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4. Process Modeling
4.6. Case Studies in Process Modeling
4.6.4. Thermal Expansion of Copper Case Study

4.6.4.1.

Background and Data

Description of the Data The response variable for this data set is the coefficient of thermal expansion for copper. The predictor variable is temperature in degrees kelvin. There were 236 data points collected.

These data were provided by the NIST scientist Thomas Hahn.

Software The analyses used in this case study can be generated using both Dataplot code and R code.
Resulting Data
 Coefficient               
  of Thermal    Temperature
   Expansion       (Degrees
   of Copper        Kelvin)
---------------------------
       0.591         24.41
       1.547         34.82
       2.902         44.09
       2.894         45.07
       4.703         54.98
       6.307         65.51
       7.030         70.53
       7.898         75.70
       9.470         89.57
       9.484         91.14
      10.072         96.40
      10.163         97.19
      11.615        114.26
      12.005        120.25
      12.478        127.08
      12.982        133.55
      12.970        133.61
      13.926        158.67
      14.452        172.74
      14.404        171.31
      15.190        202.14
      15.550        220.55
      15.528        221.05
      15.499        221.39
      16.131        250.99
      16.438        268.99
      16.387        271.80
      16.549        271.97
      16.872        321.31
      16.830        321.69
      16.926        330.14
      16.907        333.03
      16.966        333.47
      17.060        340.77
      17.122        345.65
      17.311        373.11
      17.355        373.79
      17.668        411.82
      17.767        419.51
      17.803        421.59
      17.765        422.02
      17.768        422.47
      17.736        422.61
      17.858        441.75
      17.877        447.41
      17.912        448.70
      18.046        472.89
      18.085        476.69
      18.291        522.47
      18.357        522.62
      18.426        524.43
      18.584        546.75
      18.610        549.53
      18.870        575.29
      18.795        576.00
      19.111        625.55
       0.367         20.15
       0.796         28.78
       0.892         29.57
       1.903         37.41
       2.150         39.12
       3.697         50.24
       5.870         61.38
       6.421         66.25
       7.422         73.42
       9.944         95.52
      11.023        107.32
      11.870        122.04
      12.786        134.03
      14.067        163.19
      13.974        163.48
      14.462        175.70
      14.464        179.86
      15.381        211.27
      15.483        217.78
      15.590        219.14
      16.075        262.52
      16.347        268.01
      16.181        268.62
      16.915        336.25
      17.003        337.23
      16.978        339.33
      17.756        427.38
      17.808        428.58
      17.868        432.68
      18.481        528.99
      18.486        531.08
      19.090        628.34
      16.062        253.24
      16.337        273.13
      16.345        273.66
      16.388        282.10
      17.159        346.62
      17.116        347.19
      17.164        348.78
      17.123        351.18
      17.979        450.10
      17.974        450.35
      18.007        451.92
      17.993        455.56
      18.523        552.22
      18.669        553.56
      18.617        555.74
      19.371        652.59
      19.330        656.20
       0.080         14.13
       0.248         20.41
       1.089         31.30
       1.418         33.84
       2.278         39.70
       3.624         48.83
       4.574         54.50
       5.556         60.41
       7.267         72.77
       7.695         75.25
       9.136         86.84
       9.959         94.88
       9.957         96.40
      11.600        117.37
      13.138        139.08
      13.564        147.73
      13.871        158.63
      13.994        161.84
      14.947        192.11
      15.473        206.76
      15.379        209.07
      15.455        213.32
      15.908        226.44
      16.114        237.12
      17.071        330.90
      17.135        358.72
      17.282        370.77
      17.368        372.72
      17.483        396.24
      17.764        416.59
      18.185        484.02
      18.271        495.47
      18.236        514.78
      18.237        515.65
      18.523        519.47
      18.627        544.47
      18.665        560.11
      19.086        620.77
       0.214         18.97
       0.943         28.93
       1.429         33.91
       2.241         40.03
       2.951         44.66
       3.782         49.87
       4.757         55.16
       5.602         60.90
       7.169         72.08
       8.920         85.15
      10.055         97.06
      12.035        119.63
      12.861        133.27
      13.436        143.84
      14.167        161.91
      14.755        180.67
      15.168        198.44
      15.651        226.86
      15.746        229.65
      16.216        258.27
      16.445        273.77
      16.965        339.15
      17.121        350.13
      17.206        362.75
      17.250        371.03
      17.339        393.32
      17.793        448.53
      18.123        473.78
      18.49         511.12
      18.566        524.70
      18.645        548.75
      18.706        551.64
      18.924        574.02
      19.100        623.86
       0.375         21.46
       0.471         24.33
       1.504         33.43
       2.204         39.22
       2.813         44.18
       4.765         55.02
       9.835         94.33
      10.040         96.44
      11.946        118.82
      12.596        128.48
      13.303        141.94
      13.922        156.92
      14.440        171.65
      14.951        190.00
      15.627        223.26
      15.639        223.88
      15.814        231.50
      16.315        265.05
      16.334        269.44
      16.430        271.78
      16.423        273.46
      17.024        334.61
      17.009        339.79
      17.165        349.52
      17.134        358.18
      17.349        377.98
      17.576        394.77
      17.848        429.66
      18.090        468.22
      18.276        487.27
      18.404        519.54
      18.519        523.03
      19.133        612.99
      19.074        638.59
      19.239        641.36
      19.280        622.05
      19.101        631.50
      19.398        663.97
      19.252        646.90
      19.890        748.29
      20.007        749.21
      19.929        750.14
      19.268        647.04
      19.324        646.89
      20.049        746.90
      20.107        748.43
      20.062        747.35
      20.065        749.27
      19.286        647.61
      19.972        747.78
      20.088        750.51
      20.743        851.37
      20.830        845.97
      20.935        847.54
      21.035        849.93
      20.930        851.61
      21.074        849.75
      21.085        850.98
      20.935        848.23
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