/* NIST/ITL StRD
Linear Regression
Difficulty=Higher Polynomial k=11 N=82 Observed
Dataset Name: Filippelli (filippelli.dat)
Procedure: Linear Least Squares Regression
Reference: Filippelli, A., NIST.
Data: 1 Response Variable (y)
1 Predictor Variable (x)
82 Observations
Higher Level of Difficulty
Observed Data
Model: Polynomial Class
11 Parameters (B0,B1,...,B10)
y = B0 + B1*x + B2*(x**2) + ... + B9*(x**9) + B10*(x**10) + e
Certified Regression Statistics
Standard Deviation
Parameter Estimate of Estimate
B0 -1467.48961422980 298.084530995537
B1 -2772.17959193342 559.779865474950
B2 -2316.37108160893 466.477572127796
B3 -1127.97394098372 227.204274477751
B4 -354.478233703349 71.6478660875927
B5 -75.1242017393757 15.2897178747400
B6 -10.8753180355343 2.23691159816033
B7 -1.06221498588947 0.221624321934227
B8 -0.670191154593408E-01 0.142363763154724E-01
B9 -0.246781078275479E-02 0.535617408889821E-03
B10 -0.402962525080404E-04 0.896632837373868E-05
Residual
Standard Deviation 0.334801051324544E-02
R-Squared 0.996727416185620
Certified Analysis of Variance Table
Source of Degrees of Sums of Mean
Variation Freedom Squares Squares F Statistic
Regression 10 0.242391619837339 0.242391619837339E-01 2162.43954511489
Residual 71 0.795851382172941E-03 0.112091743968020E-04
*/
clear
scalar N = 82
scalar df_r = 71
scalar df_m = 10
scalar rmse = 0.334801051324544E-02
scalar r2 = 0.996727416185620
scalar mss = 0.242391619837339
scalar F = 2162.43954511489
scalar rss = 0.795851382172941E-03
scalar b_cons = -1467.48961422980
scalar se_cons = 298.084530995537
scalar bx1 = -2772.17959193342
scalar sex1 = 559.779865474950
scalar bx2 = -2316.37108160893
scalar sex2 = 466.477572127796
scalar bx3 = -1127.97394098372
scalar sex3 = 227.204274477751
scalar bx4 = -354.478233703349
scalar sex4 = 71.6478660875927
scalar bx5 = -75.1242017393757
scalar sex5 = 15.2897178747400
scalar bx6 = -10.8753180355343
scalar sex6 = 2.23691159816033
scalar bx7 = -1.06221498588947
scalar sex7 = 0.221624321934227
scalar bx8 = -0.670191154593408E-01
scalar sex8 = 0.142363763154724E-01
scalar bx9 = -0.246781078275479E-02
scalar sex9 = 0.535617408889821E-03
scalar bx10 = -0.402962525080404E-04
scalar sex10 = 0.896632837373868E-05
qui input double (y x1)
0.8116 -6.860120914
0.9072 -4.324130045
0.9052 -4.358625055
0.9039 -4.358426747
0.8053 -6.955852379
0.8377 -6.661145254
0.8667 -6.355462942
0.8809 -6.118102026
0.7975 -7.115148017
0.8162 -6.815308569
0.8515 -6.519993057
0.8766 -6.204119983
0.8885 -5.853871964
0.8859 -6.109523091
0.8959 -5.79832982
0.8913 -5.482672118
0.8959 -5.171791386
0.8971 -4.851705903
0.9021 -4.517126416
0.909 -4.143573228
0.9139 -3.709075441
0.9199 -3.499489089
0.8692 -6.300769497
0.8872 -5.953504836
0.89 -5.642065153
0.891 -5.031376979
0.8977 -4.680685696
0.9035 -4.329846955
0.9078 -3.928486195
0.7675 -8.56735134
0.7705 -8.363211311
0.7713 -8.107682739
0.7736 -7.823908741
0.7775 -7.522878745
0.7841 -7.218819279
0.7971 -6.920818754
0.8329 -6.628932138
0.8641 -6.323946875
0.8804 -5.991399828
0.7668 -8.781464495
0.7633 -8.663140179
0.7678 -8.473531488
0.7697 -8.247337057
0.77 -7.971428747
0.7749 -7.676129393
0.7796 -7.352812702
0.7897 -7.072065318
0.8131 -6.774174009
0.8498 -6.478861916
0.8741 -6.159517513
0.8061 -6.835647144
0.846 -6.53165267
0.8751 -6.224098421
0.8856 -5.910094889
0.8919 -5.598599459
0.8934 -5.290645224
0.894 -4.974284616
0.8957 -4.64454848
0.9047 -4.290560426
0.9129 -3.885055584
0.9209 -3.408378962
0.9219 -3.13200249
0.7739 -8.726767166
0.7681 -8.66695597
0.7665 -8.511026475
0.7703 -8.165388579
0.7702 -7.886056648
0.7761 -7.588043762
0.7809 -7.283412422
0.7961 -6.995678626
0.8253 -6.691862621
0.8602 -6.392544977
0.8809 -6.067374056
0.8301 -6.684029655
0.8664 -6.378719832
0.8834 -6.065855188
0.8898 -5.752272167
0.8964 -5.132414673
0.8963 -4.811352704
0.9074 -4.098269308
0.9119 -3.66174277
0.9228 -3.2644011
end
gen double x2 = x1*x1
gen double x3 = x1*x2
gen double x4 = x1*x3
gen double x5 = x1*x4
gen double x6 = x1*x5
gen double x7 = x1*x6
gen double x8 = x1*x7
gen double x9 = x1*x8
gen double x10 = x1*x9
reg y x1-x10
di "R-squared = " %20.15f e(r2)
assert N == e(N)
cap noi assert df_r == e(df_r)
cap noi assert df_m == e(df_m)
lrecomp _b[_cons] b_cons _b[x1] bx1 _b[x2] bx2 /*
*/ _b[x3] bx3 _b[x4] bx4 _b[x5] bx5 _b[x6] bx6 /*
*/ _b[x7] bx7 _b[x8] bx8 _b[x9] bx9 _b[x10] bx10 () /*
*/ _se[_cons] se_cons _se[x1] sex1 _se[x2] sex2 /*
*/ _se[x3] sex3 _se[x4] sex4 _se[x5] sex5 _se[x6] sex6 /*
*/ _se[x7] sex7 _se[x8] sex8 _se[x9] sex9 _se[x10] sex10 () /*
*/ e(rmse) rmse e(r2) r2 e(mss) mss e(F) F e(rss) rss
* Do alternative calculation of rmse
predict double res, residual
gen double ss = res*res
qui summarize ss
scalar rmsea = sqrt(r(sum)/e(df_r))
di _n in gr "RMSE standard = " in ye %22.15e rmse _n /*
*/ in gr "RMSE from residual = " in ye %22.15e rmsea _n /*
*/ in gr "abs(std. - res.) = " in ye %22.15e abs(rmsea-rmse) _n /*
*/ in gr "RMSE from regress = " in ye %22.15e e(rmse) _n /*
*/ in gr "abs(res. - regress) = " in ye %22.15e abs(rmsea-e(rmse))
* Use -orthog-
orthog x*, gen(u*) mat(R)
reg y u*
matrix b = e(b)*inv(R)'
lrecomp b[1,11] b_cons b[1,1] bx1 b[1,2] bx2 /*
*/ b[1,3] bx3 b[1,4] bx4 b[1,5] bx5 b[1,6] bx6 /*
*/ b[1,7] bx7 b[1,8] bx8 b[1,9] bx9 b[1,10] bx10 () /*
*/ e(rmse) rmse e(r2) r2 e(mss) mss e(F) F e(rss) rss