| Multiple Linear Regression - Estimated Regression Equation |
| Werkl[t] = -147852.690708943 + 0.580375867857886x[t] + 0.277926825333554`y-1`[t] -0.140289064798996`y-2`[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) | -147852.690708943 | 18219.49076 | -8.1151 | 0 | 0 |
| x | 0.580375867857886 | 0.056927 | 10.195 | 0 | 0 |
| `y-1` | 0.277926825333554 | 0.115569 | 2.4049 | 0.019129 | 0.009564 |
| `y-2` | -0.140289064798996 | 0.076182 | -1.8415 | 0.070258 | 0.035129 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.96869559474749 |
| R-squared | 0.938371155283192 |
| Adjusted R-squared | 0.935436448391915 |
| F-TEST (value) | 319.749532081892 |
| F-TEST (DF numerator) | 3 |
| F-TEST (DF denominator) | 63 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 7360.18421802616 |
| Sum Squared Residuals | 3412855638.56672 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 209465 | 203474.891945086 | 5990.10805491365 |
| 2 | 204045 | 195891.072668006 | 8153.92733199406 |
| 3 | 200237 | 190936.913404469 | 9300.08659553062 |
| 4 | 203666 | 194156.012544029 | 9509.98745597146 |
| 5 | 241476 | 225130.981480975 | 16345.0185190247 |
| 6 | 260307 | 245159.960874436 | 15147.0391255638 |
| 7 | 243324 | 246162.966737779 | -2838.96673777943 |
| 8 | 244460 | 238053.047590241 | 6406.95240975902 |
| 9 | 233575 | 230793.792886463 | 2781.2071135365 |
| 10 | 237217 | 228356.134757029 | 8860.8652429708 |
| 11 | 235243 | 228232.045867631 | 7010.95413236877 |
| 12 | 230354 | 226310.047000788 | 4043.95299921197 |
| 13 | 227184 | 222354.752443881 | 4829.24755611889 |
| 14 | 221678 | 215585.099814282 | 6092.9001857181 |
| 15 | 217142 | 211223.909651218 | 5918.09034878173 |
| 16 | 219452 | 211648.016026561 | 7803.98397343887 |
| 17 | 256446 | 242935.873190338 | 13510.1268096624 |
| 18 | 265845 | 257622.913374215 | 8222.08662578468 |
| 19 | 248624 | 254666.888876508 | -6042.88887650801 |
| 20 | 241114 | 239209.376986863 | 1904.62301313672 |
| 21 | 229245 | 229838.242634003 | -593.242634002951 |
| 22 | 231805 | 228601.212903229 | 3203.7870967714 |
| 23 | 219277 | 228811.253371468 | -9534.2533714683 |
| 24 | 219313 | 223034.112202630 | -3721.11220263019 |
| 25 | 212610 | 218839.45768164 | -6229.45768163995 |
| 26 | 214771 | 213724.841160299 | 1046.15883970064 |
| 27 | 211142 | 214435.861140156 | -3293.86114015606 |
| 28 | 211457 | 213221.022791922 | -1764.02279192223 |
| 29 | 240048 | 240877.703596932 | -829.703596931786 |
| 30 | 240636 | 252402.424571801 | -11766.4245718007 |
| 31 | 230580 | 245134.685904142 | -14554.6859041422 |
| 32 | 208795 | 223516.446629487 | -14721.4466294872 |
| 33 | 197922 | 206172.192458880 | -8250.19245888028 |
| 34 | 194596 | 201291.868514654 | -6695.86851465409 |
| 35 | 194581 | 203809.248010821 | -9228.2480108209 |
| 36 | 185686 | 197468.514614932 | -11782.5146149322 |
| 37 | 178106 | 185027.022053896 | -6921.0220538959 |
| 38 | 172608 | 180828.725205600 | -8220.72520560036 |
| 39 | 167302 | 171727.501341500 | -4425.50134149966 |
| 40 | 168053 | 163841.399143936 | 4211.6008560645 |
| 41 | 202300 | 197701.807675127 | 4598.19232487339 |
| 42 | 202388 | 212470.899459121 | -10082.8994591212 |
| 43 | 182516 | 194380.537264127 | -11864.5372641266 |
| 44 | 173476 | 180379.287168953 | -6903.28716895294 |
| 45 | 166444 | 170658.259015639 | -4214.25901563902 |
| 46 | 171297 | 172532.709054665 | -1235.70905466538 |
| 47 | 169701 | 176414.121953649 | -6713.12195364906 |
| 48 | 164182 | 169856.829409930 | -5674.82940992951 |
| 49 | 161914 | 159876.617518404 | 2037.38248159614 |
| 50 | 159612 | 158639.820637539 | 972.179362460882 |
| 51 | 151001 | 146196.478308506 | 4804.52169149441 |
| 52 | 158114 | 148898.626604121 | 9215.37339587896 |
| 53 | 186530 | 181566.062961016 | 4963.9370389845 |
| 54 | 187069 | 191490.094159186 | -4421.09415918596 |
| 55 | 174330 | 178573.462200076 | -4243.46220007587 |
| 56 | 169362 | 168125.73222567 | 1236.26777433011 |
| 57 | 166827 | 166031.874915155 | 795.125084844574 |
| 58 | 178037 | 174309.152000528 | 3727.84799947241 |
| 59 | 186412 | 184791.865351373 | 1620.13464862669 |
| 60 | 189226 | 188109.801929606 | 1116.19807039449 |
| 61 | 191563 | 189855.071795591 | 1707.92820440901 |
| 62 | 188906 | 190233.433417905 | -1327.43341790487 |
| 63 | 186005 | 181658.223320213 | 4346.77667978696 |
| 64 | 195309 | 188547.307969854 | 6761.69203014573 |
| 65 | 223532 | 220765.524931591 | 2766.47506840876 |
| 66 | 226899 | 233121.891963498 | -6222.89196349773 |
| 67 | 214126 | 220771.072736230 | -6645.07273622968 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 7 | 0.0124535393265639 | 0.0249070786531278 | 0.987546460673436 |
| 8 | 0.133482942297697 | 0.266965884595393 | 0.866517057702303 |
| 9 | 0.0621035277243901 | 0.124207055448780 | 0.93789647227561 |
| 10 | 0.0412308038570813 | 0.0824616077141626 | 0.958769196142919 |
| 11 | 0.0214595476349838 | 0.0429190952699676 | 0.978540452365016 |
| 12 | 0.0107329598909859 | 0.0214659197819719 | 0.989267040109014 |
| 13 | 0.00525615179683045 | 0.0105123035936609 | 0.99474384820317 |
| 14 | 0.00253700418136886 | 0.00507400836273772 | 0.997462995818631 |
| 15 | 0.00122695310018604 | 0.00245390620037209 | 0.998773046899814 |
| 16 | 0.00068000612050678 | 0.00136001224101356 | 0.999319993879493 |
| 17 | 0.00102417660516893 | 0.00204835321033786 | 0.998975823394831 |
| 18 | 0.00130185197797444 | 0.00260370395594888 | 0.998698148022026 |
| 19 | 0.00689232024469384 | 0.0137846404893877 | 0.993107679755306 |
| 20 | 0.00627480324566658 | 0.0125496064913332 | 0.993725196754333 |
| 21 | 0.007778385865499 | 0.015556771730998 | 0.992221614134501 |
| 22 | 0.0143733247472643 | 0.0287466494945285 | 0.985626675252736 |
| 23 | 0.48197328305656 | 0.96394656611312 | 0.51802671694344 |
| 24 | 0.687299727961171 | 0.625400544077657 | 0.312700272038829 |
| 25 | 0.867571998941058 | 0.264856002117884 | 0.132428001058942 |
| 26 | 0.901651220294192 | 0.196697559411615 | 0.0983487797058076 |
| 27 | 0.940700671221018 | 0.118598657557965 | 0.0592993287789824 |
| 28 | 0.956454117177422 | 0.0870917656451554 | 0.0435458828225777 |
| 29 | 0.96634443494253 | 0.0673111301149418 | 0.0336555650574709 |
| 30 | 0.988575516972577 | 0.0228489660548462 | 0.0114244830274231 |
| 31 | 0.994078513099285 | 0.0118429738014292 | 0.00592148690071462 |
| 32 | 0.996998151791162 | 0.0060036964176757 | 0.00300184820883785 |
| 33 | 0.996682721051003 | 0.00663455789799418 | 0.00331727894899709 |
| 34 | 0.996402616603555 | 0.00719476679289049 | 0.00359738339644524 |
| 35 | 0.99754028286198 | 0.00491943427603813 | 0.00245971713801907 |
| 36 | 0.99908283801015 | 0.00183432397970143 | 0.000917161989850717 |
| 37 | 0.998986254501863 | 0.00202749099627315 | 0.00101374549813657 |
| 38 | 0.999406624844267 | 0.00118675031146500 | 0.000593375155732502 |
| 39 | 0.99924015173685 | 0.00151969652630059 | 0.000759848263150295 |
| 40 | 0.998782868536152 | 0.00243426292769616 | 0.00121713146384808 |
| 41 | 0.997818773399655 | 0.00436245320068934 | 0.00218122660034467 |
| 42 | 0.998343022827077 | 0.0033139543458465 | 0.00165697717292325 |
| 43 | 0.999143111060975 | 0.00171377787805020 | 0.000856888939025102 |
| 44 | 0.999487906676788 | 0.00102418664642351 | 0.000512093323211753 |
| 45 | 0.999528955649122 | 0.000942088701755075 | 0.000471044350877538 |
| 46 | 0.999449684725629 | 0.00110063054874265 | 0.000550315274371323 |
| 47 | 0.999851300211615 | 0.00029739957677086 | 0.00014869978838543 |
| 48 | 0.999986026737189 | 2.79465256229865e-05 | 1.39732628114933e-05 |
| 49 | 0.999965455537933 | 6.90889241332596e-05 | 3.45444620666298e-05 |
| 50 | 0.999937213798089 | 0.000125572403822229 | 6.27862019111144e-05 |
| 51 | 0.999866326760358 | 0.000267346479283125 | 0.000133673239641562 |
| 52 | 0.999833665408743 | 0.000332669182515103 | 0.000166334591257551 |
| 53 | 0.99958486815449 | 0.000830263691019128 | 0.000415131845509564 |
| 54 | 0.99880530414138 | 0.00238939171724105 | 0.00119469585862052 |
| 55 | 0.998275227979447 | 0.00344954404110677 | 0.00172477202055338 |
| 56 | 0.996584773594472 | 0.00683045281105569 | 0.00341522640552784 |
| 57 | 0.99571379478854 | 0.00857241042292164 | 0.00428620521146082 |
| 58 | 0.993759155545653 | 0.0124816889086935 | 0.00624084445434673 |
| 59 | 0.981893055870801 | 0.0362138882583978 | 0.0181069441291989 |
| 60 | 0.943390148348929 | 0.113219703302143 | 0.0566098516510713 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 31 | 0.574074074074074 | NOK |
| 5% type I error level | 43 | 0.796296296296296 | NOK |
| 10% type I error level | 46 | 0.851851851851852 | NOK |
