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NIST/ITL StRD
Dataset Name: Hahn1 (Hahn1.dat)
File Format: ASCII
Starting Values (lines 41 to 47)
Certified Values (lines 41 to 52)
Data (lines 61 to 296)
Procedure: Nonlinear Least Squares Regression
Description: These data are the result of a NIST study involving
the thermal expansion of copper. The response
variable is the coefficient of thermal expansion, and
the predictor variable is temperature in degrees
kelvin.
Reference: Hahn, T., NIST (197?).
Copper Thermal Expansion Study.
Data: 1 Response (y = coefficient of thermal expansion)
1 Predictor (x = temperature, degrees kelvin)
236 Observations
Average Level of Difficulty
Observed Data
Model: Rational Class (cubic/cubic)
7 Parameters (b1 to b7)
y = (b1+b2*x+b3*x**2+b4*x**3) /
(1+b5*x+b6*x**2+b7*x**3) + e
Starting values Certified Values
Start 1 Start 2 Parameter Standard Deviation
b1 = 10 1 1.0776351733E+00 1.7070154742E-01
b2 = -1 -0.1 -1.2269296921E-01 1.2000289189E-02
b3 = 0.05 0.005 4.0863750610E-03 2.2508314937E-04
b4 = -0.00001 -0.000001 -1.4262662514E-06 2.7578037666E-07
b5 = -0.05 -0.005 -5.7609940901E-03 2.4712888219E-04
b6 = 0.001 0.0001 2.4053735503E-04 1.0449373768E-05
b7 = -0.000001 -0.0000001 -1.2314450199E-07 1.3027335327E-08
Residual Sum of Squares: 1.5324382854E+00
Residual Standard Deviation: 8.1803852243E-02
Degrees of Freedom: 229
Number of Observations: 236
Data: y x
.591E0 24.41E0
1.547E0 34.82E0
2.902E0 44.09E0
2.894E0 45.07E0
4.703E0 54.98E0
6.307E0 65.51E0
7.03E0 70.53E0
7.898E0 75.70E0
9.470E0 89.57E0
9.484E0 91.14E0
10.072E0 96.40E0
10.163E0 97.19E0
11.615E0 114.26E0
12.005E0 120.25E0
12.478E0 127.08E0
12.982E0 133.55E0
12.970E0 133.61E0
13.926E0 158.67E0
14.452E0 172.74E0
14.404E0 171.31E0
15.190E0 202.14E0
15.550E0 220.55E0
15.528E0 221.05E0
15.499E0 221.39E0
16.131E0 250.99E0
16.438E0 268.99E0
16.387E0 271.80E0
16.549E0 271.97E0
16.872E0 321.31E0
16.830E0 321.69E0
16.926E0 330.14E0
16.907E0 333.03E0
16.966E0 333.47E0
17.060E0 340.77E0
17.122E0 345.65E0
17.311E0 373.11E0
17.355E0 373.79E0
17.668E0 411.82E0
17.767E0 419.51E0
17.803E0 421.59E0
17.765E0 422.02E0
17.768E0 422.47E0
17.736E0 422.61E0
17.858E0 441.75E0
17.877E0 447.41E0
17.912E0 448.7E0
18.046E0 472.89E0
18.085E0 476.69E0
18.291E0 522.47E0
18.357E0 522.62E0
18.426E0 524.43E0
18.584E0 546.75E0
18.610E0 549.53E0
18.870E0 575.29E0
18.795E0 576.00E0
19.111E0 625.55E0
.367E0 20.15E0
.796E0 28.78E0
0.892E0 29.57E0
1.903E0 37.41E0
2.150E0 39.12E0
3.697E0 50.24E0
5.870E0 61.38E0
6.421E0 66.25E0
7.422E0 73.42E0
9.944E0 95.52E0
11.023E0 107.32E0
11.87E0 122.04E0
12.786E0 134.03E0
14.067E0 163.19E0
13.974E0 163.48E0
14.462E0 175.70E0
14.464E0 179.86E0
15.381E0 211.27E0
15.483E0 217.78E0
15.59E0 219.14E0
16.075E0 262.52E0
16.347E0 268.01E0
16.181E0 268.62E0
16.915E0 336.25E0
17.003E0 337.23E0
16.978E0 339.33E0
17.756E0 427.38E0
17.808E0 428.58E0
17.868E0 432.68E0
18.481E0 528.99E0
18.486E0 531.08E0
19.090E0 628.34E0
16.062E0 253.24E0
16.337E0 273.13E0
16.345E0 273.66E0
16.388E0 282.10E0
17.159E0 346.62E0
17.116E0 347.19E0
17.164E0 348.78E0
17.123E0 351.18E0
17.979E0 450.10E0
17.974E0 450.35E0
18.007E0 451.92E0
17.993E0 455.56E0
18.523E0 552.22E0
18.669E0 553.56E0
18.617E0 555.74E0
19.371E0 652.59E0
19.330E0 656.20E0
0.080E0 14.13E0
0.248E0 20.41E0
1.089E0 31.30E0
1.418E0 33.84E0
2.278E0 39.70E0
3.624E0 48.83E0
4.574E0 54.50E0
5.556E0 60.41E0
7.267E0 72.77E0
7.695E0 75.25E0
9.136E0 86.84E0
9.959E0 94.88E0
9.957E0 96.40E0
11.600E0 117.37E0
13.138E0 139.08E0
13.564E0 147.73E0
13.871E0 158.63E0
13.994E0 161.84E0
14.947E0 192.11E0
15.473E0 206.76E0
15.379E0 209.07E0
15.455E0 213.32E0
15.908E0 226.44E0
16.114E0 237.12E0
17.071E0 330.90E0
17.135E0 358.72E0
17.282E0 370.77E0
17.368E0 372.72E0
17.483E0 396.24E0
17.764E0 416.59E0
18.185E0 484.02E0
18.271E0 495.47E0
18.236E0 514.78E0
18.237E0 515.65E0
18.523E0 519.47E0
18.627E0 544.47E0
18.665E0 560.11E0
19.086E0 620.77E0
0.214E0 18.97E0
0.943E0 28.93E0
1.429E0 33.91E0
2.241E0 40.03E0
2.951E0 44.66E0
3.782E0 49.87E0
4.757E0 55.16E0
5.602E0 60.90E0
7.169E0 72.08E0
8.920E0 85.15E0
10.055E0 97.06E0
12.035E0 119.63E0
12.861E0 133.27E0
13.436E0 143.84E0
14.167E0 161.91E0
14.755E0 180.67E0
15.168E0 198.44E0
15.651E0 226.86E0
15.746E0 229.65E0
16.216E0 258.27E0
16.445E0 273.77E0
16.965E0 339.15E0
17.121E0 350.13E0
17.206E0 362.75E0
17.250E0 371.03E0
17.339E0 393.32E0
17.793E0 448.53E0
18.123E0 473.78E0
18.49E0 511.12E0
18.566E0 524.70E0
18.645E0 548.75E0
18.706E0 551.64E0
18.924E0 574.02E0
19.1E0 623.86E0
0.375E0 21.46E0
0.471E0 24.33E0
1.504E0 33.43E0
2.204E0 39.22E0
2.813E0 44.18E0
4.765E0 55.02E0
9.835E0 94.33E0
10.040E0 96.44E0
11.946E0 118.82E0
12.596E0 128.48E0
13.303E0 141.94E0
13.922E0 156.92E0
14.440E0 171.65E0
14.951E0 190.00E0
15.627E0 223.26E0
15.639E0 223.88E0
15.814E0 231.50E0
16.315E0 265.05E0
16.334E0 269.44E0
16.430E0 271.78E0
16.423E0 273.46E0
17.024E0 334.61E0
17.009E0 339.79E0
17.165E0 349.52E0
17.134E0 358.18E0
17.349E0 377.98E0
17.576E0 394.77E0
17.848E0 429.66E0
18.090E0 468.22E0
18.276E0 487.27E0
18.404E0 519.54E0
18.519E0 523.03E0
19.133E0 612.99E0
19.074E0 638.59E0
19.239E0 641.36E0
19.280E0 622.05E0
19.101E0 631.50E0
19.398E0 663.97E0
19.252E0 646.9E0
19.89E0 748.29E0
20.007E0 749.21E0
19.929E0 750.14E0
19.268E0 647.04E0
19.324E0 646.89E0
20.049E0 746.9E0
20.107E0 748.43E0
20.062E0 747.35E0
20.065E0 749.27E0
19.286E0 647.61E0
19.972E0 747.78E0
20.088E0 750.51E0
20.743E0 851.37E0
20.83E0 845.97E0
20.935E0 847.54E0
21.035E0 849.93E0
20.93E0 851.61E0
21.074E0 849.75E0
21.085E0 850.98E0
20.935E0 848.23E0
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