.59553819 3.46934416 3.3475753 7.12088382 9.85106967 1.69408246 4.51643422 0.63661611 4.58296457 2.61421552 3.53495895 6.85628834 0.25971252 0.09979553 4.97116001 8.54609821 4.16974395 0.51362651 0.05310221 6.06769005 8.08526872 4.96871853 1.15024262 0.19013031 52.8147054 0.00023284 69.394437 1.95455196 0.00735427 91.4096357 3.54221187 31.4231978 73.8832768 12.0363489 11.2062604 50.7069863 97.0435737 2.86991538 20.398178 0.40528007 21.0035642 6.8341228 12.4959348 47.0086898 0.06745059 0.00995915 24.7124318 73.0357946 17.3867646 0.2638122 0.00281984 36.8168626 65.3715702 24.6881638 1.32305809 0.03614954
a
b
c
a
b c 1.99767339 -0.30074057 0.50014972
Run the Macro by hitting ALT+F8 then plot the coefficients against N You will see that the first couple of coefficients sets will not be well identified, which makes sense because we are, for exa As you take more and more data into the computation the coefficients converge to their true values
Prediction squared resid sum of squared residuals takes N squared residuals N 26.2273399 1.0248E-05 1.0248E-05 1.99320077 0.00010897 0.00011922 34.200013 3.0076E-07 0.00011952 <- takes the first 3 residuals into the sum 2.55479078 0.00025072 0.00037024 1.97556101 0.00020657 0.00057681 44.8408453 0.00017036 0.00074717 3.20329293 0.00034767 0.00109484 <- takes the first 7 residuals into the sum 16.0281338 3.2333E-07 0.00109516 and so forth 36.3653468 7.3623E-05 0.00116878 6.97427741 6.0423E-05 0.00122921 6.59572973 1.4244E-05 0.00124345 25.2172199 0.00028548 0.00152893 47.5713736 0.00054647 0.0020754 2.92358145 4.3888E-05 0.00211929 10.8415415 2.6192E-05 0.00214548 2.00891781 0.0003401 0.00248559 11.1243169 9.6308E-06 0.00249522 4.62955735 6.4174E-07 0.00249586 7.18440615 1.9555E-05 0.00251542 23.4470925 1.0818E-05 0.00252623 1.9533027 5.7921E-07 0.00252681 1.97264189 1.6988E-06 0.00252851 12.8625598 0.00024757 0.00277609 35.9563474 9.812E-06 0.0027859 9.43964773 9.0215E-07 0.0027868 1.97515066 6.0742E-06 0.00279287 1.98311375 0.00048786 0.00328074 18.5868165 9.9292E-05 0.00338003 32.2616778 0.00049654 0.00387657 12.8511564 1.7971E-05 0.00389454 2.31347591 0.00038396 0.0042785 1.95857367 0.00018665 0.00446515
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
ified, which makes sense because we are, for example, fitting 2 datapoints with 3 parameters nverge to their true values
26.2241386 1.98276181 34.2005614 2.57062484 1.98993353 44.8538976 3.18464712 16.0275651 36.3739272 6.96650419 6.59195558 25.2003237 47.5479969 2.91695666 10.8364237 1.99047589 11.1212135 4.62875627 7.18882824 23.4438035 1.95254163 1.97133851 12.8782943 35.953215 9.44059754 1.97268607 2.00520138 18.596781 32.283961 12.8469173 2.33307082 1.9449117
7.26737266 0.01525926 8.33033235 1.39805292 0.08575701 9.56083865 1.88207648 5.60563982 8.59553819 3.46934416 3.3475753 7.12088382 9.85106967 1.69408246 4.51643422 0.63661611 4.58296457 2.61421552 3.53495895 6.85628834 0.25971252 0.09979553 4.97116001 8.54609821 4.16974395 0.51362651 0.05310221 6.06769005 8.08526872 4.96871853 1.15024262 0.19013031