| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 586.7804012508 -1.42669564850463X[t] + 12.0494979595140M1[t] + 8.44581355654682M2[t] + 14.6086479566102M3[t] -5.90728858834744M4[t] -14.4134526969954M5[t] -3.74449074871385M6[t] + 13.1997510290256M7[t] + 38.1263347080594M8[t] + 56.1630560508234M9[t] + 42.5115962852315M10[t] + 11.7074756774717M11[t] + 2.38749164561372t + 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) | 586.7804012508 | 66.421625 | 8.8342 | 0 | 0 |
| X | -1.42669564850463 | 0.703358 | -2.0284 | 0.047119 | 0.02356 |
| M1 | 12.0494979595140 | 10.86877 | 1.1086 | 0.272164 | 0.136082 |
| M2 | 8.44581355654682 | 10.890023 | 0.7756 | 0.441163 | 0.220581 |
| M3 | 14.6086479566102 | 13.912429 | 1.05 | 0.298054 | 0.149027 |
| M4 | -5.90728858834744 | 11.311053 | -0.5223 | 0.60348 | 0.30174 |
| M5 | -14.4134526969954 | 11.245576 | -1.2817 | 0.205048 | 0.102524 |
| M6 | -3.74449074871385 | 13.812299 | -0.2711 | 0.787278 | 0.393639 |
| M7 | 13.1997510290256 | 13.904571 | 0.9493 | 0.346402 | 0.173201 |
| M8 | 38.1263347080594 | 10.925984 | 3.4895 | 0.000931 | 0.000466 |
| M9 | 56.1630560508234 | 14.006585 | 4.0098 | 0.000176 | 8.8e-05 |
| M10 | 42.5115962852315 | 14.464508 | 2.939 | 0.00472 | 0.00236 |
| M11 | 11.7074756774717 | 11.934092 | 0.981 | 0.330662 | 0.165331 |
| t | 2.38749164561372 | 0.126694 | 18.8445 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.952013796598217 |
| R-squared | 0.906330268913351 |
| Adjusted R-squared | 0.885335329187034 |
| F-TEST (value) | 43.1689864666408 |
| F-TEST (DF numerator) | 13 |
| F-TEST (DF denominator) | 58 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 18.7094421164429 |
| Sum Squared Residuals | 20302.5070098946 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 467 | 460.259860783672 | 6.74013921632807 |
| 2 | 460 | 456.61828542386 | 3.38171457614026 |
| 3 | 448 | 451.044324549341 | -3.04432454934088 |
| 4 | 443 | 452.889618729062 | -9.88961872906187 |
| 5 | 436 | 438.924120199252 | -2.92412019925211 |
| 6 | 431 | 445.845782504578 | -14.8457825045775 |
| 7 | 484 | 501.130246270247 | -17.1302462702472 |
| 8 | 510 | 508.898591210381 | 1.10140878961863 |
| 9 | 513 | 520.33462161318 | -7.33462161318013 |
| 10 | 503 | 497.086410045763 | 5.91358995423699 |
| 11 | 471 | 478.799320188 | -7.79932018799969 |
| 12 | 471 | 486.029005678795 | -15.0290056787953 |
| 13 | 476 | 492.619169217148 | -16.6191692171476 |
| 14 | 475 | 491.545646024645 | -16.5456460246447 |
| 15 | 470 | 485.971685150126 | -15.9716851501259 |
| 16 | 461 | 471.980657631445 | -10.9806576314454 |
| 17 | 455 | 467.431350381766 | -12.4313503817663 |
| 18 | 456 | 476.635725724699 | -20.6357257246990 |
| 19 | 517 | 522.646667775089 | -5.64666777508872 |
| 20 | 525 | 541.257899643858 | -16.257899643858 |
| 21 | 523 | 540.567017034367 | -17.5670170343673 |
| 22 | 519 | 521.170883717913 | -2.17088371791268 |
| 23 | 509 | 508.305237324467 | 0.69476267553299 |
| 24 | 512 | 512.824201083104 | -0.824201083103979 |
| 25 | 519 | 519.557034186307 | -0.557034186306691 |
| 26 | 517 | 518.911519688355 | -1.91151968835504 |
| 27 | 510 | 515.477602286593 | -5.47760228659326 |
| 28 | 509 | 501.201235638212 | 7.79876436178816 |
| 29 | 501 | 501.645363158299 | -0.64536315829888 |
| 30 | 507 | 505.570964601765 | 1.42903539823544 |
| 31 | 569 | 549.299193614547 | 19.7008063854532 |
| 32 | 580 | 573.046529817933 | 6.95347018206725 |
| 33 | 578 | 565.079499401068 | 12.9205005989315 |
| 34 | 565 | 551.104809548931 | 13.8951904510686 |
| 35 | 547 | 541.377893582196 | 5.62210641780406 |
| 36 | 555 | 534.483292152796 | 20.5167078472041 |
| 37 | 562 | 551.488333925232 | 10.5116660747681 |
| 38 | 561 | 547.56141943572 | 13.4385805642804 |
| 39 | 555 | 533.712623799874 | 21.2873762001260 |
| 40 | 544 | 529.565796255876 | 14.4342037441245 |
| 41 | 537 | 531.293949859617 | 5.70605014038332 |
| 42 | 543 | 524.376664374447 | 18.6233356255528 |
| 43 | 594 | 577.949093361911 | 16.0509066380886 |
| 44 | 611 | 591.852229590615 | 19.1477704093846 |
| 45 | 613 | 587.594607859863 | 25.4053921401368 |
| 46 | 611 | 581.752083204203 | 29.2479167957975 |
| 47 | 594 | 562.466306392486 | 31.533693607514 |
| 48 | 595 | 556.427722352189 | 38.5722776478113 |
| 49 | 591 | 580.851581496849 | 10.1484185031512 |
| 50 | 589 | 577.780684396439 | 11.2193156035607 |
| 51 | 584 | 573.776088735276 | 10.2239112647243 |
| 52 | 573 | 558.35836556809 | 14.6416344319094 |
| 53 | 567 | 558.945162653028 | 8.05483734697193 |
| 54 | 569 | 549.45982500055 | 19.5401749994498 |
| 55 | 621 | 615.872514824556 | 5.12748517544391 |
| 56 | 629 | 622.071494551335 | 6.92850544866493 |
| 57 | 628 | 617.528533690882 | 10.4714663091181 |
| 58 | 612 | 616.679443804987 | -4.67944380498741 |
| 59 | 595 | 584.125397462178 | 10.8746025378221 |
| 60 | 597 | 584.0789351456 | 12.9210648543999 |
| 61 | 593 | 603.224020390793 | -10.2240203907930 |
| 62 | 590 | 599.582445030982 | -9.58244503098164 |
| 63 | 580 | 587.01767547879 | -7.01767547879024 |
| 64 | 574 | 590.004326177315 | -16.0043261773148 |
| 65 | 573 | 570.760053748038 | 2.23994625196203 |
| 66 | 573 | 577.111037793962 | -4.11103779396155 |
| 67 | 620 | 638.10228415365 | -18.1022841536498 |
| 68 | 626 | 643.873255185877 | -17.8732551858774 |
| 69 | 620 | 643.895720400639 | -23.8957204006391 |
| 70 | 588 | 630.206369678203 | -42.206369678203 |
| 71 | 566 | 606.925845050674 | -40.9258450506735 |
| 72 | 557 | 613.156843587516 | -56.156843587516 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 17 | 0.0109086222103468 | 0.0218172444206935 | 0.989091377789653 |
| 18 | 0.00524911246947433 | 0.0104982249389487 | 0.994750887530526 |
| 19 | 0.004631789273461 | 0.009263578546922 | 0.99536821072654 |
| 20 | 0.00145754088455363 | 0.00291508176910726 | 0.998542459115446 |
| 21 | 0.00169651537569875 | 0.00339303075139749 | 0.998303484624301 |
| 22 | 0.000557471703950607 | 0.00111494340790121 | 0.99944252829605 |
| 23 | 0.00180092392328063 | 0.00360184784656126 | 0.99819907607672 |
| 24 | 0.00392344787453324 | 0.00784689574906649 | 0.996076552125467 |
| 25 | 0.00410392640060009 | 0.00820785280120019 | 0.9958960735994 |
| 26 | 0.00428611375719737 | 0.00857222751439473 | 0.995713886242803 |
| 27 | 0.00482659848239559 | 0.00965319696479118 | 0.995173401517604 |
| 28 | 0.00670809883423725 | 0.0134161976684745 | 0.993291901165763 |
| 29 | 0.00796815794345321 | 0.0159363158869064 | 0.992031842056547 |
| 30 | 0.0183020345643516 | 0.0366040691287032 | 0.981697965435648 |
| 31 | 0.0304236075193163 | 0.0608472150386325 | 0.969576392480684 |
| 32 | 0.0352910817662505 | 0.0705821635325011 | 0.96470891823375 |
| 33 | 0.0349272256229785 | 0.069854451245957 | 0.965072774377022 |
| 34 | 0.0257304227461135 | 0.051460845492227 | 0.974269577253887 |
| 35 | 0.0313800723737206 | 0.0627601447474413 | 0.96861992762628 |
| 36 | 0.0296818421174464 | 0.0593636842348929 | 0.970318157882554 |
| 37 | 0.0265457225440852 | 0.0530914450881704 | 0.973454277455915 |
| 38 | 0.0244250438933834 | 0.0488500877867669 | 0.975574956106616 |
| 39 | 0.0194568362678570 | 0.0389136725357141 | 0.980543163732143 |
| 40 | 0.0181115949653338 | 0.0362231899306676 | 0.981888405034666 |
| 41 | 0.0413472168140153 | 0.0826944336280306 | 0.958652783185985 |
| 42 | 0.0761551610237206 | 0.152310322047441 | 0.92384483897628 |
| 43 | 0.117762110999070 | 0.235524221998139 | 0.88223788900093 |
| 44 | 0.181738249330519 | 0.363476498661039 | 0.81826175066948 |
| 45 | 0.284273798492761 | 0.568547596985522 | 0.715726201507239 |
| 46 | 0.240415761783845 | 0.480831523567691 | 0.759584238216155 |
| 47 | 0.196203890952877 | 0.392407781905754 | 0.803796109047123 |
| 48 | 0.142183645180205 | 0.28436729036041 | 0.857816354819795 |
| 49 | 0.112067738177282 | 0.224135476354563 | 0.887932261822718 |
| 50 | 0.084541915615606 | 0.169083831231212 | 0.915458084384394 |
| 51 | 0.0510994929703597 | 0.102198985940719 | 0.94890050702964 |
| 52 | 0.0501014662125156 | 0.100202932425031 | 0.949898533787484 |
| 53 | 0.046280126185852 | 0.092560252371704 | 0.953719873814148 |
| 54 | 0.0728243324450573 | 0.145648664890115 | 0.927175667554943 |
| 55 | 0.0896965841079253 | 0.179393168215851 | 0.910303415892075 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 9 | 0.230769230769231 | NOK |
| 5% type I error level | 17 | 0.435897435897436 | NOK |
| 10% type I error level | 26 | 0.666666666666667 | NOK |
