Question

3. (Exercise 4.32, using R) (2 pt) Cooling method for gas turbines. Recall the Journal of Engineering for Gas Turbines and Power (January 2005) study of a high-pressure inlet fogging
method for a gas turbine engine, where we fitted a first-order model for heat rate (y) as a function of speed of the engine (x1), inlet temperature (x2), exhaust temperature (x3), cycle pressure ratio (x4), and air mass flow rate (x5). Now, in this example, a researcher hypothesized that the linear relationship between heat rate (y) and inlet and exhaust temperatures (x2 and x3) depends on air flow rate (x5). Based on the hypothesis, the interaction regression model is written as
y = β0 + β1x2 + β2x3 + β3x2x5 + β5x3x5 + ε.    Equation (1)
(a) Use R to fit the interaction model to the data in the GASTURBINE file. Print your R code and outputs for the interaction model in Equation (1). (What is the table of R output a.k.a. data gathered from R?)

Gas Turbine Data:
ENGINE SHAFTS RPM CPRATIO INLETTEMP EXHTEMP AIRFLOW POWER HEATRATE (Columns)
Traditional 1 27245 9.2 1134 602 7 1630 14622
Traditional 1 14000 12.2 950 446 15 2726 13196
Traditional 1 17384 14.8 1149 537 20 5247 11948
Traditional 1 11085 11.8 1024 478 27 6726 11289
Traditional 1 14045 13.2 1149 553 29 7726 11964
Traditional 1 6211 15.7 1172 517 176 52600 10526
Traditional 1 6210 17.4 1177 510 193 57500 10387
Traditional 1 3600 13.5 1146 503 315 89600 10592
Traditional 1 3000 15.1 1146 524 375 113700 10460
Traditional 1 3000 15.0 1171 525 514 164300 10086
Traditional 1 18000 12.7 1038 525 11 2000 14628
Traditional 1 11140 9.1 1038 523 25 5223 13396
Traditional 1 16630 15.0 1232 571 19 5500 11726
Traditional 2 7900 15.6 1077 482 47 11700 11252
Traditional 1 5100 10.0 963 485 123 26555 12449
Traditional 1 5160 12.3 1135 542 144 42170 11030
Traditional 1 3600 12.6 1113 534 295 86650 10787
Traditional 1 3000 12.3 1124 541 410 124700 10603
Traditional 1 3000 14.2 1204 553 515 172985 10144
Traditional 1 14000 15.9 1177 521 27 6930 11674
Traditional 1 3660 14.6 1135 526 56 14838 11510
Traditional 1 5400 15.3 1149 514 172 49500 10946
Traditional 1 3600 14.2 1141 526 362 109370 10508
Traditional 1 3600 11.0 1149 544 354 108719 10604
Traditional 1 3600 14.2 1177 525 378 120500 10270
Traditional 1 3000 14.2 1116 511 448 132220 10529
Traditional 1 3000 11.1 1149 537 500 157010 10360
Traditional 1 22516 6.6 899 512 7 1210 14796
Traditional 1 14950 9.7 916 444 19 3515 12913
Traditional 1 14950 10.7 1054 517 19 4600 12270
Traditional 1 14950 12.0 1093 513 22 5500 11842
Traditional 1 14950 15.0 1121 490 27 7520 10656
Traditional 2 8568 16.2 1066 464 39 9286 11360
Traditional 2 8568 17.6 1104 487 42 10685 11136
Traditional 1 11220 15.8 1121 493 49 13500 10814
Traditional 1 4473 8.9 960 517 158 32776 13523
Traditional 1 3600 12.4 1079 515 311 81600 11289
Traditional 1 3000 12.5 1041 490 400 100500 11183
Traditional 2 10400 15.0 1057 479 26 6844 10951
Advanced 1 6600 20.0 1288 546 120 43000 9722
Advanced 1 5100 14.8 1288 590 204 70905 10481
Advanced 1 3600 15.5 1327 599 448 174000 9812
Advanced 1 3600 18.5 1371 626 445 186600 9669
Advanced 1 3000 14.6 1327 599 648 259670 9643
Advanced 1 3000 23.2 1427 566 685 282000 9115
Advanced 1 3000 23.2 1427 621 685 331000 9115
Advanced 1 7280 14.3 1271 556 49 13680 11588
Advanced 1 7280 14.6 1271 556 88 27010 10888
Advanced 1 3600 16.0 1343 607 453 185400 9738
Advanced 1 3600 20.0 1427 596 567 254000 9295
Advanced 1 3000 17.0 1343 586 651 270300 9421
Advanced 1 3000 21.0 1427 587 737 334000 9105
Advanced 1 5400 16.1 1288 531 188 62300 10233
Advanced 1 5400 16.2 1310 589 187 68000 10186
Advanced 1 3600 16.0 1288 551 425 153600 9918
Advanced 1 3600 16.9 1343 577 440 182000 9209
Advanced 1 3600 15.0 1349 590 450 186500 9532
Advanced 1 3000 14.0 1260 585 510 189000 9933
Advanced 1 3600 19.2 1427 594 550 253000 9152
Advanced 1 3000 17.0 1316 584 642 265540 9295
Aeroderiv 2 33000 6.9 888 513 3 486 16243
Aeroderiv 2 30000 8.5 1004 561 4 806 14628
Aeroderiv 2 18910 14.0 1066 532 8 1845 12766
Aeroderiv 3 3600 35.0 1288 448 152 57930 8714
Aeroderiv 3 3600 20.0 1160 456 84 25600 9469
Aeroderiv 2 16000 10.6 1232 560 14 3815 11948
Aeroderiv 1 14600 13.4 1077 536 20 4942 12414

Answer 1