1 NIST/ITL StRD 2 Dataset Name: Hahn1 (Hahn1.dat) 3 4 File Format: ASCII 5 Starting Values (lines 41 to 47) 6 Certified Values (lines 41 to 52) 7 Data (lines 61 to 296) 8 9 Procedure: Nonlinear Least Squares Regression 10 11 Description: These data are the result of a NIST study involving 12 the thermal expansion of copper. The response 13 variable is the coefficient of thermal expansion, and 14 the predictor variable is temperature in degrees 15 kelvin. 16 17 18 Reference: Hahn, T., NIST (197?). 19 Copper Thermal Expansion Study. 20 21 22 23 24 25 Data: 1 Response (y = coefficient of thermal expansion) 26 1 Predictor (x = temperature, degrees kelvin) 27 236 Observations 28 Average Level of Difficulty 29 Observed Data 30 31 Model: Rational Class (cubic/cubic) 32 7 Parameters (b1 to b7) 33 34 y = (b1+b2*x+b3*x**2+b4*x**3) / 35 (1+b5*x+b6*x**2+b7*x**3) + e 36 37 38 Starting values Certified Values 39 40 Start 1 Start 2 Parameter Standard Deviation 41 b1 = 10 1 1.0776351733E+00 1.7070154742E-01 42 b2 = -1 -0.1 -1.2269296921E-01 1.2000289189E-02 43 b3 = 0.05 0.005 4.0863750610E-03 2.2508314937E-04 44 b4 = -0.00001 -0.000001 -1.4262662514E-06 2.7578037666E-07 45 b5 = -0.05 -0.005 -5.7609940901E-03 2.4712888219E-04 46 b6 = 0.001 0.0001 2.4053735503E-04 1.0449373768E-05 47 b7 = -0.000001 -0.0000001 -1.2314450199E-07 1.3027335327E-08 48 49 Residual Sum of Squares: 1.5324382854E+00 50 Residual Standard Deviation: 8.1803852243E-02 51 Degrees of Freedom: 229 52 Number of Observations: 236 53 54 55 56 57 58 59 60 Data: y x 61 .591E0 24.41E0 62 1.547E0 34.82E0 63 2.902E0 44.09E0 64 2.894E0 45.07E0 65 4.703E0 54.98E0 66 6.307E0 65.51E0 67 7.03E0 70.53E0 68 7.898E0 75.70E0 69 9.470E0 89.57E0 70 9.484E0 91.14E0 71 10.072E0 96.40E0 72 10.163E0 97.19E0 73 11.615E0 114.26E0 74 12.005E0 120.25E0 75 12.478E0 127.08E0 76 12.982E0 133.55E0 77 12.970E0 133.61E0 78 13.926E0 158.67E0 79 14.452E0 172.74E0 80 14.404E0 171.31E0 81 15.190E0 202.14E0 82 15.550E0 220.55E0 83 15.528E0 221.05E0 84 15.499E0 221.39E0 85 16.131E0 250.99E0 86 16.438E0 268.99E0 87 16.387E0 271.80E0 88 16.549E0 271.97E0 89 16.872E0 321.31E0 90 16.830E0 321.69E0 91 16.926E0 330.14E0 92 16.907E0 333.03E0 93 16.966E0 333.47E0 94 17.060E0 340.77E0 95 17.122E0 345.65E0 96 17.311E0 373.11E0 97 17.355E0 373.79E0 98 17.668E0 411.82E0 99 17.767E0 419.51E0 100 17.803E0 421.59E0 101 17.765E0 422.02E0 102 17.768E0 422.47E0 103 17.736E0 422.61E0 104 17.858E0 441.75E0 105 17.877E0 447.41E0 106 17.912E0 448.7E0 107 18.046E0 472.89E0 108 18.085E0 476.69E0 109 18.291E0 522.47E0 110 18.357E0 522.62E0 111 18.426E0 524.43E0 112 18.584E0 546.75E0 113 18.610E0 549.53E0 114 18.870E0 575.29E0 115 18.795E0 576.00E0 116 19.111E0 625.55E0 117 .367E0 20.15E0 118 .796E0 28.78E0 119 0.892E0 29.57E0 120 1.903E0 37.41E0 121 2.150E0 39.12E0 122 3.697E0 50.24E0 123 5.870E0 61.38E0 124 6.421E0 66.25E0 125 7.422E0 73.42E0 126 9.944E0 95.52E0 127 11.023E0 107.32E0 128 11.87E0 122.04E0 129 12.786E0 134.03E0 130 14.067E0 163.19E0 131 13.974E0 163.48E0 132 14.462E0 175.70E0 133 14.464E0 179.86E0 134 15.381E0 211.27E0 135 15.483E0 217.78E0 136 15.59E0 219.14E0 137 16.075E0 262.52E0 138 16.347E0 268.01E0 139 16.181E0 268.62E0 140 16.915E0 336.25E0 141 17.003E0 337.23E0 142 16.978E0 339.33E0 143 17.756E0 427.38E0 144 17.808E0 428.58E0 145 17.868E0 432.68E0 146 18.481E0 528.99E0 147 18.486E0 531.08E0 148 19.090E0 628.34E0 149 16.062E0 253.24E0 150 16.337E0 273.13E0 151 16.345E0 273.66E0 152 16.388E0 282.10E0 153 17.159E0 346.62E0 154 17.116E0 347.19E0 155 17.164E0 348.78E0 156 17.123E0 351.18E0 157 17.979E0 450.10E0 158 17.974E0 450.35E0 159 18.007E0 451.92E0 160 17.993E0 455.56E0 161 18.523E0 552.22E0 162 18.669E0 553.56E0 163 18.617E0 555.74E0 164 19.371E0 652.59E0 165 19.330E0 656.20E0 166 0.080E0 14.13E0 167 0.248E0 20.41E0 168 1.089E0 31.30E0 169 1.418E0 33.84E0 170 2.278E0 39.70E0 171 3.624E0 48.83E0 172 4.574E0 54.50E0 173 5.556E0 60.41E0 174 7.267E0 72.77E0 175 7.695E0 75.25E0 176 9.136E0 86.84E0 177 9.959E0 94.88E0 178 9.957E0 96.40E0 179 11.600E0 117.37E0 180 13.138E0 139.08E0 181 13.564E0 147.73E0 182 13.871E0 158.63E0 183 13.994E0 161.84E0 184 14.947E0 192.11E0 185 15.473E0 206.76E0 186 15.379E0 209.07E0 187 15.455E0 213.32E0 188 15.908E0 226.44E0 189 16.114E0 237.12E0 190 17.071E0 330.90E0 191 17.135E0 358.72E0 192 17.282E0 370.77E0 193 17.368E0 372.72E0 194 17.483E0 396.24E0 195 17.764E0 416.59E0 196 18.185E0 484.02E0 197 18.271E0 495.47E0 198 18.236E0 514.78E0 199 18.237E0 515.65E0 200 18.523E0 519.47E0 201 18.627E0 544.47E0 202 18.665E0 560.11E0 203 19.086E0 620.77E0 204 0.214E0 18.97E0 205 0.943E0 28.93E0 206 1.429E0 33.91E0 207 2.241E0 40.03E0 208 2.951E0 44.66E0 209 3.782E0 49.87E0 210 4.757E0 55.16E0 211 5.602E0 60.90E0 212 7.169E0 72.08E0 213 8.920E0 85.15E0 214 10.055E0 97.06E0 215 12.035E0 119.63E0 216 12.861E0 133.27E0 217 13.436E0 143.84E0 218 14.167E0 161.91E0 219 14.755E0 180.67E0 220 15.168E0 198.44E0 221 15.651E0 226.86E0 222 15.746E0 229.65E0 223 16.216E0 258.27E0 224 16.445E0 273.77E0 225 16.965E0 339.15E0 226 17.121E0 350.13E0 227 17.206E0 362.75E0 228 17.250E0 371.03E0 229 17.339E0 393.32E0 230 17.793E0 448.53E0 231 18.123E0 473.78E0 232 18.49E0 511.12E0 233 18.566E0 524.70E0 234 18.645E0 548.75E0 235 18.706E0 551.64E0 236 18.924E0 574.02E0 237 19.1E0 623.86E0 238 0.375E0 21.46E0 239 0.471E0 24.33E0 240 1.504E0 33.43E0 241 2.204E0 39.22E0 242 2.813E0 44.18E0 243 4.765E0 55.02E0 244 9.835E0 94.33E0 245 10.040E0 96.44E0 246 11.946E0 118.82E0 247 12.596E0 128.48E0 248 13.303E0 141.94E0 249 13.922E0 156.92E0 250 14.440E0 171.65E0 251 14.951E0 190.00E0 252 15.627E0 223.26E0 253 15.639E0 223.88E0 254 15.814E0 231.50E0 255 16.315E0 265.05E0 256 16.334E0 269.44E0 257 16.430E0 271.78E0 258 16.423E0 273.46E0 259 17.024E0 334.61E0 260 17.009E0 339.79E0 261 17.165E0 349.52E0 262 17.134E0 358.18E0 263 17.349E0 377.98E0 264 17.576E0 394.77E0 265 17.848E0 429.66E0 266 18.090E0 468.22E0 267 18.276E0 487.27E0 268 18.404E0 519.54E0 269 18.519E0 523.03E0 270 19.133E0 612.99E0 271 19.074E0 638.59E0 272 19.239E0 641.36E0 273 19.280E0 622.05E0 274 19.101E0 631.50E0 275 19.398E0 663.97E0 276 19.252E0 646.9E0 277 19.89E0 748.29E0 278 20.007E0 749.21E0 279 19.929E0 750.14E0 280 19.268E0 647.04E0 281 19.324E0 646.89E0 282 20.049E0 746.9E0 283 20.107E0 748.43E0 284 20.062E0 747.35E0 285 20.065E0 749.27E0 286 19.286E0 647.61E0 287 19.972E0 747.78E0 288 20.088E0 750.51E0 289 20.743E0 851.37E0 290 20.83E0 845.97E0 291 20.935E0 847.54E0 292 21.035E0 849.93E0 293 20.93E0 851.61E0 294 21.074E0 849.75E0 295 21.085E0 850.98E0 296 20.935E0 848.23E0 297
