| Multiple Linear Regression - Estimated Regression Equation |
| QBEFRU[t] = -77762.8038393112 + 43308.2898165855PBEPIL[t] -13371.5549986481PBEFRU[t] -71801.4106895052PBEREG[t] -25052.210867151PCHEXO[t] + 79708.4302130641PAMMOORA[t] + 1884.30016541286PAMMOAPP[t] -4757.99338540753PAMMOGRA[t] -107690.203091025PSOCOLA[t] + 260892.453821228PSOLEM[t] -92735.8580943806PSTILL[t] + 0.0390542002511986BUDBEER[t] + 0.00893580719412229BUDCHIL[t] -0.0140084185334704BUDAMB[t] + 0.00419180585976342`BUDSISSS\r`[t] + 2224.18026740329Q1[t] + 1808.5633525552Q2[t] + 2022.30010055336Q3[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) | -77762.8038393112 | 110800.077985 | -0.7018 | 0.484241 | 0.242121 |
| PBEPIL | 43308.2898165855 | 59771.620073 | 0.7246 | 0.470231 | 0.235116 |
| PBEFRU | -13371.5549986481 | 18882.596805 | -0.7081 | 0.480328 | 0.240164 |
| PBEREG | -71801.4106895052 | 12493.244337 | -5.7472 | 0 | 0 |
| PCHEXO | -25052.210867151 | 15294.6052 | -1.638 | 0.104233 | 0.052117 |
| PAMMOORA | 79708.4302130641 | 29458.32359 | 2.7058 | 0.00788 | 0.00394 |
| PAMMOAPP | 1884.30016541286 | 6128.14487 | 0.3075 | 0.759047 | 0.379523 |
| PAMMOGRA | -4757.99338540753 | 3568.908872 | -1.3332 | 0.185179 | 0.092589 |
| PSOCOLA | -107690.203091025 | 57580.799211 | -1.8702 | 0.064061 | 0.03203 |
| PSOLEM | 260892.453821228 | 80705.223105 | 3.2327 | 0.001611 | 0.000806 |
| PSTILL | -92735.8580943806 | 47177.427055 | -1.9657 | 0.05181 | 0.025905 |
| BUDBEER | 0.0390542002511986 | 0.001786 | 21.8702 | 0 | 0 |
| BUDCHIL | 0.00893580719412229 | 0.011131 | 0.8028 | 0.423819 | 0.211909 |
| BUDAMB | -0.0140084185334704 | 0.006249 | -2.2417 | 0.026951 | 0.013476 |
| `BUDSISSS\r` | 0.00419180585976342 | 0.001135 | 3.6921 | 0.000345 | 0.000173 |
| Q1 | 2224.18026740329 | 2564.549759 | 0.8673 | 0.387643 | 0.193822 |
| Q2 | 1808.5633525552 | 2608.007253 | 0.6935 | 0.489453 | 0.244727 |
| Q3 | 2022.30010055336 | 2578.565378 | 0.7843 | 0.434535 | 0.217268 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.978990451586407 |
| R-squared | 0.958422304297357 |
| Adjusted R-squared | 0.952111404056777 |
| F-TEST (value) | 151.867763355631 |
| F-TEST (DF numerator) | 17 |
| F-TEST (DF denominator) | 112 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 10119.4549718129 |
| Sum Squared Residuals | 11469177319.7734 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 178421 | 174252.576441352 | 4168.42355864765 |
| 2 | 139871 | 146326.357230263 | -6455.35723026324 |
| 3 | 118159 | 117605.037680353 | 553.962319646565 |
| 4 | 109763 | 112449.081990878 | -2686.08199087846 |
| 5 | 97415 | 101653.009022982 | -4238.00902298225 |
| 6 | 119190 | 120275.410975313 | -1085.41097531269 |
| 7 | 97903 | 106507.621150224 | -8604.62115022355 |
| 8 | 96953 | 101053.073909253 | -4100.07390925259 |
| 9 | 87888 | 93659.4976417386 | -5771.49764173862 |
| 10 | 84637 | 86991.0364956655 | -2354.03649566549 |
| 11 | 90549 | 91119.6688360451 | -570.668836045131 |
| 12 | 95680 | 95673.6583945825 | 6.34160541749409 |
| 13 | 99371 | 127630.376605148 | -28259.3766051476 |
| 14 | 79984 | 94128.0875274437 | -14144.0875274437 |
| 15 | 86752 | 76725.0317757164 | 10026.9682242836 |
| 16 | 85733 | 75384.0617378975 | 10348.9382621025 |
| 17 | 84906 | 72221.9167505317 | 12684.0832494683 |
| 18 | 78356 | 69511.4663703241 | 8844.53362967595 |
| 19 | 108895 | 123602.102781653 | -14707.1027816529 |
| 20 | 101768 | 94101.7333518862 | 7666.26664811379 |
| 21 | 73285 | 47644.6328224596 | 25640.3671775404 |
| 22 | 65724 | 51185.8434529899 | 14538.1565470101 |
| 23 | 67457 | 56599.4686309781 | 10857.5313690219 |
| 24 | 67203 | 62648.3642198543 | 4554.63578014569 |
| 25 | 69273 | 59120.1367417516 | 10152.8632582484 |
| 26 | 80807 | 83534.8887210426 | -2727.88872104259 |
| 27 | 75129 | 78478.6435434903 | -3349.64354349031 |
| 28 | 74991 | 83267.6490473722 | -8276.64904737224 |
| 29 | 68157 | 66916.2859351044 | 1240.71406489561 |
| 30 | 73858 | 85029.3319896892 | -11171.3319896892 |
| 31 | 71349 | 72752.450009957 | -1403.45000995695 |
| 32 | 85634 | 83095.7829641759 | 2538.21703582406 |
| 33 | 91624 | 88879.7036234318 | 2744.29637656821 |
| 34 | 116014 | 118074.910089184 | -2060.91008918371 |
| 35 | 120033 | 129778.236111574 | -9745.23611157394 |
| 36 | 108651 | 94641.3163517066 | 14009.6836482934 |
| 37 | 105378 | 118143.125319222 | -12765.1253192218 |
| 38 | 138939 | 145695.730863025 | -6756.73086302471 |
| 39 | 132974 | 127893.415191295 | 5080.58480870503 |
| 40 | 135277 | 147227.403882359 | -11950.4038823594 |
| 41 | 152741 | 141469.960374525 | 11271.0396254754 |
| 42 | 158417 | 153698.785568886 | 4718.21443111414 |
| 43 | 157460 | 151187.594456918 | 6272.40554308191 |
| 44 | 193997 | 181566.679997093 | 12430.320002907 |
| 45 | 154089 | 152692.562881359 | 1396.43711864106 |
| 46 | 147570 | 149942.965528782 | -2372.96552878168 |
| 47 | 162924 | 177938.137402041 | -15014.1374020405 |
| 48 | 153629 | 152440.339118667 | 1188.66088133288 |
| 49 | 155907 | 150483.51411135 | 5423.48588865042 |
| 50 | 197675 | 196408.466134685 | 1266.5338653154 |
| 51 | 250708 | 240506.821580113 | 10201.1784198869 |
| 52 | 266652 | 248437.121879641 | 18214.8781203594 |
| 53 | 209842 | 213000.915126675 | -3158.91512667521 |
| 54 | 165826 | 163113.609734985 | 2712.39026501531 |
| 55 | 137152 | 141279.70892976 | -4127.70892975958 |
| 56 | 150581 | 155660.473530942 | -5079.47353094177 |
| 57 | 145973 | 148121.870456837 | -2148.87045683697 |
| 58 | 126532 | 114341.927212092 | 12190.0727879081 |
| 59 | 115437 | 101182.11569567 | 14254.8843043304 |
| 60 | 119526 | 116939.415971765 | 2586.58402823465 |
| 61 | 110856 | 113361.963557992 | -2505.96355799232 |
| 62 | 97243 | 97484.0373703408 | -241.037370340758 |
| 63 | 103876 | 104437.390727651 | -561.390727650967 |
| 64 | 116370 | 123790.786885116 | -7420.78688511552 |
| 65 | 109616 | 107112.125215033 | 2503.87478496683 |
| 66 | 98365 | 94151.2884198339 | 4213.71158016605 |
| 67 | 90440 | 85823.7730361493 | 4616.22696385073 |
| 68 | 88899 | 82026.803584437 | 6872.19641556298 |
| 69 | 92358 | 90303.6637323336 | 2054.33626766642 |
| 70 | 88394 | 83922.5577807722 | 4471.44221922775 |
| 71 | 98219 | 107973.621212342 | -9754.62121234163 |
| 72 | 113546 | 118961.412749289 | -5415.41274928863 |
| 73 | 107168 | 108848.706519286 | -1680.7065192858 |
| 74 | 77540 | 64660.3423896674 | 12879.6576103326 |
| 75 | 74944 | 71247.1069409256 | 3696.89305907438 |
| 76 | 75641 | 75679.4366843709 | -38.4366843709458 |
| 77 | 75910 | 80189.963968932 | -4279.963968932 |
| 78 | 87384 | 100885.41892478 | -13501.4189247804 |
| 79 | 84615 | 86733.4703155061 | -2118.47031550612 |
| 80 | 80420 | 87148.4902119244 | -6728.49021192437 |
| 81 | 80784 | 93498.5853520564 | -12714.5853520564 |
| 82 | 79933 | 88900.4914115843 | -8967.49141158425 |
| 83 | 82118 | 93466.1322593413 | -11348.1322593413 |
| 84 | 91420 | 104223.788601321 | -12803.7886013211 |
| 85 | 112426 | 128929.455503187 | -16503.4555031868 |
| 86 | 114528 | 117049.700792609 | -2521.70079260946 |
| 87 | 131025 | 124100.862444534 | 6924.13755546634 |
| 88 | 116460 | 127356.447435406 | -10896.4474354065 |
| 89 | 111258 | 124375.409256979 | -13117.4092569792 |
| 90 | 155318 | 153079.261188904 | 2238.73881109569 |
| 91 | 155078 | 166970.128304246 | -11892.1283042463 |
| 92 | 134794 | 148310.763909865 | -13516.7639098653 |
| 93 | 139985 | 150146.960651852 | -10161.960651852 |
| 94 | 198778 | 212034.08828941 | -13256.0882894099 |
| 95 | 172436 | 171601.498863907 | 834.501136092926 |
| 96 | 169585 | 164280.591993222 | 5304.40800677783 |
| 97 | 203702 | 204147.117789087 | -445.117789086595 |
| 98 | 282392 | 275030.811007427 | 7361.18899257318 |
| 99 | 220658 | 210523.096406792 | 10134.9035932079 |
| 100 | 194472 | 189228.282284058 | 5243.71771594188 |
| 101 | 269246 | 260275.090170381 | 8970.90982961866 |
| 102 | 215340 | 188185.254695678 | 27154.7453043222 |
| 103 | 218319 | 207426.658300345 | 10892.3416996553 |
| 104 | 195724 | 201283.540272683 | -5559.54027268276 |
| 105 | 174614 | 166956.576527847 | 7657.423472153 |
| 106 | 172085 | 164724.732879779 | 7360.26712022059 |
| 107 | 152347 | 148366.386675142 | 3980.61332485836 |
| 108 | 189615 | 186392.325947431 | 3222.67405256864 |
| 109 | 173804 | 165365.600180675 | 8438.39981932471 |
| 110 | 145683 | 141858.696406207 | 3824.30359379344 |
| 111 | 133550 | 134032.668039587 | -482.668039586615 |
| 112 | 121156 | 123122.596478158 | -1966.59647815834 |
| 113 | 112040 | 109601.946433787 | 2438.05356621251 |
| 114 | 120767 | 128990.8956592 | -8223.89565919975 |
| 115 | 127019 | 116316.526850406 | 10702.4731495935 |
| 116 | 136295 | 139682.580235073 | -3387.58023507308 |
| 117 | 113425 | 118244.442397444 | -4819.44239744417 |
| 118 | 107815 | 119221.176684486 | -11406.1766844858 |
| 119 | 100298 | 110761.549833771 | -10463.5498337714 |
| 120 | 97048 | 80614.2507550354 | 16433.7492449646 |
| 121 | 98750 | 99751.7602932835 | -1001.76029328348 |
| 122 | 98235 | 121390.161926378 | -23155.1619263779 |
| 123 | 101254 | 112919.499788694 | -11665.4997886939 |
| 124 | 139589 | 152655.266632129 | -13066.2666321287 |
| 125 | 134921 | 125932.319255405 | 8988.68074459526 |
| 126 | 80355 | 61104.0048312421 | 19250.9951687579 |
| 127 | 80396 | 73616.5762248748 | 6779.42377512523 |
| 128 | 82183 | 79911.478992407 | 2271.52100759298 |
| 129 | 79709 | 71910.2293399717 | 7798.77066002829 |
| 130 | 90781 | 93404.2614473332 | -2623.26144733324 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 21 | 0.209430815103728 | 0.418861630207455 | 0.790569184896272 |
| 22 | 0.261774521587883 | 0.523549043175766 | 0.738225478412117 |
| 23 | 0.157739632576147 | 0.315479265152294 | 0.842260367423853 |
| 24 | 0.53182908037825 | 0.936341839243501 | 0.46817091962175 |
| 25 | 0.427488877048039 | 0.854977754096077 | 0.572511122951961 |
| 26 | 0.319576946358566 | 0.639153892717131 | 0.680423053641434 |
| 27 | 0.241817886380484 | 0.483635772760967 | 0.758182113619516 |
| 28 | 0.181905098490818 | 0.363810196981637 | 0.818094901509182 |
| 29 | 0.130030411985119 | 0.260060823970237 | 0.869969588014881 |
| 30 | 0.0942482105660625 | 0.188496421132125 | 0.905751789433938 |
| 31 | 0.0615378925377014 | 0.123075785075403 | 0.938462107462299 |
| 32 | 0.0481332581154367 | 0.0962665162308734 | 0.951866741884563 |
| 33 | 0.0379608548374735 | 0.0759217096749471 | 0.962039145162526 |
| 34 | 0.0322776525314527 | 0.0645553050629055 | 0.967722347468547 |
| 35 | 0.0402010250382717 | 0.0804020500765433 | 0.959798974961728 |
| 36 | 0.0289869178560667 | 0.0579738357121334 | 0.971013082143933 |
| 37 | 0.108897507769004 | 0.217795015538008 | 0.891102492230996 |
| 38 | 0.10508463145922 | 0.21016926291844 | 0.89491536854078 |
| 39 | 0.0863355312056636 | 0.172671062411327 | 0.913664468794336 |
| 40 | 0.0906834113603387 | 0.181366822720677 | 0.909316588639661 |
| 41 | 0.225855529441355 | 0.451711058882711 | 0.774144470558645 |
| 42 | 0.224955913028814 | 0.449911826057627 | 0.775044086971187 |
| 43 | 0.245515964270913 | 0.491031928541826 | 0.754484035729087 |
| 44 | 0.330060329109349 | 0.660120658218699 | 0.669939670890651 |
| 45 | 0.283589310958455 | 0.56717862191691 | 0.716410689041545 |
| 46 | 0.235467599437815 | 0.47093519887563 | 0.764532400562185 |
| 47 | 0.2502495695264 | 0.500499139052801 | 0.7497504304736 |
| 48 | 0.203932576726303 | 0.407865153452606 | 0.796067423273697 |
| 49 | 0.166246755585511 | 0.332493511171022 | 0.833753244414489 |
| 50 | 0.144760468297024 | 0.289520936594049 | 0.855239531702976 |
| 51 | 0.203703807881186 | 0.407407615762371 | 0.796296192118814 |
| 52 | 0.283593879805733 | 0.567187759611465 | 0.716406120194267 |
| 53 | 0.279122724211975 | 0.558245448423949 | 0.720877275788025 |
| 54 | 0.24619435552485 | 0.4923887110497 | 0.75380564447515 |
| 55 | 0.208219665102878 | 0.416439330205756 | 0.791780334897122 |
| 56 | 0.188970261752467 | 0.377940523504933 | 0.811029738247533 |
| 57 | 0.160730162030044 | 0.321460324060088 | 0.839269837969956 |
| 58 | 0.172364903611615 | 0.34472980722323 | 0.827635096388385 |
| 59 | 0.181450715311397 | 0.362901430622794 | 0.818549284688603 |
| 60 | 0.182798958938621 | 0.365597917877242 | 0.817201041061379 |
| 61 | 0.156303941664537 | 0.312607883329075 | 0.843696058335463 |
| 62 | 0.151892379380073 | 0.303784758760146 | 0.848107620619927 |
| 63 | 0.120827122639671 | 0.241654245279341 | 0.879172877360329 |
| 64 | 0.113225819872095 | 0.22645163974419 | 0.886774180127905 |
| 65 | 0.115011640133115 | 0.23002328026623 | 0.884988359866885 |
| 66 | 0.0980927906019994 | 0.196185581203999 | 0.901907209398001 |
| 67 | 0.0847397760460696 | 0.169479552092139 | 0.91526022395393 |
| 68 | 0.0898008085279028 | 0.179601617055806 | 0.910199191472097 |
| 69 | 0.0975851504170878 | 0.195170300834176 | 0.902414849582912 |
| 70 | 0.100971923829086 | 0.201943847658171 | 0.899028076170915 |
| 71 | 0.137610434501274 | 0.275220869002548 | 0.862389565498726 |
| 72 | 0.128638527289996 | 0.257277054579991 | 0.871361472710005 |
| 73 | 0.1255007158579 | 0.251001431715799 | 0.8744992841421 |
| 74 | 0.3650000545737 | 0.7300001091474 | 0.6349999454263 |
| 75 | 0.347109291960103 | 0.694218583920205 | 0.652890708039897 |
| 76 | 0.324538044851019 | 0.649076089702037 | 0.675461955148981 |
| 77 | 0.302575115984475 | 0.605150231968951 | 0.697424884015525 |
| 78 | 0.385842581894647 | 0.771685163789295 | 0.614157418105353 |
| 79 | 0.350630307232831 | 0.701260614465661 | 0.649369692767169 |
| 80 | 0.324641620501465 | 0.649283241002931 | 0.675358379498535 |
| 81 | 0.323211436212257 | 0.646422872424513 | 0.676788563787743 |
| 82 | 0.324775645619336 | 0.649551291238671 | 0.675224354380664 |
| 83 | 0.334032779191314 | 0.668065558382628 | 0.665967220808686 |
| 84 | 0.380723397071182 | 0.761446794142365 | 0.619276602928818 |
| 85 | 0.443815418573585 | 0.88763083714717 | 0.556184581426415 |
| 86 | 0.383415792013235 | 0.766831584026469 | 0.616584207986765 |
| 87 | 0.359427083678567 | 0.718854167357134 | 0.640572916321433 |
| 88 | 0.351440369019948 | 0.702880738039896 | 0.648559630980052 |
| 89 | 0.635453054266142 | 0.729093891467715 | 0.364546945733858 |
| 90 | 0.592649754248082 | 0.814700491503836 | 0.407350245751918 |
| 91 | 0.595969193764561 | 0.808061612470878 | 0.404030806235439 |
| 92 | 0.595218346643655 | 0.80956330671269 | 0.404781653356345 |
| 93 | 0.524449396898712 | 0.951101206202577 | 0.475550603101288 |
| 94 | 0.503056521777342 | 0.993886956445317 | 0.496943478222658 |
| 95 | 0.532960353599306 | 0.934079292801388 | 0.467039646400694 |
| 96 | 0.466070528546187 | 0.932141057092373 | 0.533929471453813 |
| 97 | 0.546503994418878 | 0.906992011162244 | 0.453496005581122 |
| 98 | 0.506155457331572 | 0.987689085336856 | 0.493844542668428 |
| 99 | 0.552196507376857 | 0.895606985246286 | 0.447803492623143 |
| 100 | 0.497415126463507 | 0.994830252927014 | 0.502584873536493 |
| 101 | 0.513046794857288 | 0.973906410285424 | 0.486953205142712 |
| 102 | 0.493764518142473 | 0.987529036284945 | 0.506235481857527 |
| 103 | 0.728421303496943 | 0.543157393006115 | 0.271578696503057 |
| 104 | 0.632710536729423 | 0.734578926541154 | 0.367289463270577 |
| 105 | 0.63541243115823 | 0.729175137683541 | 0.36458756884177 |
| 106 | 0.743163759321462 | 0.513672481357077 | 0.256836240678538 |
| 107 | 0.732556488931527 | 0.534887022136946 | 0.267443511068473 |
| 108 | 0.594783104768286 | 0.810433790463429 | 0.405216895231714 |
| 109 | 0.458853469646809 | 0.917706939293618 | 0.541146530353191 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 0 | 0 | OK |
| 5% type I error level | 0 | 0 | OK |
| 10% type I error level | 5 | 0.0561797752808989 | OK |
