| Multiple Linear Regression - Estimated Regression Equation |
| QBEPIL[t] = + 937628.048735503 + 8056925.15259668PBEPIL[t] + 235921.324377866PBEABD[t] -1529426.31137177PBEWIT[t] -9625944.17979685PWABR[t] + 8079834.06250011PWAPL[t] -3415028.9892527PSOCOLA[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) | 937628.048735503 | 1901642.098018 | 0.4931 | 0.622848 | 0.311424 |
| PBEPIL | 8056925.15259668 | 1020057.250454 | 7.8985 | 0 | 0 |
| PBEABD | 235921.324377866 | 363468.560544 | 0.6491 | 0.517495 | 0.258747 |
| PBEWIT | -1529426.31137177 | 671513.069409 | -2.2776 | 0.024478 | 0.012239 |
| PWABR | -9625944.17979685 | 2669247.442907 | -3.6062 | 0.00045 | 0.000225 |
| PWAPL | 8079834.06250011 | 2613468.701554 | 3.0916 | 0.002463 | 0.001232 |
| PSOCOLA | -3415028.9892527 | 1297500.524522 | -2.632 | 0.009576 | 0.004788 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.660347895790128 |
| R-squared | 0.43605934347445 |
| Adjusted R-squared | 0.40855004315613 |
| F-TEST (value) | 15.8513425797333 |
| F-TEST (DF numerator) | 6 |
| F-TEST (DF denominator) | 123 |
| p-value | 1.97508676080815e-13 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 338579.761706063 |
| Sum Squared Residuals | 14100259369542.9 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 4264830 | 3773901.59528071 | 490928.404719285 |
| 2 | 3924674 | 3633248.38735207 | 291425.612647932 |
| 3 | 3734753 | 3561949.15074197 | 172803.849258034 |
| 4 | 3762290 | 3661356.74987532 | 100933.250124678 |
| 5 | 3609739 | 3557213.04508299 | 52525.9549170115 |
| 6 | 3877594 | 3695461.152169 | 182132.847830998 |
| 7 | 3636415 | 3676114.84069675 | -39699.8406967531 |
| 8 | 3578195 | 3493077.04032179 | 85117.9596782147 |
| 9 | 3604342 | 3288369.07357363 | 315972.92642637 |
| 10 | 3459513 | 3454910.06041357 | 4602.93958643298 |
| 11 | 3366571 | 3480614.63782468 | -114043.637824678 |
| 12 | 3371277 | 3641593.90084071 | -270316.900840706 |
| 13 | 3724848 | 3611023.05378469 | 113824.946215309 |
| 14 | 3350830 | 3428793.19240323 | -77963.1924032347 |
| 15 | 3305159 | 3381311.92548248 | -76152.9254824845 |
| 16 | 3390736 | 3438230.04537835 | -47494.0453783493 |
| 17 | 3349758 | 3404431.45239825 | -54673.4523982517 |
| 18 | 3253655 | 3330710.75150459 | -77055.7515045864 |
| 19 | 3734250 | 3353889.27761267 | 380360.722387331 |
| 20 | 3455433 | 3316223.1116539 | 139209.888346102 |
| 21 | 2966726 | 3258061.07946501 | -291335.079465012 |
| 22 | 2993716 | 3471511.80259057 | -477795.802590572 |
| 23 | 3009320 | 3547362.62762898 | -538042.627628982 |
| 24 | 3169713 | 3452655.73396095 | -282942.733960951 |
| 25 | 3170061 | 3404598.24860669 | -234537.248606689 |
| 26 | 3368934 | 3368691.55682914 | 242.443170857564 |
| 27 | 3292638 | 3300188.82249281 | -7550.82249281102 |
| 28 | 3337344 | 3364324.82725401 | -26980.8272540144 |
| 29 | 3208306 | 3399568.21319874 | -191262.21319874 |
| 30 | 3359130 | 3230146.44769795 | 128983.552302048 |
| 31 | 3223078 | 3441886.1665786 | -218808.166578596 |
| 32 | 3437159 | 3589391.13513619 | -152232.135136194 |
| 33 | 3400156 | 3579147.65889805 | -178991.65889805 |
| 34 | 3657576 | 3683202.51972535 | -25626.5197253523 |
| 35 | 3765613 | 3742785.62032777 | 22827.3796722345 |
| 36 | 3481921 | 3937038.70091016 | -455117.700910163 |
| 37 | 3604800 | 4131624.48350309 | -526824.483503087 |
| 38 | 3981340 | 3977270.96431319 | 4069.03568681212 |
| 39 | 3734078 | 4118689.43363315 | -384611.433633148 |
| 40 | 4018173 | 4170862.53411621 | -152689.534116208 |
| 41 | 3887417 | 3939730.61616447 | -52313.6161644683 |
| 42 | 3919880 | 4032199.20519831 | -112319.205198311 |
| 43 | 4014466 | 3808951.55024094 | 205514.449759064 |
| 44 | 4197758 | 4007364.8178205 | 190393.182179504 |
| 45 | 3896531 | 3930082.35326174 | -33551.3532617393 |
| 46 | 3964742 | 3978324.35584667 | -13582.3558466711 |
| 47 | 4201847 | 4095219.90900876 | 106627.090991243 |
| 48 | 4050512 | 3834201.15945063 | 216310.840549365 |
| 49 | 3997402 | 3786869.05141771 | 210532.948582285 |
| 50 | 4314479 | 3783370.85452289 | 531108.14547711 |
| 51 | 4925744 | 3989482.25236397 | 936261.747636035 |
| 52 | 5130631 | 3876892.83509022 | 1253738.16490978 |
| 53 | 4444855 | 3883970.47482155 | 560884.525178448 |
| 54 | 3967319 | 3753024.57083877 | 214294.42916123 |
| 55 | 3931250 | 3723727.43899768 | 207522.561002321 |
| 56 | 4235952 | 3591494.66635569 | 644457.333644309 |
| 57 | 4169219 | 3599440.83876733 | 569778.161232669 |
| 58 | 3779064 | 3407254.31555941 | 371809.68444059 |
| 59 | 3558810 | 3507029.63342362 | 51780.3665763767 |
| 60 | 3699466 | 3488839.98477384 | 210626.01522616 |
| 61 | 3650693 | 3490970.10891858 | 159722.891081415 |
| 62 | 3525633 | 3376250.56750009 | 149382.432499909 |
| 63 | 3470276 | 3409032.78464254 | 61243.2153574623 |
| 64 | 3859094 | 3487638.75008301 | 371455.24991699 |
| 65 | 3661155 | 3487638.75008301 | 173516.24991699 |
| 66 | 3356365 | 3587765.72300884 | -231400.72300884 |
| 67 | 3344440 | 3496910.03887855 | -152470.038878545 |
| 68 | 3338684 | 3288872.328797 | 49811.6712030041 |
| 69 | 3404294 | 3400093.67332067 | 4200.32667933453 |
| 70 | 3289319 | 3434882.13291479 | -145563.132914791 |
| 71 | 3469252 | 3627104.1765368 | -157852.176536797 |
| 72 | 3571850 | 3715683.16724467 | -143833.167244671 |
| 73 | 3639914 | 3768751.39333328 | -128837.393333282 |
| 74 | 3091730 | 3852575.32533109 | -760845.325331088 |
| 75 | 3078149 | 4042479.31365896 | -964330.313658965 |
| 76 | 3188115 | 3975317.71752496 | -787202.717524957 |
| 77 | 3246082 | 3820018.94544021 | -573936.945440206 |
| 78 | 3486992 | 3874942.66059819 | -387950.66059819 |
| 79 | 3378187 | 3814782.02583178 | -436595.025831782 |
| 80 | 3282306 | 3649397.70181431 | -367091.70181431 |
| 81 | 3288345 | 3651424.55467007 | -363079.554670072 |
| 82 | 3325749 | 3660694.56958594 | -334945.569585937 |
| 83 | 3352262 | 3575943.0638647 | -223681.0638647 |
| 84 | 3531954 | 3656512.31539067 | -124558.315390667 |
| 85 | 3722622 | 3760656.020183 | -38034.0201829999 |
| 86 | 3809365 | 3905553.39172418 | -96188.3917241844 |
| 87 | 3750617 | 4061001.32269676 | -310384.322696765 |
| 88 | 3615286 | 4144158.87656554 | -528872.876565545 |
| 89 | 3696556 | 4133519.47316912 | -436963.473169117 |
| 90 | 4123959 | 4087100.51153568 | 36858.4884643229 |
| 91 | 4136163 | 4128616.52945089 | 7546.47054910995 |
| 92 | 3933392 | 3939991.76990806 | -6599.76990806121 |
| 93 | 4035576 | 3906237.40717382 | 129338.592826182 |
| 94 | 4551202 | 4005042.19494842 | 546159.805051584 |
| 95 | 4032195 | 3976421.48053361 | 55773.5194663858 |
| 96 | 3970893 | 4171519.61501809 | -200626.615018086 |
| 97 | 4489016 | 4523662.84232425 | -34646.8423242516 |
| 98 | 5426127 | 4464615.91401413 | 961511.085985875 |
| 99 | 4578224 | 4468861.73497966 | 109362.265020337 |
| 100 | 4126390 | 4195853.18844645 | -69463.1884464534 |
| 101 | 4892100 | 4326799.09242924 | 565300.907570764 |
| 102 | 4128697 | 4282572.50598032 | -153875.505980325 |
| 103 | 4408721 | 4172388.1895492 | 236332.810450799 |
| 104 | 4199465 | 4101728.39652037 | 97736.6034796313 |
| 105 | 4074767 | 3930550.22913456 | 144216.770865439 |
| 106 | 4161758 | 4105686.08734374 | 56071.9126562556 |
| 107 | 3891319 | 4248663.15017332 | -357344.150173322 |
| 108 | 4470302 | 4178705.05176554 | 291596.948234457 |
| 109 | 4283111 | 3836010.17352578 | 447100.82647422 |
| 110 | 3845962 | 3613936.86056229 | 232025.13943771 |
| 111 | 3911471 | 3612037.14124706 | 299433.858752937 |
| 112 | 3798478 | 3618624.49628496 | 179853.50371504 |
| 113 | 3644313 | 3411347.52186759 | 232965.478132408 |
| 114 | 3784029 | 3775108.1396196 | 8920.86038039648 |
| 115 | 3647134 | 3595649.78208115 | 51484.2179188527 |
| 116 | 3994662 | 3484883.40575889 | 509778.59424111 |
| 117 | 3607836 | 3526979.86806306 | 80856.1319369438 |
| 118 | 3566008 | 3389411.25069954 | 176596.749300463 |
| 119 | 3511412 | 3454132.34579727 | 57279.6542027324 |
| 120 | 3258665 | 3574317.93777403 | -315652.937774032 |
| 121 | 3486573 | 3635558.55699917 | -148985.55699917 |
| 122 | 3369443 | 3690338.95472695 | -320895.954726946 |
| 123 | 3465544 | 3717114.60284296 | -251570.60284296 |
| 124 | 3905224 | 3687350.37904997 | 217873.620950026 |
| 125 | 3733881 | 3786441.63961374 | -52560.6396137406 |
| 126 | 3220642 | 3513108.33071586 | -292466.330715859 |
| 127 | 3225812 | 3482248.37940971 | -256436.379409708 |
| 128 | 3354461 | 3578111.89404939 | -223650.894049392 |
| 129 | 3352261 | 3605580.47136887 | -253319.471368867 |
| 130 | 3450652 | 3372333.19821884 | 78318.8017811562 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 10 | 0.126880781099326 | 0.253761562198653 | 0.873119218900674 |
| 11 | 0.0483431579486499 | 0.0966863158972999 | 0.95165684205135 |
| 12 | 0.0285675024528223 | 0.0571350049056446 | 0.971432497547178 |
| 13 | 0.0167257909620989 | 0.0334515819241978 | 0.983274209037901 |
| 14 | 0.00615245201120722 | 0.0123049040224144 | 0.993847547988793 |
| 15 | 0.00321735939138666 | 0.00643471878277331 | 0.996782640608613 |
| 16 | 0.00113440425674615 | 0.00226880851349231 | 0.998865595743254 |
| 17 | 0.000602023680231333 | 0.00120404736046267 | 0.999397976319769 |
| 18 | 0.000253853379940655 | 0.00050770675988131 | 0.999746146620059 |
| 19 | 0.00785389976726845 | 0.0157077995345369 | 0.992146100232732 |
| 20 | 0.0039945143343168 | 0.0079890286686336 | 0.996005485665683 |
| 21 | 0.00886116999205084 | 0.0177223399841017 | 0.991138830007949 |
| 22 | 0.0221292205579058 | 0.0442584411158117 | 0.977870779442094 |
| 23 | 0.0337464349386697 | 0.0674928698773394 | 0.96625356506133 |
| 24 | 0.0216521028850563 | 0.0433042057701126 | 0.978347897114944 |
| 25 | 0.0214713602103858 | 0.0429427204207716 | 0.978528639789614 |
| 26 | 0.0149997291770326 | 0.0299994583540652 | 0.985000270822967 |
| 27 | 0.0148541726208841 | 0.0297083452417682 | 0.985145827379116 |
| 28 | 0.00999397821446234 | 0.0199879564289247 | 0.990006021785538 |
| 29 | 0.00617155724308673 | 0.0123431144861735 | 0.993828442756913 |
| 30 | 0.00377283009762021 | 0.00754566019524042 | 0.99622716990238 |
| 31 | 0.00311971248373663 | 0.00623942496747326 | 0.996880287516263 |
| 32 | 0.00195623289715565 | 0.00391246579431129 | 0.998043767102844 |
| 33 | 0.00166171433439018 | 0.00332342866878037 | 0.99833828566561 |
| 34 | 0.000960544780172627 | 0.00192108956034525 | 0.999039455219827 |
| 35 | 0.000578929057390824 | 0.00115785811478165 | 0.999421070942609 |
| 36 | 0.001275900383729 | 0.00255180076745801 | 0.998724099616271 |
| 37 | 0.000980903536827217 | 0.00196180707365443 | 0.999019096463173 |
| 38 | 0.00154676903773144 | 0.00309353807546287 | 0.998453230962269 |
| 39 | 0.00112945255338943 | 0.00225890510677886 | 0.998870547446611 |
| 40 | 0.00119070671560105 | 0.0023814134312021 | 0.998809293284399 |
| 41 | 0.00108925325149954 | 0.00217850650299908 | 0.9989107467485 |
| 42 | 0.000735245919072254 | 0.00147049183814451 | 0.999264754080928 |
| 43 | 0.00126150121517905 | 0.0025230024303581 | 0.998738498784821 |
| 44 | 0.00146776606798991 | 0.00293553213597983 | 0.99853223393201 |
| 45 | 0.000975768908176671 | 0.00195153781635334 | 0.999024231091823 |
| 46 | 0.000660954773971821 | 0.00132190954794364 | 0.999339045226028 |
| 47 | 0.000615009997462287 | 0.00123001999492457 | 0.999384990002538 |
| 48 | 0.000623160522897635 | 0.00124632104579527 | 0.999376839477102 |
| 49 | 0.00058801481309617 | 0.00117602962619234 | 0.999411985186904 |
| 50 | 0.00139864522489541 | 0.00279729044979082 | 0.998601354775105 |
| 51 | 0.0218232703038849 | 0.0436465406077698 | 0.978176729696115 |
| 52 | 0.333673943333152 | 0.667347886666305 | 0.666326056666848 |
| 53 | 0.388459608222097 | 0.776919216444194 | 0.611540391777903 |
| 54 | 0.355071953771394 | 0.710143907542789 | 0.644928046228606 |
| 55 | 0.321301249435248 | 0.642602498870495 | 0.678698750564752 |
| 56 | 0.429998936424501 | 0.859997872849001 | 0.570001063575499 |
| 57 | 0.506991606515536 | 0.986016786968927 | 0.493008393484464 |
| 58 | 0.51626950498647 | 0.96746099002706 | 0.48373049501353 |
| 59 | 0.478247273325193 | 0.956494546650387 | 0.521752726674807 |
| 60 | 0.457643334162932 | 0.915286668325865 | 0.542356665837068 |
| 61 | 0.431588163708436 | 0.863176327416872 | 0.568411836291564 |
| 62 | 0.404732559736862 | 0.809465119473724 | 0.595267440263138 |
| 63 | 0.381615460742177 | 0.763230921484354 | 0.618384539257823 |
| 64 | 0.461859604744664 | 0.923719209489329 | 0.538140395255336 |
| 65 | 0.510511973326822 | 0.978976053346356 | 0.489488026673178 |
| 66 | 0.514234265258522 | 0.971531469482957 | 0.485765734741478 |
| 67 | 0.51984467124152 | 0.960310657516959 | 0.48015532875848 |
| 68 | 0.530265457485252 | 0.939469085029495 | 0.469734542514748 |
| 69 | 0.537198860144475 | 0.925602279711049 | 0.462801139855525 |
| 70 | 0.547953697159885 | 0.904092605680229 | 0.452046302840115 |
| 71 | 0.581395377909336 | 0.837209244181329 | 0.418604622090664 |
| 72 | 0.586677544661611 | 0.826644910676778 | 0.413322455338389 |
| 73 | 0.567725387883327 | 0.864549224233346 | 0.432274612116673 |
| 74 | 0.659868896121459 | 0.680262207757082 | 0.340131103878541 |
| 75 | 0.857393158817177 | 0.285213682365645 | 0.142606841182823 |
| 76 | 0.944065456759029 | 0.111869086481943 | 0.0559345432409714 |
| 77 | 0.950893841641381 | 0.0982123167172387 | 0.0491061583586194 |
| 78 | 0.944368035879153 | 0.111263928241695 | 0.0556319641208475 |
| 79 | 0.933312235108956 | 0.133375529782088 | 0.0666877648910439 |
| 80 | 0.921927074189684 | 0.156145851620633 | 0.0780729258103164 |
| 81 | 0.911776781071534 | 0.176446437856932 | 0.0882232189284658 |
| 82 | 0.90526500967994 | 0.189469980640121 | 0.0947349903200605 |
| 83 | 0.891968575096173 | 0.216062849807655 | 0.108031424903827 |
| 84 | 0.872008057634515 | 0.255983884730969 | 0.127991942365485 |
| 85 | 0.843451082804557 | 0.313097834390885 | 0.156548917195443 |
| 86 | 0.81007834829744 | 0.37984330340512 | 0.18992165170256 |
| 87 | 0.821751094563132 | 0.356497810873735 | 0.178248905436868 |
| 88 | 0.88556296879841 | 0.22887406240318 | 0.11443703120159 |
| 89 | 0.937790612553539 | 0.124418774892922 | 0.0622093874464609 |
| 90 | 0.925010630854551 | 0.149978738290898 | 0.074989369145449 |
| 91 | 0.907373068375322 | 0.185253863249356 | 0.0926269316246782 |
| 92 | 0.893386335334208 | 0.213227329331584 | 0.106613664665792 |
| 93 | 0.867460288899578 | 0.265079422200844 | 0.132539711100422 |
| 94 | 0.91577932776467 | 0.16844134447066 | 0.0842206722353299 |
| 95 | 0.90786360887104 | 0.184272782257921 | 0.0921363911289604 |
| 96 | 0.907095936714197 | 0.185808126571607 | 0.0929040632858033 |
| 97 | 0.913808659170836 | 0.172382681658328 | 0.086191340829164 |
| 98 | 0.993737805704836 | 0.0125243885903275 | 0.00626219429516377 |
| 99 | 0.990276435325421 | 0.0194471293491571 | 0.00972356467457855 |
| 100 | 0.994343669859255 | 0.0113126602814898 | 0.00565633014074488 |
| 101 | 0.997067956266916 | 0.00586408746616869 | 0.00293204373308435 |
| 102 | 0.997784921014705 | 0.00443015797059098 | 0.00221507898529549 |
| 103 | 0.996171508782763 | 0.0076569824344737 | 0.00382849121723685 |
| 104 | 0.99548687085628 | 0.00902625828743915 | 0.00451312914371957 |
| 105 | 0.99391148732308 | 0.0121770253538395 | 0.00608851267691975 |
| 106 | 0.991224677776436 | 0.0175506444471288 | 0.00877532222356438 |
| 107 | 0.998183866571249 | 0.0036322668575013 | 0.00181613342875065 |
| 108 | 0.99714056432082 | 0.00571887135835999 | 0.00285943567917999 |
| 109 | 0.998732122539968 | 0.00253575492006369 | 0.00126787746003184 |
| 110 | 0.99904162573303 | 0.00191674853393971 | 0.000958374266969853 |
| 111 | 0.997766515509427 | 0.00446696898114574 | 0.00223348449057287 |
| 112 | 0.99495901420241 | 0.0100819715951802 | 0.00504098579759008 |
| 113 | 0.990105904162108 | 0.0197881916757843 | 0.00989409583789213 |
| 114 | 0.979254456515282 | 0.0414910869694353 | 0.0207455434847176 |
| 115 | 0.966993323765666 | 0.0660133524686675 | 0.0330066762343337 |
| 116 | 0.976788780216451 | 0.0464224395670984 | 0.0232112197835492 |
| 117 | 0.979952697197108 | 0.0400946056057846 | 0.0200473028028923 |
| 118 | 0.974021740784216 | 0.0519565184315672 | 0.0259782592157836 |
| 119 | 0.957421853216045 | 0.0851562935679092 | 0.0425781467839546 |
| 120 | 0.902829425228853 | 0.194341149542295 | 0.0971705747711474 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 35 | 0.315315315315315 | NOK |
| 5% type I error level | 57 | 0.513513513513513 | NOK |
| 10% type I error level | 64 | 0.576576576576577 | NOK |
