| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 17.0254941272264 -2.97333759398567X[t] + 1.41303661442087Y1[t] -0.370434738549315Y2[t] -0.0226275979163081Y3[t] -0.0678756241040444Y4[t] + 0.163198807114589t + 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) | 17.0254941272264 | 6.601448 | 2.5791 | 0.011278 | 0.005639 |
| X | -2.97333759398567 | 3.315291 | -0.8969 | 0.371828 | 0.185914 |
| Y1 | 1.41303661442087 | 0.096648 | 14.6204 | 0 | 0 |
| Y2 | -0.370434738549315 | 0.168032 | -2.2046 | 0.029647 | 0.014824 |
| Y3 | -0.0226275979163081 | 0.168536 | -0.1343 | 0.893452 | 0.446726 |
| Y4 | -0.0678756241040444 | 0.097449 | -0.6965 | 0.487624 | 0.243812 |
| t | 0.163198807114589 | 0.069208 | 2.3581 | 0.020203 | 0.010101 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.997970467716217 |
| R-squared | 0.995945054433724 |
| Adjusted R-squared | 0.995715529212992 |
| F-TEST (value) | 4339.153018805 |
| F-TEST (DF numerator) | 6 |
| F-TEST (DF denominator) | 106 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 7.27639098080917 |
| Sum Squared Residuals | 5612.2617647937 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 405.7 | 401.824544380568 | 3.87545561943187 |
| 2 | 406.7 | 405.276621312325 | 1.42337868767535 |
| 3 | 407.2 | 405.398183638451 | 1.80181636154907 |
| 4 | 412.4 | 405.856734904048 | 6.54326509595179 |
| 5 | 415.9 | 412.996977641111 | 2.90302235888937 |
| 6 | 414 | 416.10035453518 | -2.1003545351796 |
| 7 | 411.8 | 412.130660868755 | -0.330660868755126 |
| 8 | 409.9 | 409.456855289339 | 0.443144710660566 |
| 9 | 412.4 | 407.55566870554 | 4.84433129446036 |
| 10 | 415.9 | 412.134029453164 | 3.76597054683632 |
| 11 | 416.3 | 416.509088373448 | -0.209088373447860 |
| 12 | 417.2 | 416.013374932415 | 1.18662506758483 |
| 13 | 421.8 | 417.051247144122 | 4.74875285587844 |
| 14 | 421.4 | 423.134407389347 | -1.73440738934716 |
| 15 | 415.1 | 420.9808766656 | -5.88087666560015 |
| 16 | 412.4 | 412.224943685174 | 0.175056314825548 |
| 17 | 411.8 | 410.603505654501 | 1.19649434549879 |
| 18 | 408.8 | 411.088760403561 | -2.28876040356085 |
| 19 | 404.5 | 407.723821156772 | -3.22382115677194 |
| 20 | 402.5 | 403.119107481355 | -0.619107481355438 |
| 21 | 409.4 | 402.157710603602 | 7.24228939639828 |
| 22 | 410.7 | 413.112657070671 | -2.41265707067113 |
| 23 | 413.4 | 412.893924160023 | 0.506075839977374 |
| 24 | 415.2 | 416.370377488545 | -1.17037748854498 |
| 25 | 417.7 | 417.579110723925 | 0.120889276075128 |
| 26 | 417.8 | 420.458785711994 | -2.65878571199355 |
| 27 | 417.9 | 419.613207472847 | -1.71320747284674 |
| 28 | 418.4 | 419.70192134937 | -1.30192134937036 |
| 29 | 418.2 | 420.362643169789 | -2.16264316978871 |
| 30 | 416.6 | 420.048966962542 | -3.44896696254241 |
| 31 | 418.9 | 418.007292772925 | 0.892707227074969 |
| 32 | 421 | 421.983759082418 | -0.983759082417645 |
| 33 | 423.5 | 424.31211416264 | -0.812114162639592 |
| 34 | 432.3 | 427.286549078212 | 5.01345092178829 |
| 35 | 432.3 | 438.754751354793 | -6.45475135479311 |
| 36 | 428.6 | 435.459016657264 | -6.85901665726445 |
| 37 | 426.7 | 430.025168069098 | -3.32516806909827 |
| 38 | 427.3 | 428.27690034933 | -0.976900349330005 |
| 39 | 428.5 | 430.075469240631 | -1.57546924063121 |
| 40 | 437 | 432.006183387147 | 4.99381661285283 |
| 41 | 442 | 443.851058857628 | -1.85105885762786 |
| 42 | 444.9 | 447.862866967216 | -2.96286696721563 |
| 43 | 441.4 | 449.997912932191 | -8.59791293219065 |
| 44 | 440.3 | 443.451142052573 | -3.15114205257325 |
| 45 | 447.1 | 442.95152401427 | 4.14847598572999 |
| 46 | 455.3 | 453.013207294656 | 2.28679270534389 |
| 47 | 478.6 | 462.506805159959 | 16.0931948400415 |
| 48 | 486.5 | 492.476987747659 | -5.97698774765852 |
| 49 | 487.8 | 494.524945853678 | -6.72494585367764 |
| 50 | 485.9 | 492.514854675897 | -6.61485467589668 |
| 51 | 483.8 | 487.751458690334 | -3.95145869033436 |
| 52 | 488.4 | 485.085473302696 | 3.31452669730423 |
| 53 | 494 | 492.481307611806 | 1.51869238819444 |
| 54 | 493.6 | 499.029993303772 | -5.42999330377211 |
| 55 | 487.3 | 496.591994789446 | -9.29199478944569 |
| 56 | 482.1 | 487.562294401919 | -5.46229440191858 |
| 57 | 484.2 | 482.340389211089 | 1.85961078891073 |
| 58 | 496.8 | 487.566929665458 | 9.23307033454159 |
| 59 | 501.1 | 505.301756804343 | -4.20175680434267 |
| 60 | 499.8 | 507.178970637462 | -7.37897063746242 |
| 61 | 495.5 | 503.484705925704 | -7.98470592570384 |
| 62 | 498.1 | 497.100880916172 | 0.99911908382831 |
| 63 | 503.8 | 502.268394990186 | 1.53160500981355 |
| 64 | 516.2 | 509.708309161647 | 6.49169083835291 |
| 65 | 526.1 | 525.514717406914 | 0.585282593085601 |
| 66 | 527.1 | 534.76813400799 | -7.66813400799054 |
| 67 | 525.1 | 532.009592246333 | -6.90959224633251 |
| 68 | 528.9 | 527.910612127794 | 0.989387872205504 |
| 69 | 540.1 | 533.489623270261 | 6.61037672973944 |
| 70 | 549 | 548.04855972413 | 0.95144027586986 |
| 71 | 556 | 556.688681703964 | -0.688681703964186 |
| 72 | 568.9 | 562.934911170678 | 5.96508882932204 |
| 73 | 589.1 | 577.771646522556 | 11.328353477444 |
| 74 | 590.3 | 600.937090573746 | -10.6370905737459 |
| 75 | 603.3 | 594.54612621762 | 8.7538737823794 |
| 76 | 638.8 | 611.301606297096 | 27.4983937029043 |
| 77 | 643 | 655.413712590609 | -12.4137125906087 |
| 78 | 656.7 | 647.985622437953 | 8.71437756204665 |
| 79 | 656.1 | 664.265934121345 | -8.16593412134524 |
| 80 | 654.1 | 656.00173447474 | -1.90173447473958 |
| 81 | 659.9 | 652.966045183452 | 6.93395481654834 |
| 82 | 662.1 | 661.14940633983 | 0.950593660169812 |
| 83 | 669.2 | 662.35874478538 | 6.84125521462021 |
| 84 | 673.1 | 671.744058310368 | 1.35594168963245 |
| 85 | 678.3 | 674.344553934804 | 3.95544606519593 |
| 86 | 677.4 | 680.10086533833 | -2.70086533833003 |
| 87 | 678.5 | 676.495905988997 | 2.00409401100289 |
| 88 | 672.4 | 678.164457893499 | -5.76445789349856 |
| 89 | 665.3 | 668.968066733025 | -3.66806673302521 |
| 90 | 667.9 | 661.394555186888 | 6.5054448131119 |
| 91 | 672.1 | 667.925100995972 | 4.17489900402786 |
| 92 | 662.5 | 673.634620515667 | -11.1346205156667 |
| 93 | 682.3 | 659.09992709899 | 23.2000729010099 |
| 94 | 692.1 | 690.525911827792 | 1.57408817220781 |
| 95 | 702.7 | 697.134408951715 | 5.5655910482855 |
| 96 | 721.4 | 708.849114986563 | 12.5508850134370 |
| 97 | 733.2 | 729.943802437885 | 3.25619756211501 |
| 98 | 747.7 | 738.948670030161 | 8.7513299698388 |
| 99 | 737.6 | 754.087152134959 | -16.4871521349586 |
| 100 | 729.3 | 733.0710976013 | -3.77109760129934 |
| 101 | 706.1 | 724.118450833854 | -18.0184508338545 |
| 102 | 674.3 | 693.81815070581 | -19.5181507058105 |
| 103 | 659 | 658.514223974842 | 0.485776025158301 |
| 104 | 645.7 | 649.926115218907 | -4.2261152189072 |
| 105 | 646.1 | 639.257850646981 | 6.8421493530187 |
| 106 | 633 | 644.444355623212 | -11.4443556232125 |
| 107 | 622.3 | 627.288044987073 | -4.98804498707281 |
| 108 | 628.2 | 618.078141856297 | 10.1218581437027 |
| 109 | 637.3 | 630.811179674035 | 6.48882032596509 |
| 110 | 639.6 | 642.778732688406 | -3.17873268840567 |
| 111 | 638.5 | 643.413725938097 | -4.9137259380967 |
| 112 | 650.5 | 640.564207247433 | 9.93579275256742 |
| 113 | 655.4 | 657.421611985447 | -2.02161198544754 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 10 | 0.0532720146394707 | 0.106544029278941 | 0.94672798536053 |
| 11 | 0.0165236760293821 | 0.0330473520587643 | 0.983476323970618 |
| 12 | 0.00564820605724697 | 0.0112964121144939 | 0.994351793942753 |
| 13 | 0.0043117864823602 | 0.0086235729647204 | 0.99568821351764 |
| 14 | 0.00145624428416534 | 0.00291248856833068 | 0.998543755715835 |
| 15 | 0.00149652385760621 | 0.00299304771521243 | 0.998503476142394 |
| 16 | 0.000547234217799026 | 0.00109446843559805 | 0.9994527657822 |
| 17 | 0.000425035311243594 | 0.000850070622487188 | 0.999574964688756 |
| 18 | 0.000417972654252295 | 0.00083594530850459 | 0.999582027345748 |
| 19 | 0.000190746788129147 | 0.000381493576258295 | 0.99980925321187 |
| 20 | 6.38627785698852e-05 | 0.000127725557139770 | 0.99993613722143 |
| 21 | 0.000149419619871325 | 0.00029883923974265 | 0.999850580380129 |
| 22 | 7.50041848527208e-05 | 0.000150008369705442 | 0.999924995815147 |
| 23 | 5.13559479874637e-05 | 0.000102711895974927 | 0.999948644052013 |
| 24 | 1.86608872214456e-05 | 3.73217744428912e-05 | 0.999981339112779 |
| 25 | 8.67637480874332e-06 | 1.73527496174866e-05 | 0.999991323625191 |
| 26 | 3.00552095746989e-06 | 6.01104191493977e-06 | 0.999996994479043 |
| 27 | 1.07778191072874e-06 | 2.15556382145748e-06 | 0.99999892221809 |
| 28 | 3.75309826427624e-07 | 7.50619652855249e-07 | 0.999999624690174 |
| 29 | 1.2125394178203e-07 | 2.4250788356406e-07 | 0.999999878746058 |
| 30 | 3.86348245074370e-08 | 7.72696490148741e-08 | 0.999999961365176 |
| 31 | 2.28301951754785e-08 | 4.56603903509570e-08 | 0.999999977169805 |
| 32 | 7.9097420867311e-09 | 1.58194841734622e-08 | 0.999999992090258 |
| 33 | 3.79559636741921e-09 | 7.59119273483842e-09 | 0.999999996204404 |
| 34 | 4.68148204914326e-08 | 9.36296409828652e-08 | 0.99999995318518 |
| 35 | 2.11885750837688e-08 | 4.23771501675376e-08 | 0.999999978811425 |
| 36 | 7.72114613779455e-09 | 1.54422922755891e-08 | 0.999999992278854 |
| 37 | 2.52651635098144e-09 | 5.05303270196289e-09 | 0.999999997473484 |
| 38 | 1.03685776461038e-09 | 2.07371552922076e-09 | 0.999999998963142 |
| 39 | 3.99284355974862e-10 | 7.98568711949725e-10 | 0.999999999600716 |
| 40 | 4.37612120623795e-09 | 8.75224241247591e-09 | 0.999999995623879 |
| 41 | 1.81180819039469e-09 | 3.62361638078937e-09 | 0.999999998188192 |
| 42 | 8.26637666212131e-10 | 1.65327533242426e-09 | 0.999999999173362 |
| 43 | 4.88249334042997e-10 | 9.76498668085993e-10 | 0.99999999951175 |
| 44 | 1.93863335889733e-10 | 3.87726671779465e-10 | 0.999999999806137 |
| 45 | 5.03063835514618e-10 | 1.00612767102924e-09 | 0.999999999496936 |
| 46 | 3.88639550646753e-10 | 7.77279101293506e-10 | 0.99999999961136 |
| 47 | 1.83966241515281e-06 | 3.67932483030561e-06 | 0.999998160337585 |
| 48 | 1.50603034866150e-06 | 3.01206069732299e-06 | 0.999998493969651 |
| 49 | 8.28950826127074e-07 | 1.65790165225415e-06 | 0.999999171049174 |
| 50 | 4.27765254061355e-07 | 8.5553050812271e-07 | 0.999999572234746 |
| 51 | 2.38473642953617e-07 | 4.76947285907233e-07 | 0.999999761526357 |
| 52 | 1.27741584388530e-07 | 2.55483168777060e-07 | 0.999999872258416 |
| 53 | 6.22207638783779e-08 | 1.24441527756756e-07 | 0.999999937779236 |
| 54 | 5.75404165003672e-08 | 1.15080833000734e-07 | 0.999999942459584 |
| 55 | 7.54332259129016e-08 | 1.50866451825803e-07 | 0.999999924566774 |
| 56 | 4.23991443181684e-08 | 8.47982886363368e-08 | 0.999999957600856 |
| 57 | 2.04788544157639e-08 | 4.09577088315279e-08 | 0.999999979521146 |
| 58 | 3.70346482775592e-08 | 7.40692965551185e-08 | 0.999999962965352 |
| 59 | 2.65806501537123e-08 | 5.31613003074245e-08 | 0.99999997341935 |
| 60 | 1.89134759333784e-08 | 3.78269518667568e-08 | 0.999999981086524 |
| 61 | 1.6962144823663e-08 | 3.3924289647326e-08 | 0.999999983037855 |
| 62 | 9.25130273445294e-09 | 1.85026054689059e-08 | 0.999999990748697 |
| 63 | 4.02602988655916e-09 | 8.05205977311832e-09 | 0.99999999597397 |
| 64 | 4.24061109482202e-09 | 8.48122218964405e-09 | 0.999999995759389 |
| 65 | 2.14749453614351e-09 | 4.29498907228703e-09 | 0.999999997852505 |
| 66 | 2.47084276148594e-09 | 4.94168552297187e-09 | 0.999999997529157 |
| 67 | 4.01096077768932e-09 | 8.02192155537864e-09 | 0.99999999598904 |
| 68 | 3.93597895746357e-09 | 7.87195791492715e-09 | 0.999999996064021 |
| 69 | 3.0156687393205e-09 | 6.031337478641e-09 | 0.999999996984331 |
| 70 | 1.71008198864545e-09 | 3.4201639772909e-09 | 0.999999998289918 |
| 71 | 2.12223151849986e-09 | 4.24446303699972e-09 | 0.999999997877768 |
| 72 | 7.62566033566779e-09 | 1.52513206713356e-08 | 0.99999999237434 |
| 73 | 2.243017201485e-08 | 4.48603440297e-08 | 0.999999977569828 |
| 74 | 2.01837987634177e-06 | 4.03675975268355e-06 | 0.999997981620124 |
| 75 | 1.91228249219319e-05 | 3.82456498438637e-05 | 0.999980877175078 |
| 76 | 0.000775905684035355 | 0.00155181136807071 | 0.999224094315965 |
| 77 | 0.0130035678894402 | 0.0260071357788804 | 0.98699643211056 |
| 78 | 0.0179346434775202 | 0.0358692869550404 | 0.98206535652248 |
| 79 | 0.113384522604281 | 0.226769045208561 | 0.886615477395719 |
| 80 | 0.153407108986637 | 0.306814217973274 | 0.846592891013363 |
| 81 | 0.120538603474843 | 0.241077206949686 | 0.879461396525157 |
| 82 | 0.100555165861474 | 0.201110331722948 | 0.899444834138526 |
| 83 | 0.0792671815588644 | 0.158534363117729 | 0.920732818441136 |
| 84 | 0.0606848241573943 | 0.121369648314789 | 0.939315175842606 |
| 85 | 0.043784974962598 | 0.087569949925196 | 0.956215025037402 |
| 86 | 0.0392679268634444 | 0.0785358537268889 | 0.960732073136556 |
| 87 | 0.0273297845383606 | 0.0546595690767213 | 0.97267021546164 |
| 88 | 0.0336525715592372 | 0.0673051431184743 | 0.966347428440763 |
| 89 | 0.0392717118778147 | 0.0785434237556295 | 0.960728288122185 |
| 90 | 0.0268839861963212 | 0.0537679723926425 | 0.973116013803679 |
| 91 | 0.0173133651188421 | 0.0346267302376843 | 0.982686634881158 |
| 92 | 0.207206492359526 | 0.414412984719051 | 0.792793507640474 |
| 93 | 0.241196162812895 | 0.48239232562579 | 0.758803837187105 |
| 94 | 0.284970322750422 | 0.569940645500845 | 0.715029677249578 |
| 95 | 0.264363254336483 | 0.528726508672965 | 0.735636745663517 |
| 96 | 0.274584924626957 | 0.549169849253914 | 0.725415075373043 |
| 97 | 0.220956402087038 | 0.441912804174076 | 0.779043597912962 |
| 98 | 0.347863299296102 | 0.695726598592203 | 0.652136700703898 |
| 99 | 0.361057225051362 | 0.722114450102724 | 0.638942774948638 |
| 100 | 0.730022143570548 | 0.539955712858905 | 0.269977856429452 |
| 101 | 0.7151800305288 | 0.569639938942402 | 0.284819969471201 |
| 102 | 0.687501704669693 | 0.624996590660614 | 0.312498295330307 |
| 103 | 0.821732439162005 | 0.35653512167599 | 0.178267560837995 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 64 | 0.680851063829787 | NOK |
| 5% type I error level | 69 | 0.73404255319149 | NOK |
| 10% type I error level | 75 | 0.797872340425532 | NOK |
