/* NIST StRD benchmark from http://www.nist.gov/itl/div898/strd/ Nonlinear Regression Difficulty=Average Exponential k=3 N=128 Observed Dataset Name: Nelson (Nelson.dat) Procedure: Nonlinear Least Squares Regression Description: These data are the result of a study involving the analysis of performance degradation data from accelerated tests, published in IEEE Transactions on Reliability. The response variable is dialectric breakdown strength in kilo-volts, and the predictor variables are time in weeks and temperature in degrees Celcius. Reference: Nelson, W. (1981). Analysis of Performance-Degradation Data. IEEE Transactions on Reliability. Vol. 2, R-30, No. 2, pp. 149-155. Data: 1 Response ( y = dialectric breakdown strength) 2 Predictors (x1 = time; x2 = temperature) 128 Observations Average Level of Difficulty Observed Data Model: Exponential Class 3 Parameters (b1 to b3) log[y] = b1 - b2*x1 * exp[-b3*x2] + e Starting values Certified Values Start 1 Start 2 Parameter Standard Deviation b1 = 2 2.5 2.5906836021E+00 1.9149996413E-02 b2 = 0.0001 0.000000005 5.6177717026E-09 6.1124096540E-09 b3 = -0.01 -0.05 -5.7701013174E-02 3.9572366543E-03 Residual Sum of Squares: 3.7976833176E+00 Residual Standard Deviation: 1.7430280130E-01 Degrees of Freedom: 125 Number of Observations: 128 */ clear scalar N = 128 scalar df_r = 125 scalar df_m = 3 scalar rss = 3.7976833176E+00 scalar rmse = 1.7430280130E-01 scalar b1 = 2.5906836021E+00 scalar seb1 = 1.9149996413E-02 scalar b2 = 5.6177717026E-09 scalar seb2 = 6.1124096540E-09 scalar b3 = -5.7701013174E-02 scalar seb3 = 3.9572366543E-03 qui input double (y x1 x2) 15.00E0 1E0 180E0 17.00E0 1E0 180E0 15.50E0 1E0 180E0 16.50E0 1E0 180E0 15.50E0 1E0 225E0 15.00E0 1E0 225E0 16.00E0 1E0 225E0 14.50E0 1E0 225E0 15.00E0 1E0 250E0 14.50E0 1E0 250E0 12.50E0 1E0 250E0 11.00E0 1E0 250E0 14.00E0 1E0 275E0 13.00E0 1E0 275E0 14.00E0 1E0 275E0 11.50E0 1E0 275E0 14.00E0 2E0 180E0 16.00E0 2E0 180E0 13.00E0 2E0 180E0 13.50E0 2E0 180E0 13.00E0 2E0 225E0 13.50E0 2E0 225E0 12.50E0 2E0 225E0 12.50E0 2E0 225E0 12.50E0 2E0 250E0 12.00E0 2E0 250E0 11.50E0 2E0 250E0 12.00E0 2E0 250E0 13.00E0 2E0 275E0 11.50E0 2E0 275E0 13.00E0 2E0 275E0 12.50E0 2E0 275E0 13.50E0 4E0 180E0 17.50E0 4E0 180E0 17.50E0 4E0 180E0 13.50E0 4E0 180E0 12.50E0 4E0 225E0 12.50E0 4E0 225E0 15.00E0 4E0 225E0 13.00E0 4E0 225E0 12.00E0 4E0 250E0 13.00E0 4E0 250E0 12.00E0 4E0 250E0 13.50E0 4E0 250E0 10.00E0 4E0 275E0 11.50E0 4E0 275E0 11.00E0 4E0 275E0 9.50E0 4E0 275E0 15.00E0 8E0 180E0 15.00E0 8E0 180E0 15.50E0 8E0 180E0 16.00E0 8E0 180E0 13.00E0 8E0 225E0 10.50E0 8E0 225E0 13.50E0 8E0 225E0 14.00E0 8E0 225E0 12.50E0 8E0 250E0 12.00E0 8E0 250E0 11.50E0 8E0 250E0 11.50E0 8E0 250E0 6.50E0 8E0 275E0 5.50E0 8E0 275E0 6.00E0 8E0 275E0 6.00E0 8E0 275E0 18.50E0 16E0 180E0 17.00E0 16E0 180E0 15.30E0 16E0 180E0 16.00E0 16E0 180E0 13.00E0 16E0 225E0 14.00E0 16E0 225E0 12.50E0 16E0 225E0 11.00E0 16E0 225E0 12.00E0 16E0 250E0 12.00E0 16E0 250E0 11.50E0 16E0 250E0 12.00E0 16E0 250E0 6.00E0 16E0 275E0 6.00E0 16E0 275E0 5.00E0 16E0 275E0 5.50E0 16E0 275E0 12.50E0 32E0 180E0 13.00E0 32E0 180E0 16.00E0 32E0 180E0 12.00E0 32E0 180E0 11.00E0 32E0 225E0 9.50E0 32E0 225E0 11.00E0 32E0 225E0 11.00E0 32E0 225E0 11.00E0 32E0 250E0 10.00E0 32E0 250E0 10.50E0 32E0 250E0 10.50E0 32E0 250E0 2.70E0 32E0 275E0 2.70E0 32E0 275E0 2.50E0 32E0 275E0 2.40E0 32E0 275E0 13.00E0 48E0 180E0 13.50E0 48E0 180E0 16.50E0 48E0 180E0 13.60E0 48E0 180E0 11.50E0 48E0 225E0 10.50E0 48E0 225E0 13.50E0 48E0 225E0 12.00E0 48E0 225E0 7.00E0 48E0 250E0 6.90E0 48E0 250E0 8.80E0 48E0 250E0 7.90E0 48E0 250E0 1.20E0 48E0 275E0 1.50E0 48E0 275E0 1.00E0 48E0 275E0 1.50E0 48E0 275E0 13.00E0 64E0 180E0 12.50E0 64E0 180E0 16.50E0 64E0 180E0 16.00E0 64E0 180E0 11.00E0 64E0 225E0 11.50E0 64E0 225E0 10.50E0 64E0 225E0 10.00E0 64E0 225E0 7.27E0 64E0 250E0 7.50E0 64E0 250E0 6.70E0 64E0 250E0 7.60E0 64E0 250E0 1.50E0 64E0 275E0 1.00E0 64E0 275E0 1.20E0 64E0 275E0 1.20E0 64E0 275E0 end gen double lny = ln(y) nl ( lny = {b1} - {b2}*x1 * exp(-{b3}*x2) ), /// init(b1 2 b2 0.0001 b3 -0.01) eps(1e-10) assert N == e(N) cap noi assert df_r == e(df_r) cap noi assert df_m == e(df_m) lrecomp [b1]_b[_cons] b1 [b2]_b[_cons] b2 [b3]_b[_cons] b3 () /* */ [b1]_se[_cons] seb1 [b2]_se[_cons] seb2 [b3]_se[_cons] seb3 () /* */ e(rmse) rmse e(rss) rss