___ ____ ____ ____ ____ tm /__ / ____/ / ____/ ___/ / /___/ / /___/ 10.0 Copyright 1984-2007 Statistics/Data Analysis StataCorp 4905 Lakeway Drive College Station, Texas 77845 USA 800-STATA-PC http://www.stata.com 979-696-4600 stata@stata.com 979-696-4601 (fax) 3-user Stata for Linux64 (network) perpetual license: Serial number: 999 Licensed to: Brian P. Poi, PhD StataCorp LP Notes: 1. (-m# option or -set memory-) 1.00 MB allocated to data 2. Command line editing disabled 3. Stata running in batch mode running /home/bpp/bin/profile.do ... . do fil.do . /* NIST StRD benchmark from http://www.nist.gov/itl/div898/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 2162.43954511 > 489 > 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) . . 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 Source | SS df MS Number of obs = 82 -------------+------------------------------ F( 8, 73) = 2059.23 Model | .242114595 8 .030264324 Prob > F = 0.0000 Residual | .001072876 73 .000014697 R-squared = 0.9956 -------------+------------------------------ Adj R-squared = 0.9951 Total | .243187471 81 .003002314 Root MSE = .00383 ------------------------------------------------------------------------------ y | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- x1 | 9.585386 1.609771 5.95 0.000 6.377117 12.79365 x2 | (dropped) x3 | -1.419962 .2137125 -6.64 0.000 -1.84589 -.9940332 x4 | (dropped) x5 | .305533 .0417248 7.32 0.000 .2223755 .3886904 x6 | .1216212 .0159331 7.63 0.000 .0898665 .1533759 x7 | .0228691 .0028893 7.92 0.000 .0171107 .0286275 x8 | .0023607 .0002892 8.16 0.000 .0017843 .0029371 x9 | .0001291 .0000154 8.37 0.000 .0000984 .0001599 x10 | 2.94e-06 3.44e-07 8.55 0.000 2.25e-06 3.62e-06 _cons | 13.83021 2.29365 6.03 0.000 9.258975 18.40145 ------------------------------------------------------------------------------ . di "R-squared = " %20.15f e(r2) R-squared = 0.995588274825264 . . assert N == e(N) . cap noi assert df_r == e(df_r) assertion is false . cap noi assert df_m == e(df_m) assertion is false . . 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 _b[_cons] 0.0 _b[x1] 0.0 _b[x2] 0.0 _b[x3] 0.0 _b[x4] 0.0 _b[x5] 0.0 _b[x6] 0.0 _b[x7] 0.0 _b[x8] 0.0 _b[x9] 0.0 _b[x10] 0.0 ------------------------- min 0.0 _se[_cons] 0.0 _se[x1] 0.0 _se[x2] 0.0 _se[x3] 0.0 _se[x4] 0.0 _se[x5] 0.0 _se[x6] 0.0 _se[x7] 0.0 _se[x8] 0.0 _se[x9] 0.0 _se[x10] 0.0 ------------------------- min 0.0 e(rmse) 0.8 e(r2) 2.9 e(mss) 2.9 e(F) 1.3 e(rss) 0.5 . . * 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)) RMSE standard = 3.348010513245440e-03 RMSE from residual = 3.833658235315113e-03 abs(std. - res.) = 4.856477220696732e-04 RMSE from regress = 3.833658235315113e-03 abs(res. - regress) = 0.000000000000000e+00 . . * Use -orthog- . . orthog x*, gen(u*) mat(R) . reg y u* Source | SS df MS Number of obs = 82 -------------+------------------------------ F( 10, 71) = 2162.44 Model | .24239162 10 .024239162 Prob > F = 0.0000 Residual | .000795851 71 .000011209 R-squared = 0.9967 -------------+------------------------------ Adj R-squared = 0.9963 Total | .243187471 81 .003002314 Root MSE = .00335 ------------------------------------------------------------------------------ y | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- u1 | .050952 .0003697 137.81 0.000 .0502148 .0516893 u2 | -.0095854 .0003697 -25.93 0.000 -.0103226 -.0088482 u3 | -.0091315 .0003697 -24.70 0.000 -.0098687 -.0083943 u4 | .0106835 .0003697 28.90 0.000 .0099463 .0114207 u5 | .0019273 .0003697 5.21 0.000 .0011901 .0026645 u6 | -.0068122 .0003697 -18.43 0.000 -.0075494 -.006075 u7 | .0007362 .0003697 1.99 0.050 -1.03e-06 .0014734 u8 | .0037573 .0003697 10.16 0.000 .0030201 .0044945 u9 | -.0017154 .0003697 -4.64 0.000 -.0024526 -.0009782 u10 | -.0016616 .0003697 -4.49 0.000 -.0023988 -.0009244 _cons | .8495756 .0003697 2297.85 0.000 .8488384 .8503128 ------------------------------------------------------------------------------ . 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 b[1,11] 8.6 b[1,1] 8.8 b[1,2] 9.0 b[1,3] 9.3 b[1,4] 10.4 b[1,5] 9.2 b[1,6] 8.9 b[1,7] 8.7 b[1,8] 8.6 b[1,9] 8.5 b[1,10] 8.4 ------------------------- min 8.4 e(rmse) 8.8 e(r2) 11.0 e(mss) 11.0 e(F) 8.5 e(rss) 8.5 . . end of do-file