| Multiple Linear Regression - Estimated Regression Equation |
| Werkl[t] = -176351.657431817 + 0.682260307575196X[t] + e[t] |
| Multiple Linear Regression - Ordinary Least Squares | |||||
| Variable | Parameter | S.D. | T-STAT H0: parameter = 0 | 2-tail p-value | 1-tail p-value |
| (Intercept) | -176351.657431817 | 12756.565583 | -13.8244 | 0 | 0 |
| X | 0.682260307575196 | 0.02278 | 29.9503 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.964623948671983 |
| R-squared | 0.930499362351528 |
| Adjusted R-squared | 0.929462039401551 |
| F-TEST (value) | 897.019932290117 |
| F-TEST (DF numerator) | 1 |
| F-TEST (DF denominator) | 67 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 7594.04708356363 |
| Sum Squared Residuals | 3863859924.19455 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 216234 | 207300.370025404 | 8933.62997459586 |
| 2 | 213587 | 206296.765112962 | 7290.23488703831 |
| 3 | 209465 | 202529.323694531 | 6935.6763054686 |
| 4 | 204045 | 194524.363505752 | 9520.63649424837 |
| 5 | 200237 | 189791.523752102 | 10445.4762478975 |
| 6 | 203666 | 193926.021216008 | 9739.97878399182 |
| 7 | 241476 | 228590.302923289 | 12885.6970767113 |
| 8 | 260307 | 240347.694803732 | 19959.3051962679 |
| 9 | 243324 | 241609.876372746 | 1714.12362725380 |
| 10 | 244460 | 240730.442836282 | 3729.55716371823 |
| 11 | 233575 | 229024.902739214 | 4550.09726078587 |
| 12 | 237217 | 229902.971755063 | 7314.02824493659 |
| 13 | 235243 | 226772.079203601 | 8470.92079639916 |
| 14 | 230354 | 225758.240386544 | 4595.75961345591 |
| 15 | 227184 | 222380.369603739 | 4803.6303962607 |
| 16 | 221678 | 214651.724839527 | 7026.27516047252 |
| 17 | 217142 | 210801.047663573 | 6340.95233642693 |
| 18 | 219452 | 211873.560867081 | 7578.43913291872 |
| 19 | 256446 | 247151.194590872 | 9294.80540912806 |
| 20 | 265845 | 252710.933837302 | 13134.0661626978 |
| 21 | 248624 | 252266.100116763 | -3642.10011676318 |
| 22 | 241114 | 241271.475260189 | -157.475260188899 |
| 23 | 229245 | 229868.858739685 | -623.85873968465 |
| 24 | 231805 | 231053.944893943 | 751.055106057238 |
| 25 | 219277 | 228507.067165765 | -9230.06716576456 |
| 26 | 219313 | 226231.046779694 | -6918.0467796937 |
| 27 | 212610 | 219222.186639974 | -6612.18663997372 |
| 28 | 214771 | 215405.622479398 | -634.622479398071 |
| 29 | 211142 | 214429.990239566 | -3287.99023956554 |
| 30 | 211457 | 214543.927710931 | -3086.9277109306 |
| 31 | 240048 | 246354.314551624 | -6306.31455162411 |
| 32 | 240636 | 250612.983391508 | -9976.98339150848 |
| 33 | 230580 | 246592.423398968 | -16012.4233989679 |
| 34 | 208795 | 224561.555807057 | -15766.5558070572 |
| 35 | 197922 | 209631.653496389 | -11709.6534963892 |
| 36 | 194596 | 203854.273211842 | -9258.27321184243 |
| 37 | 194581 | 206107.096747456 | -11526.0967474557 |
| 38 | 185686 | 198109.641422059 | -12423.6414220593 |
| 39 | 178106 | 186387.72707761 | -8281.72707760984 |
| 40 | 172608 | 182462.001267822 | -9854.00126782216 |
| 41 | 167302 | 172309.285630796 | -5007.28563079567 |
| 42 | 168053 | 163865.632064245 | 4187.36793575496 |
| 43 | 202300 | 202549.791503759 | -249.791503758653 |
| 44 | 202388 | 208846.37188237 | -6458.37188237014 |
| 45 | 182516 | 193199.413988441 | -10683.4139884406 |
| 46 | 173476 | 183247.282881841 | -9771.28288184121 |
| 47 | 166444 | 171496.031344166 | -5052.03134416603 |
| 48 | 171297 | 174506.163821188 | -3209.1638211878 |
| 49 | 169701 | 176323.705280568 | -6622.70528056812 |
| 50 | 164182 | 169937.066541357 | -5755.06654135672 |
| 51 | 161914 | 159744.779806491 | 2169.22019350914 |
| 52 | 159612 | 158121.682534769 | 1490.31746523053 |
| 53 | 151001 | 143871.993750754 | 7129.00624924607 |
| 54 | 158114 | 149482.220259945 | 8631.77974005523 |
| 55 | 186530 | 184140.361624457 | 2389.63837554286 |
| 56 | 187069 | 187695.620087231 | -626.620087231485 |
| 57 | 174330 | 177021.657575218 | -2691.65757521755 |
| 58 | 169362 | 168990.77149475 | 371.228505250083 |
| 59 | 166827 | 166051.594089716 | 775.405910284033 |
| 60 | 178037 | 175790.859980352 | 2246.14001964811 |
| 61 | 186412 | 184033.246756168 | 2378.75324383216 |
| 62 | 189226 | 187046.10827442 | 2179.89172558010 |
| 63 | 191563 | 189559.555247527 | 2003.44475247308 |
| 64 | 188906 | 189704.876693040 | -798.87669304044 |
| 65 | 186005 | 180877.792833633 | 5127.20716636744 |
| 66 | 195309 | 189485.871134309 | 5823.1288656912 |
| 67 | 223532 | 223841.771182565 | -309.771182565367 |
| 68 | 226899 | 230680.748505699 | -3781.74850569913 |
| 69 | 214126 | 219716.143102658 | -5590.14310265816 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 5 | 0.00491966394577273 | 0.00983932789154546 | 0.995080336054227 |
| 6 | 0.0006567240485604 | 0.0013134480971208 | 0.99934327595144 |
| 7 | 0.00443748092864668 | 0.00887496185729335 | 0.995562519071353 |
| 8 | 0.0168383846579393 | 0.0336767693158786 | 0.98316161534206 |
| 9 | 0.231858331024210 | 0.463716662048420 | 0.76814166897579 |
| 10 | 0.233451713827529 | 0.466903427655058 | 0.766548286172471 |
| 11 | 0.194739137194513 | 0.389478274389025 | 0.805260862805487 |
| 12 | 0.144270665913464 | 0.288541331826928 | 0.855729334086536 |
| 13 | 0.108804047988061 | 0.217608095976123 | 0.891195952011939 |
| 14 | 0.0893313260607567 | 0.178662652121513 | 0.910668673939243 |
| 15 | 0.0717984469328172 | 0.143596893865634 | 0.928201553067183 |
| 16 | 0.0543947937942393 | 0.108789587588479 | 0.94560520620576 |
| 17 | 0.0418849262913311 | 0.0837698525826622 | 0.958115073708669 |
| 18 | 0.0333192086392894 | 0.0666384172785787 | 0.96668079136071 |
| 19 | 0.0392576926799665 | 0.0785153853599331 | 0.960742307320033 |
| 20 | 0.133533198027726 | 0.267066396055453 | 0.866466801972274 |
| 21 | 0.336648304132395 | 0.67329660826479 | 0.663351695867605 |
| 22 | 0.415538202805836 | 0.831076405611673 | 0.584461797194164 |
| 23 | 0.495624628631763 | 0.991249257263525 | 0.504375371368237 |
| 24 | 0.561153155359583 | 0.877693689280834 | 0.438846844640417 |
| 25 | 0.822426106093126 | 0.355147787813748 | 0.177573893906874 |
| 26 | 0.894433227022836 | 0.211133545954328 | 0.105566772977164 |
| 27 | 0.931167821981663 | 0.137664356036674 | 0.0688321780183372 |
| 28 | 0.932944856248818 | 0.134110287502364 | 0.0670551437511819 |
| 29 | 0.936618457099105 | 0.12676308580179 | 0.063381542900895 |
| 30 | 0.937380885997054 | 0.125238228005892 | 0.062619114002946 |
| 31 | 0.948591875577706 | 0.102816248844587 | 0.0514081244222936 |
| 32 | 0.960039236268569 | 0.0799215274628622 | 0.0399607637314311 |
| 33 | 0.98090922532091 | 0.0381815493581801 | 0.0190907746790900 |
| 34 | 0.994425387307547 | 0.0111492253849055 | 0.00557461269245276 |
| 35 | 0.997220355878917 | 0.00555928824216534 | 0.00277964412108267 |
| 36 | 0.99780504111435 | 0.00438991777129975 | 0.00219495888564988 |
| 37 | 0.998786555759978 | 0.00242688848004422 | 0.00121344424002211 |
| 38 | 0.999588836527082 | 0.000822326945835043 | 0.000411163472917521 |
| 39 | 0.999667943405856 | 0.000664113188288777 | 0.000332056594144389 |
| 40 | 0.999848793722908 | 0.000302412554183457 | 0.000151206277091728 |
| 41 | 0.999810887679184 | 0.000378224641631663 | 0.000189112320815831 |
| 42 | 0.999683238884373 | 0.000633522231253034 | 0.000316761115626517 |
| 43 | 0.999409680030634 | 0.00118063993873141 | 0.000590319969365706 |
| 44 | 0.999094953076174 | 0.00181009384765228 | 0.000905046923826138 |
| 45 | 0.999664670603207 | 0.000670658793586074 | 0.000335329396793037 |
| 46 | 0.9999174243196 | 0.000165151360802194 | 8.25756804010972e-05 |
| 47 | 0.999931748203431 | 0.000136503593137172 | 6.82517965685861e-05 |
| 48 | 0.999905859445324 | 0.000188281109352024 | 9.41405546760121e-05 |
| 49 | 0.99997314104329 | 5.37179134199009e-05 | 2.68589567099505e-05 |
| 50 | 0.999997019192907 | 5.96161418561084e-06 | 2.98080709280542e-06 |
| 51 | 0.999992536816315 | 1.49263673709942e-05 | 7.46318368549712e-06 |
| 52 | 0.999986028260543 | 2.79434789146822e-05 | 1.39717394573411e-05 |
| 53 | 0.999965177442685 | 6.96451146296929e-05 | 3.48225573148465e-05 |
| 54 | 0.999960223049072 | 7.95539018555393e-05 | 3.97769509277696e-05 |
| 55 | 0.999885316519607 | 0.000229366960786783 | 0.000114683480393392 |
| 56 | 0.999682439828571 | 0.000635120342857605 | 0.000317560171428803 |
| 57 | 0.999722282686254 | 0.000555434627493128 | 0.000277717313746564 |
| 58 | 0.999494974800023 | 0.00101005039995307 | 0.000505025199976536 |
| 59 | 0.99941175638941 | 0.00117648722118182 | 0.000588243610590908 |
| 60 | 0.998435693601795 | 0.00312861279640940 | 0.00156430639820470 |
| 61 | 0.994942554422003 | 0.0101148911559944 | 0.00505744557799722 |
| 62 | 0.984405659174114 | 0.0311886816517721 | 0.0155943408258860 |
| 63 | 0.955038601896549 | 0.089922796206902 | 0.044961398103451 |
| 64 | 0.94444668215872 | 0.11110663568256 | 0.05555331784128 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 29 | 0.483333333333333 | NOK |
| 5% type I error level | 34 | 0.566666666666667 | NOK |
| 10% type I error level | 39 | 0.65 | NOK |
