$ontext Non-Linear Least Squares Regression example Erwin Kalvelagen, may 2008 Reference: http://www.statsci.org/data/general/dolphin.html Sound Pressure of Dolphin Sonar -------------------------------------------------------------------------------- Description The data give the sound pressure of sonar signals ("clicks") from a dolphin at various ranges to target. The measurements were made off the coast of Iceland near Keflavik in 1998. The pressure measurement given is raw pressure + a Range where a is a known constant depending on the water density. Pressure is expected to increase with distance even after the adjustment. -------------------------------------------------------------------------------- Variable Description -------------------------------------------------------------------------------- Range Distance to dolphin in metres SoundPressure Water sound pressure adjusted for water density -------------------------------------------------------------------------------- Source Marianne Rasmussen, Department of Biology, Odense University, Denmark. Analysis A simple power growth curve SoundPressure = a*Range^b seems adequate. There is an outlier. $offtext set i /i1*i1634/; table data(i,*) Range SoundPressure i1 8.5 201.2 i2 9.1 204.3 i3 10.8 208.5 i4 12 231.7 i5 8.9 213.4 i6 9.3 213.2 i7 9.9 213.2 i8 1.6 200.4 i9 1.8 199.3 i10 1.5 188.3 i11 3.7 198.7 i12 3.1 205.3 i13 1.3 193.1 i14 1.2 193.3 i15 4 193.8 i16 3.8 198.3 i17 4.9 202 i18 5.8 203.3 i19 4.7 200.5 i20 4.4 200.1 i21 5.4 202.2 i22 5.8 203.7 i23 5.5 195.9 i24 5.2 208.3 i25 4.7 198 i26 5.6 199.1 i27 5.4 194.7 i28 4.7 196.9 i29 4.7 199.7 i30 5.5 203.1 i31 4.8 201.1 i32 4.5 200.7 i33 5.2 201.2 i34 5.2 200.4 i35 4.9 200.4 i36 4.6 200.8 i37 4.7 201.2 i38 5.5 204.5 i39 4.5 200.6 i40 4.8 200 i41 4.7 198.2 i42 5.1 196.4 i43 4.8 198.6 i44 13 205.2 i45 10 205.8 i46 11.4 206.3 i47 1.1 182.8 i48 11.4 210.2 i49 1.1 198.1 i50 11.6 210.5 i51 13.6 213.8 i52 10.3 210.7 i53 11.8 212.3 i54 11.8 209.7 i55 11.8 209.9 i56 11.8 211.2 i57 11.8 209.6 i58 11.8 210 i59 12.4 210.2 i60 9.1 207.6 i61 8.8 206.8 i62 14.2 211.7 i63 11.3 209.7 i64 7 204.1 i65 6 203.8 i66 5.6 204.7 i67 4.9 200.8 i68 12.9 212.2 i69 11.5 213.2 i70 12.9 215 i71 14.8 213.8 i72 3.9 203.4 i73 3.8 203.3 i74 3.8 204.2 i75 3.8 205.6 i76 3.8 202.5 i77 3.9 204.2 i78 3.6 204.8 i79 3.5 204.1 i80 3.7 201.2 i81 3.2 201.2 i82 3.1 198.9 i83 5.1 211.9 i84 5.8 213 i85 6 214.3 i86 5.9 211.9 i87 5.2 212.2 i88 7.9 206.8 i89 6.8 209.4 i90 6.8 209.5 i91 7.3 207.1 i92 6.3 205.2 i93 7.3 207 i94 7.3 204.6 i95 5.2 199.9 i96 5.8 206.7 i97 5.4 209.8 i98 5.1 207.9 i99 4.8 205.9 i100 3.8 202.3 i101 3.7 203 i102 3.8 204.8 i103 3.4 202.4 i104 3.9 205.8 i105 3.5 202.8 i106 3.6 206.2 i107 3.5 201.7 i108 3.6 203.2 i109 3.2 201.6 i110 3.2 200.8 i111 7 204.2 i112 6.7 202.9 i113 6.5 205 i114 6.4 203.8 i115 6.5 203.8 i116 6.5 205.5 i117 5.7 202.7 i118 6.6 204.5 i119 5.4 205.3 i120 3.3 199.2 i121 3.7 197.7 i122 3 202.4 i123 3 198.7 i124 3.2 199.1 i125 3 199.2 i126 2.9 200 i127 3.2 202 i128 3.2 202.2 i129 2.9 201.4 i130 2.9 201.5 i131 3.1 204 i132 2.9 205.1 i133 3 203.7 i134 2.7 202.7 i135 9.5 212.4 i136 2.4 198 i137 2.4 196.2 i138 2.5 197.1 i139 2.7 195.2 i140 2.9 196.4 i141 2.7 196.4 i142 3.1 198 i143 2.9 200.1 i144 2.8 200.6 i145 3.1 198.9 i146 2.7 198.4 i147 2.9 197 i148 2.8 199.6 i149 2.6 196.8 i150 2.7 199.1 i151 2.6 201.5 i152 2.9 201.3 i153 2.5 200.8 i154 2.6 200.1 i155 2.3 198.3 i156 2.2 200 i157 2.3 201.3 i158 2.3 201.2 i159 2.2 199.5 i160 2 200.6 i161 1.7 200 i162 1.9 199.9 i163 2.2 198.7 i164 2.6 195.3 i165 2.4 194.6 i166 3.7 198.1 i167 3.6 199.2 i168 3.6 198.7 i169 3.7 198.2 i170 4.3 200.1 i171 4.8 201 i172 4.7 199.4 i173 4.6 200.7 i174 4.7 200.6 i175 4.2 198.9 i176 4.4 199 i177 4.1 200.9 i178 4.1 200.4 i179 4.1 200.6 i180 4.8 202 i181 5.3 204.6 i182 5.6 205.2 i183 6 205 i184 6 202 i185 5 201.6 i186 6 202 i187 4.9 201.3 i188 4.9 200.9 i189 5.4 201.1 i190 5.1 202.3 i191 5.4 203.3 i192 4.6 202.3 i193 5.4 203.5 i194 5.7 203.8 i195 5.1 202.5 i196 4.8 201.7 i197 5.7 204.3 i198 4.6 202.8 i199 4.3 200.4 i200 4.3 199.5 i201 4.4 202 i202 4.7 203.2 i203 4.2 201.9 i204 4.4 201.2 i205 4.6 201.4 i206 4.4 200.4 i207 4.4 200.8 i208 3.8 201.4 i209 3.9 203.8 i210 4.1 203.1 i211 3.9 202 i212 3.6 200.4 i213 3.7 199.3 i214 3.8 198.8 i215 4.2 200.5 i216 4 200.7 i217 3.6 198.4 i218 4.1 201 i219 4.3 202.5 i220 4.3 202.7 i221 4.6 203.3 i222 3.9 201.7 i223 4.3 203.9 i224 4.3 203.3 i225 4.5 203.1 i226 4.8 202.2 i227 4.5 203.2 i228 4.7 202.4 i229 4.3 200 i230 4.4 198.3 i231 4.2 205.2 i232 4 204.6 i233 3.6 201.1 i234 3.3 201.9 i235 3.3 203.5 i236 3 200.3 i237 3.2 202 i238 3.7 198.6 i239 3 199.9 i240 2.6 201.3 i241 2.9 204.7 i242 2.7 205.6 i243 2.8 206.4 i244 2.8 206.2 i245 9.8 206.5 i246 8.6 206.5 i247 6.8 204.5 i248 6.8 207 i249 6.2 206.9 i250 6.1 209.3 i251 7.3 207.9 i252 12.3 211.2 i253 14.1 214.8 i254 5.7 202.9 i255 5.4 204 i256 5.1 203.4 i257 4.8 205.1 i258 4.8 205.1 i259 5.1 205.7 i260 4.4 204.3 i261 4.8 207.2 i262 4.6 208 i263 4.8 206 i264 4.4 202.6 i265 4.8 201.5 i266 4.4 202.7 i267 4.4 202.6 i268 4.6 203.4 i269 3.1 200.2 i270 3.2 202.9 i271 2.6 202.9 i272 3.3 204.8 i273 2.9 205.1 i274 3.2 205.2 i275 3.2 205.4 i276 3.3 205.6 i277 4 200.6 i278 3.5 202.3 i279 3.8 203.2 i280 3.7 205.8 i281 3.7 207.4 i282 3.6 207.3 i283 4 209.3 i284 3.8 204.7 i285 3 199.8 i286 3.7 205.3 i287 3.7 204.9 i288 3.9 204.7 i289 3.9 206.9 i290 3.6 207.1 i291 2.9 198.8 i292 1.7 196.7 i293 9.5 207.5 i294 10.4 208.1 i295 9.5 207.7 i296 8.4 204.7 i297 9.2 205.4 i298 8.4 205.5 i299 13 209.7 i300 9.1 206.1 i301 10 210.3 i302 12.5 214.1 i303 11.1 209.7 i304 10.4 209.8 i305 10.4 209.1 i306 10.4 206.6 i307 9.5 207 i308 8 204.6 i309 7.3 208.2 i310 7.1 207.8 i311 7.6 207.9 i312 8.1 208.9 i313 5.7 201.3 i314 6.2 205.4 i315 6.7 207.4 i316 7.2 207.4 i317 7.1 206.5 i318 4.6 203.8 i319 5.9 204.4 i320 3.4 201.6 i321 6.5 206.1 i322 5.4 205.9 i323 4.7 204.6 i324 3.9 202.6 i325 4.6 204.4 i326 13.1 211 i327 11.5 212.8 i328 11.5 209.2 i329 13.1 208.7 i330 11.5 208.7 i331 9.1 210.1 i332 10.2 210.7 i333 9.2 208.2 i334 10.2 208.8 i335 9.2 211.1 i336 9.2 210.9 i337 10.2 209.7 i338 9.1 209.3 i339 9.1 210.1 i340 10.2 209.6 i341 7.6 208 i342 7.6 207.9 i343 9.1 211.7 i344 10 214.5 i345 11.2 215.4 i346 8.4 208 i347 8.4 210.2 i348 9.2 212.4 i349 11.8 213.7 i350 6.4 205.8 i351 8.1 209.6 i352 8.1 210.2 i353 10 213 i354 10 211.7 i355 10 210.7 i356 7.9 204.7 i357 10 210.2 i358 6.8 205.3 i359 6.2 204.4 i360 5.7 206 i361 6.2 204.4 i362 5.7 202.4 i363 5.7 200.8 i364 6.6 207.1 i365 5.6 209.9 i366 5.2 207.8 i367 5.2 206.3 i368 6.6 210.2 i369 5.5 204.7 i370 6.4 205.5 i371 6.8 208.9 i372 6.3 206.5 i373 6.8 205.9 i374 4.4 199.9 i375 4.5 205 i376 2.5 200.9 i377 2.4 200.1 i378 2.4 198.3 i379 2.5 195.1 i380 2.3 195.1 i381 2.5 197.5 i382 2.4 198.3 i383 2.3 198 i384 2.3 198.3 i385 2.3 198 i386 2.1 197.3 i387 2.1 195.8 i388 1.9 195.4 i389 2.2 196.6 i390 2.1 197.3 i391 2 196 i392 2.1 198.6 i393 2.1 198.8 i394 2 198.6 i395 2 195 i396 2 192.6 i397 2.2 194.2 i398 2.2 196.9 i399 2.2 196.8 i400 2.2 197.1 i401 2.1 195.8 i402 2.3 194.9 i403 2.2 194.3 i404 2.3 194.4 i405 2.3 196.4 i406 2.3 195.3 i407 2.4 198.8 i408 2.6 199.7 i409 2.1 195.4 i410 2.2 194.4 i411 3 198.8 i412 3.3 199.5 i413 2.9 199.3 i414 3.2 200 i415 3.4 201.9 i416 3.1 199.8 i417 3.5 200.1 i418 3.2 199.3 i419 3.2 199.3 i420 3.1 197.5 i421 3.1 198.5 i422 2.8 198.1 i423 2.8 198.2 i424 2.9 198.6 i425 3.1 200 i426 3.1 200.1 i427 3 199.9 i428 3 199.2 i429 2.9 199 i430 3.1 198.8 i431 2.9 198.3 i432 3.1 200.3 i433 3.3 205.3 i434 2.8 200.8 i435 2.9 202.3 i436 3 200.5 i437 6 203.9 i438 8.3 206.8 i439 7.5 205.4 i440 5.6 202.3 i441 7.7 208.9 i442 5.9 208.2 i443 7.7 209.1 i444 7 206 i445 7.8 204.6 i446 5.6 202.8 i447 5.6 200.3 i448 5.6 201.8 i449 5.2 202.7 i450 5.6 204.2 i451 5.6 204.2 i452 4.9 201.5 i453 5.2 203.4 i454 5.2 205 i455 5.2 203.5 i456 4.4 205.2 i457 5.2 201 i458 4.9 202.1 i459 5.2 200.6 i460 5.1 198.4 i461 3.8 195.1 i462 1.7 190.3 i463 1.9 193.5 i464 1.9 189.2 i465 1.9 191.1 i466 1.7 195 i467 1.7 192.2 i468 1.2 191 i469 1 190.8 i470 6.5 200.4 i471 7 201.5 i472 6.1 199.6 i473 2.5 193.6 i474 2.4 193.9 i475 3.2 197.5 i476 2.5 196.7 i477 1.1 185 i478 1.1 186.7 i479 1.1 187.6 i480 1 186.4 i481 1 186.1 i482 12 206 i483 10.5 208 i484 12.2 208.7 i485 12.3 206.4 i486 8.6 205.9 i487 7.7 206.7 i488 8.6 208.7 i489 9.8 210.8 i490 8.6 207.9 i491 9.8 209 i492 11.4 211 i493 8.5 207.4 i494 7.6 207.4 i495 9.7 209.2 i496 8.6 209 i497 9.9 210.4 i498 7.7 206.2 i499 14.8 210.7 i500 14.8 211.2 i501 14.8 208.6 i502 14.7 210.3 i503 14.7 208.9 i504 14.7 209.1 i505 14.7 206.5 i506 5.1 201.3 i507 4.6 200.2 i508 4.9 199.6 i509 5.4 200.8 i510 5.1 198.8 i511 4.3 196.3 i512 4.5 199 i513 4 198.6 i514 4.6 198 i515 4.4 199.4 i516 4.4 199.2 i517 4.2 199.9 i518 5.1 199.7 i519 4.4 201.9 i520 4.6 200.9 i521 4.7 202.1 i522 4.3 200.1 i523 4.2 199.1 i524 3.8 198.7 i525 3.9 198.5 i526 3.9 198.1 i527 4.3 199.4 i528 4.1 200.3 i529 4.1 199.6 i530 4.1 201 i531 4.1 201.2 i532 4.1 203 i533 4.3 204.6 i534 3.5 202.2 i535 3.8 201 i536 3.6 195.9 i537 3.7 198.6 i538 3.8 202.4 i539 4 202.5 i540 3.2 202.4 i541 3.3 202.3 i542 3.5 202 i543 3 198.2 i544 3.6 199 i545 3.5 199.5 i546 4 198.3 i547 3.5 195.3 i548 3.1 195.6 i549 3.1 197.4 i550 2.6 197.8 i551 2.4 196.3 i552 2.4 196.2 i553 2.7 194.3 i554 2.6 196.4 i555 2.9 196.6 i556 2.8 199.3 i557 2.7 198.3 i558 2.8 199 i559 2.4 196.9 i560 2.3 193.1 i561 2.3 194.3 i562 14.8 206.9 i563 13 207.7 i564 12.9 209.8 i565 10.3 205.1 i566 14.7 209.4 i567 9.4 205.6 i568 11.5 209.5 i569 11.5 208 i570 12.9 211.9 i571 12.7 211.4 i572 11.3 209.9 i573 14.5 211.6 i574 10.1 206.4 i575 11.2 208.7 i576 11.4 208.6 i577 12.8 212.1 i578 11.4 211.7 i579 11.4 211.7 i580 11.5 207.7 i581 13 210.3 i582 14.8 211 i583 14.8 210 i584 13 211.8 i585 14.8 215.3 i586 13 210.9 i587 11.4 210.3 i588 11.4 208.1 i589 11.4 208.2 i590 10.2 205.9 i591 10.2 205.2 i592 10.2 206.4 i593 9.3 205.1 i594 11.4 208.4 i595 9.3 210 i596 10.3 208.6 i597 2 191.1 i598 1.7 193.1 i599 1.8 193.8 i600 2 194.1 i601 1.4 190.2 i602 1.5 192.6 i603 1.6 191.1 i604 1.5 191.2 i605 1.4 190.4 i606 1.4 189.6 i607 1.5 190.5 i608 1.4 191.8 i609 1.4 188.4 i610 10.2 207.6 i611 8.5 203.9 i612 8.5 204 i613 9.2 208.5 i614 10.2 207.9 i615 7.8 203.3 i616 7.7 204.4 i617 8.3 205.1 i618 9.1 206.7 i619 9.1 205.1 i620 5.4 200.1 i621 6.4 202.9 i622 6.9 203.4 i623 6.4 202.2 i624 6.4 203.1 i625 6.4 206.9 i626 6 206.3 i627 6 207.3 i628 6.4 206 i629 6.4 207.3 i630 6.4 208.9 i631 5.9 209.7 i632 5.6 202.1 i633 7.2 204.9 i634 10.5 209.3 i635 9.3 209.3 i636 6.7 204.8 i637 9.2 205.6 i638 7.5 206.5 i639 8.5 208.5 i640 6.8 208 i641 7.6 208.8 i642 11.4 211.6 i643 7.5 206.6 i644 4.6 198 i645 4 197.1 i646 6.2 208.1 i647 6.8 205.5 i648 8.5 205.6 i649 6.8 203.6 i650 6.9 203.9 i651 5.7 203.9 i652 6.2 203.3 i653 6.1 201 i654 7.8 203.7 i655 6.3 202 i656 5.7 201.3 i657 7.8 203 i658 7 202.9 i659 5.7 203.5 i660 5.8 201 i661 6.9 204.4 i662 5.8 203.1 i663 6.3 204.7 i664 7.8 204.1 i665 7 203 i666 1.5 190.8 i667 1.7 191.1 i668 1.7 194.9 i669 6.5 204 i670 2 193.9 i671 1.8 195.1 i672 1.7 196.1 i673 1.8 190.5 i674 1.9 190.5 i675 1.7 190.2 i676 1.8 191.5 i677 1.8 190.1 i678 1.5 189 i679 1.5 188.7 i680 1.8 196.2 i681 1.5 196.6 i682 1.4 200.4 i683 1.8 193.8 i684 1.4 197.4 i685 1.3 198.5 i686 1.4 200 i687 1.3 201.3 i688 1.3 198.4 i689 1.5 197 i690 2.1 191.4 i691 1.4 196 i692 1.4 191 i693 8.1 204.7 i694 10 207.9 i695 10 206.1 i696 8 204.9 i697 7.2 204.4 i698 8.7 204.8 i699 7.8 206.6 i700 8.7 207 i701 7.8 205.6 i702 7.8 206.4 i703 6.9 205 i704 5 200.5 i705 1.4 196 i706 1.3 197 i707 6.3 205.4 i708 6.3 207.2 i709 5.8 205.1 i710 6.3 205.7 i711 6.8 203.7 i712 6.8 203.3 i713 8.3 204.8 i714 6.8 202.1 i715 11.1 207.8 i716 9 204.4 i717 10 205.9 i718 8.3 206.3 i719 11 206.3 i720 8.3 204.5 i721 10 205.4 i722 7.8 204.6 i723 7.9 203.5 i724 10.3 205.2 i725 7.3 203.4 i726 9.3 205.2 i727 7.9 202.6 i728 8.6 202.6 i729 8.6 203 i730 6.3 202 i731 6.3 202.3 i732 14.3 210.2 i733 10.3 212.3 i734 12.1 214.4 i735 9.1 210.4 i736 8.1 206.9 i737 10.5 206.9 i738 12.2 208.4 i739 9.2 203.9 i740 8.2 208.6 i741 12.3 213.9 i742 12.9 209.6 i743 6.8 206.9 i744 9.3 208.5 i745 8.3 208.3 i746 8.3 207.5 i747 7.5 205.6 i748 7.8 204.2 i749 6.7 205.4 i750 9.3 205.8 i751 9.8 206.5 i752 7.8 204.4 i753 8.6 206.8 i754 8.6 205.4 i755 8.6 206.5 i756 7.7 205.3 i757 11 207.7 i758 9.6 207.2 i759 6.9 204 i760 10.1 205.9 i761 8.9 206.6 i762 10.1 206.3 i763 10.1 205 i764 7.5 204.6 i765 8.4 206.8 i766 7.5 206.3 i767 7.5 206.5 i768 8.3 205.1 i769 8.3 204.9 i770 7.4 205.9 i771 9.2 208.8 i772 9.2 210 i773 6.7 206.9 i774 4.7 212 i775 4.5 210.2 i776 3.9 204.2 i777 4 211.3 i778 4.1 215.3 i779 4.1 215.1 i780 3.9 209 i781 4.4 209 i782 3.4 208 i783 4 204.8 i784 3.6 203.9 i785 4.1 202.5 i786 4 201.7 i787 4 208.3 i788 3.6 208 i789 3.3 208.6 i790 3.5 206.8 i791 3.7 209.9 i792 3.6 209.1 i793 3.3 209.8 i794 3.6 212.3 i795 3.2 205.8 i796 3.2 205.2 i797 3 202.3 i798 3 201.6 i799 3 198.5 i800 3.1 201 i801 3.1 200.6 i802 3.1 204.2 i803 3.7 202.4 i804 3.8 204 i805 3.8 204.2 i806 3.4 202.9 i807 3.6 203 i808 3.9 203.7 i809 3.3 202.3 i810 3.4 206.8 i811 3.4 210.3 i812 3.7 211.8 i813 3.7 204.6 i814 3.4 205 i815 3.8 203 i816 3.4 203.5 i817 3.2 202.6 i818 1.9 192.9 i819 1.9 191.8 i820 1.7 195 i821 1.5 196.7 i822 2.5 202.2 i823 2.6 201.2 i824 2.5 206.7 i825 2.6 203.5 i826 3.1 210.3 i827 9.8 206 i828 5.2 201.6 i829 5.7 204.9 i830 9.3 209.9 i831 4.4 201.3 i832 9.3 211.4 i833 5.3 202.9 i834 5.7 201.5 i835 4.1 198 i836 4.7 202.4 i837 6.9 204.5 i838 5 202.2 i839 9 208.5 i840 7.3 210 i841 5.4 205 i842 11.6 214.3 i843 5.4 205.7 i844 8.9 208.4 i845 4.7 200.6 i846 7.1 204.9 i847 5.1 200 i848 7.2 204.8 i849 5.8 202.1 i850 4.3 199.1 i851 4.5 201.4 i852 6.3 203.9 i853 6.5 202.3 i854 5.3 199 i855 6.3 203.8 i856 5.9 204 i857 5.1 201 i858 5.3 199.9 i859 6.7 202 i860 4.5 201 i861 5.1 203.2 i862 8.5 207.2 i863 7 204.5 i864 4.5 200.3 i865 5.1 201.1 i866 6.3 202.8 i867 4.7 200.4 i868 5 201.8 i869 7.1 204.6 i870 8.9 209.5 i871 5.9 205 i872 5.1 203.9 i873 5.9 204.7 i874 7.9 209.1 i875 7.1 208 i876 5.8 206.3 i877 5 204.5 i878 5.8 207.2 i879 7 208.1 i880 8.7 209.3 i881 6.3 206.6 i882 5.8 205.7 i883 5 204.4 i884 6.9 203.9 i885 6.3 201.5 i886 4.9 201.6 i887 5.8 201.9 i888 7 201.7 i889 10.5 206.4 i890 7 202.2 i891 8.4 206.1 i892 4.9 203.6 i893 3.9 203.9 i894 3.7 201.6 i895 6.2 208 i896 4.1 204.2 i897 3.2 201.4 i898 5 205.4 i899 4.6 200.5 i900 5 200.7 i901 4.1 198.8 i902 3.7 200.1 i903 5.2 199.7 i904 4.4 198.1 i905 4 204.3 i906 3.9 201.4 i907 4.1 200.6 i908 3.6 198.5 i909 4.3 199.5 i910 3.9 200.2 i911 3.6 199.8 i912 5.5 199.2 i913 13.1 209.5 i914 3.2 199.9 i915 3 198.4 i916 3.1 198.2 i917 2.9 198.6 i918 3.1 199.5 i919 1.3 195.6 i920 1.3 192.1 i921 1.4 193.7 i922 1.3 186.9 i923 1.2 188.7 i924 1.2 187 i925 1.2 187.1 i926 1.2 184.7 i927 1.2 187.4 i928 1.2 186.9 i929 1.5 191.4 i930 1.4 191.5 i931 1.7 193.2 i932 1.7 191 i933 1.5 190.3 i934 1.7 189.6 i935 1.5 191 i936 1.6 190.1 i937 1.7 192.2 i938 2.6 199.7 i939 2.9 199.9 i940 2.9 201 i941 3.1 201.7 i942 4.8 197.2 i943 4.9 200.4 i944 4.5 200.1 i945 5.2 200.6 i946 5.9 204.1 i947 4.8 204.1 i948 6.4 207 i949 5.2 204.4 i950 5.9 207.5 i951 5.8 205.4 i952 5 203.2 i953 4.9 202.9 i954 4.3 201.9 i955 4.8 202 i956 4.9 206.2 i957 4.5 207.7 i958 4.5 209.4 i959 3.8 205.5 i960 4.2 202.9 i961 3.8 205.4 i962 2.8 200.2 i963 2.9 200.4 i964 4.2 205.5 i965 2.4 192.3 i966 3.2 203.4 i967 2.1 196.8 i968 2.2 196.6 i969 2.1 193.7 i970 2.2 196.9 i971 2.3 192 i972 5.1 200.5 i973 7.5 206.1 i974 7.9 208.6 i975 6.5 207.9 i976 6.6 210.5 i977 9.5 213.6 i978 8.8 210.1 i979 6.9 209.4 i980 8.9 206.1 i981 7.6 206.5 i982 7.6 205.5 i983 7.6 204.7 i984 9.8 210.2 i985 10.9 210.7 i986 7 203.9 i987 7 204 i988 7.5 200.8 i989 6.5 201.9 i990 6.8 204.2 i991 6.1 202.9 i992 6.5 203.9 i993 6.5 204.4 i994 6.1 204.9 i995 5.7 204.8 i996 6.1 202.9 i997 5.4 204.3 i998 5.1 201.9 i999 4.9 201.8 i1000 5.4 212.3 i1001 5.1 210.7 i1002 4.8 206.3 i1003 4.6 202.8 i1004 4.2 205.4 i1005 4.8 201.8 i1006 4.3 204.2 i1007 4.2 203 i1008 4 199.9 i1009 4.2 198.2 i1010 3.8 197.1 i1011 11.2 208.2 i1012 11.2 207.8 i1013 12.6 210.9 i1014 14.4 209.2 i1015 2.5 195.1 i1016 2.7 194.6 i1017 2.5 195.7 i1018 2.3 194.6 i1019 2.2 193.3 i1020 2.4 193.6 i1021 2.3 196.2 i1022 2.3 198.1 i1023 2.2 200.3 i1024 10.9 207.2 i1025 13.1 214.5 i1026 15.3 215.9 i1027 13.1 214.5 i1028 15.2 213.4 i1029 15.2 213.6 i1030 15.2 213.8 i1031 15.2 212.8 i1032 13 211.9 i1033 15.1 209.7 i1034 13 209.3 i1035 13 211.5 i1036 11.4 210.9 i1037 10.2 209.7 i1038 15.3 212.7 i1039 13.2 213.2 i1040 11.5 211 i1041 15.6 210 i1042 14.7 209 i1043 14.8 212.7 i1044 9.9 210.6 i1045 11.2 210.3 i1046 10.1 209.9 i1047 14.7 210.5 i1048 10.1 206.8 i1049 14.7 209.7 i1050 9.7 209.6 i1051 13.8 209.1 i1052 12.1 209.5 i1053 10.7 209.9 i1054 8.8 209.8 i1055 9.7 209.4 i1056 12 212.2 i1057 12 212.1 i1058 9.6 209.5 i1059 10.7 208.9 i1060 8.7 205.2 i1061 11.7 208 i1062 15.7 211.5 i1063 10.2 206.2 i1064 8.4 206.4 i1065 13.2 211.2 i1066 9.3 206 i1067 8.4 205.1 i1068 14.7 213.1 i1069 7.2 202.9 i1070 9.4 210.2 i1071 8.5 207.3 i1072 7.8 206.6 i1073 9.5 205.4 i1074 8.7 205.8 i1075 12.2 209.9 i1076 13.8 207.1 i1077 14.3 210.8 i1078 14.8 209.7 i1079 12.6 211.1 i1080 13 209.4 i1081 13 211.3 i1082 11.6 207.5 i1083 11.5 207 i1084 10.4 206.2 i1085 11.1 208.4 i1086 10.8 208 i1087 10.8 207.3 i1088 12.1 209.3 i1089 14 211.1 i1090 13.9 210.7 i1091 15.4 209.6 i1092 15.4 207.8 i1093 13.4 207.2 i1094 9.4 203.9 i1095 11.5 214.9 i1096 12.9 214 i1097 11.5 208.2 i1098 9.4 206 i1099 10.3 206.9 i1100 10.3 205.6 i1101 8 205.1 i1102 7.4 206 i1103 5.9 204.9 i1104 1.8 198.1 i1105 1.8 203.5 i1106 1.8 204.9 i1107 1.5 205.2 i1108 1.6 206.2 i1109 1.6 204.5 i1110 1.5 202.6 i1111 1.8 200.8 i1112 1.6 201.7 i1113 1.5 204.1 i1114 1.5 201.3 i1115 1.6 198.8 i1116 1.2 198.1 i1117 1.2 196.5 i1118 1 198.5 i1119 1.7 205.6 i1120 1.7 193.6 i1121 2.4 194.5 i1122 1.8 194.6 i1123 1.9 194.5 i1124 2.1 193.4 i1125 1.6 197.3 i1126 1.5 194.2 i1127 6.1 201.3 i1128 6.1 201.8 i1129 9.3 209.5 i1130 9.3 208.9 i1131 7.8 211.2 i1132 8.5 208.9 i1133 9.2 205.1 i1134 7.3 203 i1135 7.2 204.6 i1136 7.8 208.1 i1137 7.2 207.2 i1138 9.2 210 i1139 6.9 204.5 i1140 6.9 206.7 i1141 6.5 204.1 i1142 6.9 202.6 i1143 6.1 202.7 i1144 6.9 204.1 i1145 6.5 202.8 i1146 7.4 204.2 i1147 6.8 200.5 i1148 4.2 197.6 i1149 4.6 199.4 i1150 4.9 200 i1151 3.9 200.4 i1152 4.4 201.3 i1153 4.4 198.4 i1154 4 201.3 i1155 4.4 203.1 i1156 4.4 203.7 i1157 4.6 203.1 i1158 4.4 200.7 i1159 4.2 198.2 i1160 2.9 201.3 i1161 2.1 198.4 i1162 13.7 211.7 i1163 8.8 210.7 i1164 12 215.1 i1165 5.3 208.8 i1166 9.6 213.9 i1167 4.8 197.8 i1168 4.8 198.7 i1169 4.3 199.8 i1170 3.8 198.8 i1171 4.1 200.3 i1172 3.7 199.4 i1173 3.6 198.2 i1174 3.9 197.3 i1175 3.3 198.2 i1176 3.7 197.3 i1177 3.3 197.5 i1178 3.2 199 i1179 3.1 197.9 i1180 2.7 194.2 i1181 2.4 194 i1182 2.5 194.1 i1183 2 190.3 i1184 1.6 195 i1185 7.6 203.9 i1186 5 204.3 i1187 6.3 208.2 i1188 5.9 205.9 i1189 7.1 209.6 i1190 4.7 207.5 i1191 5.2 208.4 i1192 4.4 206.7 i1193 4.5 207 i1194 5 204 i1195 4.5 201.6 i1196 4.2 202.2 i1197 3.2 195.5 i1198 3 197.6 i1199 3.7 198.1 i1200 4.3 204.1 i1201 4.9 204.7 i1202 4.6 198 i1203 4.5 202.9 i1204 4.2 200.2 i1205 4.6 204 i1206 3.9 202.6 i1207 5 204.3 i1208 3.7 203.7 i1209 3.1 200.9 i1210 2.6 199.1 i1211 3.8 206.6 i1212 3.4 206 i1213 3.8 206 i1214 4.8 208.1 i1215 3.3 202.9 i1216 3.3 204.1 i1217 3.2 202.9 i1218 2.8 201.6 i1219 3.4 198.1 i1220 2.8 197.8 i1221 2.6 200.6 i1222 2.6 199.6 i1223 2.5 197.2 i1224 2.6 196.6 i1225 2.4 196.8 i1226 2.9 203.2 i1227 2.6 201.5 i1228 2.8 203.8 i1229 3.1 208.7 i1230 3.2 213.1 i1231 9.6 210.6 i1232 6 209.3 i1233 6.5 210.1 i1234 5.4 206.9 i1235 4.9 205.6 i1236 5.3 206.5 i1237 5.2 205.8 i1238 5.7 201.2 i1239 7.2 202.9 i1240 6.4 200.8 i1241 7.1 203.3 i1242 7.9 204.9 i1243 9.4 205.5 i1244 8.6 204.5 i1245 9.4 204.2 i1246 10.4 205.6 i1247 8.7 205.6 i1248 8 205.5 i1249 9.4 205.6 i1250 8.9 204 i1251 7.8 203.7 i1252 9.5 205.9 i1253 9.5 205.6 i1254 7.3 204.7 i1255 8.6 206.1 i1256 9.5 206.9 i1257 7.2 203.4 i1258 8.6 204.8 i1259 6.3 201.8 i1260 6.7 204.7 i1261 7.2 207.8 i1262 6.8 202.8 i1263 5.9 203.1 i1264 5.7 203.6 i1265 5.4 204.1 i1266 4.9 202.7 i1267 7.5 204.3 i1268 6 203.4 i1269 5.2 204.2 i1270 5.1 199 i1271 4.7 202.1 i1272 4.9 205.6 i1273 4.7 207.7 i1274 4.1 205.7 i1275 4.2 204.9 i1276 4.2 207 i1277 4.7 205.5 i1278 4.7 201.4 i1279 3.8 198.4 i1280 3.9 203.9 i1281 4 203.3 i1282 3.5 202.2 i1283 3.3 207.8 i1284 3.3 208.5 i1285 4.3 209.1 i1286 3.4 207 i1287 3.2 203.9 i1288 3.3 203.8 i1289 3.6 199.4 i1290 3.9 200.7 i1291 3.8 200.2 i1292 3.7 200.3 i1293 3.6 196.7 i1294 2.4 194.4 i1295 2.5 199.5 i1296 2.4 200.1 i1297 2.1 201.3 i1298 2.2 202.1 i1299 2.3 203.5 i1300 2.5 210.8 i1301 2.5 210.9 i1302 2.4 209.6 i1303 2.5 205.5 i1304 2.1 203.2 i1305 2.3 202.8 i1306 2.1 201.5 i1307 2 202.1 i1308 2 202.3 i1309 2 201 i1310 2.1 196.9 i1311 1.9 192.2 i1312 1 188.2 i1313 1.2 191.7 i1314 1.2 192.8 i1315 1.8 207.5 i1316 1.6 206.4 i1317 1.5 205.7 i1318 1.5 206.4 i1319 1.3 195.9 i1320 6.2 202.6 i1321 6.2 203.2 i1322 8.7 208.8 i1323 8.8 208.4 i1324 1.3 201.6 i1325 5.8 205.5 i1326 6.1 211 i1327 1.8 192.1 i1328 1.7 207 i1329 1.5 189.1 i1330 1.5 190.9 i1331 1.4 192 i1332 6.1 215.9 i1333 6 215.8 i1334 1.4 187.6 i1335 4.6 201.9 i1336 5.1 206.7 i1337 4.8 206.7 i1338 4.1 204.9 i1339 4.8 203.7 i1340 3 198.7 i1341 4.1 201.9 i1342 4.1 205.5 i1343 4.1 208.4 i1344 5.3 209.4 i1345 3.7 201.7 i1346 3.6 200.7 i1347 5 203.6 i1348 3.7 201.9 i1349 3.5 200.4 i1350 1.1 193.5 i1351 4.3 204.1 i1352 3.9 205 i1353 3 201.6 i1354 5.4 208.8 i1355 2.1 199.2 i1356 1.8 204.1 i1357 2.1 204.2 i1358 2.3 199.9 i1359 2 198.2 i1360 2 197 i1361 2.4 199 i1362 1.8 195.9 i1363 1.7 196.6 i1364 1.9 199.3 i1365 2.1 200.9 i1366 2.1 200.1 i1367 2.1 195 i1368 1.7 200.3 i1369 1.8 207.1 i1370 1.9 207 i1371 1.8 202.3 i1372 1.8 201 i1373 1.8 199.6 i1374 1.7 199.8 i1375 1.7 199.3 i1376 1.9 197.5 i1377 1.8 197 i1378 1.8 197.9 i1379 1.8 198 i1380 1.9 201.2 i1381 1.8 202 i1382 1.7 200.9 i1383 1.8 203.8 i1384 1.8 203.1 i1385 1.8 205 i1386 1.7 204.4 i1387 1.7 205.3 i1388 1.8 205 i1389 1.6 197.3 i1390 1.8 199 i1391 1.8 196.7 i1392 1.8 196.4 i1393 1.8 197.3 i1394 1.8 195.9 i1395 4.4 202.7 i1396 4.4 202.6 i1397 4.6 203.4 i1398 3.1 200.2 i1399 3.2 202.9 i1400 2.6 202.9 i1401 3.3 204.8 i1402 2.9 205.1 i1403 3.2 205.2 i1404 3.2 205.4 i1405 3.3 205.6 i1406 4 200.6 i1407 3.5 202.3 i1408 3.8 203.2 i1409 3.7 205.8 i1410 3.7 207.4 i1411 3.6 207.3 i1412 4 209.3 i1413 3.8 204.7 i1414 3 199.8 i1415 3.7 205.3 i1416 3.7 204.9 i1417 3.9 204.7 i1418 3.9 206.9 i1419 3.6 207.1 i1420 7.3 203.1 i1421 7.9 200.8 i1422 7.2 205.9 i1423 5.8 201.2 i1424 10.5 207.4 i1425 9.5 205.7 i1426 8.6 207.7 i1427 10.5 207.1 i1428 10.5 208.8 i1429 9.4 207.2 i1430 11.8 210.3 i1431 9.4 205.2 i1432 7.2 207.4 i1433 7.9 206.6 i1434 7.9 207.3 i1435 7.1 207.6 i1436 7.1 203.2 i1437 4.9 202.5 i1438 5.2 206.8 i1439 5.2 202.5 i1440 4.1 201.1 i1441 4.3 202.1 i1442 4.1 206 i1443 4.5 202.3 i1444 5.3 204.2 i1445 4 197.8 i1446 3.3 195.6 i1447 3.9 198.7 i1448 1.5 196.6 i1449 1.4 189.1 i1450 1.4 188.8 i1451 1.6 191.4 i1452 1.6 191.8 i1453 1.7 190.1 i1454 1.7 190.1 i1455 1.7 191.3 i1456 5.3 199 i1457 3.6 202.9 i1458 5.3 199.1 i1459 1 191.5 i1460 1.2 189.3 i1461 1.3 191.8 i1462 1.3 192.2 i1463 1.3 191.4 i1464 1.3 192.8 i1465 1.4 193.2 i1466 1.4 193.9 i1467 1.6 194 i1468 1.3 192.2 i1469 1.2 191.6 i1470 1.1 191.6 i1471 1.1 191.1 i1472 1 190.2 i1473 1 190 i1474 2 189.8 i1475 1.9 190.7 i1476 2.2 193.3 i1477 2.1 193.3 i1478 1.9 195.2 i1479 2.4 198.4 i1480 2.1 197.5 i1481 2.1 189.9 i1482 1.9 190.4 i1483 1.9 192.1 i1484 1.8 192.8 i1485 1.8 192.1 i1486 2.6 192.9 i1487 1.3 191.6 i1488 2.1 200.4 i1489 3.8 204.1 i1490 3.5 205.5 i1491 3.3 205.1 i1492 2.8 203.6 i1493 2.8 202.6 i1494 3 203.1 i1495 2.6 201.9 i1496 2.5 202.2 i1497 7.6 210.3 i1498 3.3 202.3 i1499 2.7 202.2 i1500 5 205.7 i1501 5.6 205.7 i1502 4.4 201.4 i1503 9.6 210.9 i1504 1.1 201.8 i1505 1.1 201.5 i1506 1 201.3 i1507 10.3 206.9 i1508 14.8 209.4 i1509 14.8 208.5 i1510 14.7 209 i1511 9.4 205.5 i1512 9.4 207.6 i1513 10.3 209.7 i1514 10.4 206.5 i1515 10.3 204.1 i1516 12.9 208.6 i1517 9.4 204.7 i1518 11.5 207.8 i1519 9.4 206.5 i1520 10.3 205.4 i1521 11.5 207.3 i1522 10.3 205.9 i1523 13 209.5 i1524 8.7 206.8 i1525 8.6 204.9 i1526 8.6 205.4 i1527 10.4 204.6 i1528 10.3 205.8 i1529 8.5 205.1 i1530 7.9 204.6 i1531 9.3 203.6 i1532 13 210 i1533 11.5 208 i1534 9.4 205.1 i1535 8.9 206.7 i1536 8.1 208.4 i1537 11.5 207.8 i1538 13 209.3 i1539 13 209 i1540 13 210.5 i1541 11.5 209 i1542 8.1 204.9 i1543 7.5 208.9 i1544 10.9 212.4 i1545 0.8 192.4 i1546 11.6 207.5 i1547 13 211.6 i1548 13 208.1 i1549 13 211.9 i1550 10.4 209.4 i1551 6.7 205.9 i1552 6.7 205.7 i1553 6.2 202.2 i1554 6.6 203.8 i1555 6.2 201.7 i1556 6.1 201.4 i1557 11.4 209.1 i1558 12.9 211 i1559 11.4 208.8 i1560 9.2 206.7 i1561 12.7 212.1 i1562 10.1 208.6 i1563 9.2 208.4 i1564 14.4 211.8 i1565 14.4 209.3 i1566 10.1 210.7 i1567 12.6 212.5 i1568 6.8 203.3 i1569 6.5 199.8 i1570 6.5 207 i1571 6.1 203.6 i1572 5.4 209.2 i1573 4.5 205.5 i1574 5.2 208.1 i1575 4.7 208.3 i1576 4.7 206.1 i1577 5.2 205.6 i1578 5.7 203.3 i1579 5.4 200 i1580 5.2 199.8 i1581 5.4 200.7 i1582 4.3 203.1 i1583 4.3 206 i1584 2.9 201.8 i1585 3.2 201.9 i1586 3.5 204.2 i1587 3.2 202.5 i1588 3.2 200.7 i1589 3.3 202.3 i1590 3 202.2 i1591 3 199.7 i1592 2.9 200 i1593 2.8 198.3 i1594 2.9 200.7 i1595 2.8 205.2 i1596 2.8 206.4 i1597 8.1 212.7 i1598 8.9 213.7 i1599 7 210.8 i1600 7.6 210.9 i1601 7.6 209.3 i1602 7 208.3 i1603 6.6 204.7 i1604 5.8 199.8 i1605 5.7 200 i1606 5.8 203.2 i1607 5.5 205 i1608 5.5 204.9 i1609 6.2 206.9 i1610 6.3 206 i1611 6.3 205.4 i1612 5.9 201.1 i1613 5.6 202.4 i1614 5 204.3 i1615 5.2 205.4 i1616 1.1 190.1 i1617 1.1 185.9 i1618 1.1 187.9 i1619 1.3 187.9 i1620 1.4 185.8 i1621 1.2 187.5 i1622 1.3 188.5 i1623 1.2 188.2 i1624 1.4 189.1 i1625 1.4 188.8 i1626 1.6 191.4 i1627 1.6 191.8 i1628 1.7 190.1 i1629 1.7 190.1 i1630 1.7 191.3 i1631 5.3 199 i1632 3.6 202.9 i1633 5.3 199.1 i1634 5.6 203 ; parameters Range(i) 'Distance to dolphin in metres' SoundPressure(i) 'Water sound pressure adjusted for water density' ; Range(i) = data(i,'Range'); SoundPressure(i) = data(i,'SoundPressure'); variables a 'parameter to be estimated' b 'parameter to be estimated' sse 'sum of squared errors' ; equation fit(i) 'equation to fit' sumsq 'dummy objective' ; sumsq.. sse =n= 0; fit(i).. SoundPressure(i) =e= a*Range(i)**b; option nlp=nls; models m /sumsq,fit/; m.optfile=1; solve m minimizing sse using nlp; $onecho > nls.opt maxn 1700 $offecho * * plot results * file pltdat /dolphin.dat/; loop(i, put pltdat Range(i):17:5,SoundPressure(i):17:5/; ); putclose; file plt /dolphin.plt/; put plt; put "a=",a.l:0:16/; put "b=",b.l:0:16/; put "fit(x)=a*x**b"/; putclose 'set term png'/ 'set key bottom'/ 'set output "dolphin.png"'/ 'plot "dolphin.dat",fit(x)'/; execute 'type dolphin.plt'; execute '=wgnuplot.exe dolphin.plt'; execute '=shellexecute dolphin.png';