| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = -96.5555117821981 -360.738224795812X[t] + 1.00748531201206Y1[t] + 0.166310440331208Y2[t] -0.188431146174605Y3[t] + 100.779769951900M1[t] + 36.3284441219571M2[t] -83.1206506007616M3[t] + 92.1137994899325M4[t] + 216.725669303820M5[t] + 77.7633337740983M6[t] + 90.034499607901M7[t] + 29.6711390219347M8[t] + 179.016831664903M9[t] + 107.290835612820M10[t] -19.5422145209566M11[t] + 3.32000008834032t + 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) | -96.5555117821981 | 127.205611 | -0.7591 | 0.449874 | 0.224937 |
| X | -360.738224795812 | 107.986594 | -3.3406 | 0.001233 | 0.000617 |
| Y1 | 1.00748531201206 | 0.104613 | 9.6306 | 0 | 0 |
| Y2 | 0.166310440331208 | 0.149316 | 1.1138 | 0.268425 | 0.134213 |
| Y3 | -0.188431146174605 | 0.106365 | -1.7716 | 0.079971 | 0.039985 |
| M1 | 100.779769951900 | 126.637313 | 0.7958 | 0.428306 | 0.214153 |
| M2 | 36.3284441219571 | 126.703162 | 0.2867 | 0.775008 | 0.387504 |
| M3 | -83.1206506007616 | 126.351095 | -0.6579 | 0.512368 | 0.256184 |
| M4 | 92.1137994899325 | 127.515034 | 0.7224 | 0.472001 | 0.236 |
| M5 | 216.725669303820 | 128.414482 | 1.6877 | 0.09505 | 0.047525 |
| M6 | 77.7633337740983 | 127.448163 | 0.6102 | 0.543349 | 0.271674 |
| M7 | 90.034499607901 | 126.673135 | 0.7108 | 0.479133 | 0.239566 |
| M8 | 29.6711390219347 | 126.795652 | 0.234 | 0.815529 | 0.407764 |
| M9 | 179.016831664903 | 130.306957 | 1.3738 | 0.173031 | 0.086515 |
| M10 | 107.290835612820 | 131.790432 | 0.8141 | 0.417809 | 0.208905 |
| M11 | -19.5422145209566 | 130.385552 | -0.1499 | 0.881206 | 0.440603 |
| t | 3.32000008834032 | 1.515248 | 2.1911 | 0.03112 | 0.01556 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.991885608386146 |
| R-squared | 0.983837060123556 |
| Adjusted R-squared | 0.980864565433635 |
| F-TEST (value) | 330.980258252291 |
| F-TEST (DF numerator) | 16 |
| F-TEST (DF denominator) | 87 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 259.673901397968 |
| Sum Squared Residuals | 5866456.55085003 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 5246.24 | 5106.26368621096 | 139.976313789040 |
| 2 | 5283.61 | 5164.66253796491 | 118.947462035086 |
| 3 | 4979.05 | 5051.74180723946 | -72.6918072394601 |
| 4 | 4825.2 | 4915.32252016608 | -90.122520166081 |
| 5 | 4695.12 | 4830.55959517543 | -135.439595175435 |
| 6 | 4711.54 | 4595.66529898151 | 115.874701018495 |
| 7 | 4727.22 | 4635.15584348757 | 92.0641565124338 |
| 8 | 4384.96 | 4621.15179360692 | -236.191793606921 |
| 9 | 4378.75 | 4428.50927173319 | -49.7592717331867 |
| 10 | 4472.93 | 4293.97078030207 | 178.959219697929 |
| 11 | 4564.07 | 4328.80235319720 | 235.267646802804 |
| 12 | 4310.54 | 4460.32005383141 | -149.780053831408 |
| 13 | 4171.38 | 4306.40316090229 | -135.023160902292 |
| 14 | 4049.38 | 4045.73187854157 | 3.64812145843335 |
| 15 | 3591.37 | 3831.31876345487 | -239.948763454874 |
| 16 | 3720.46 | 3554.36707046051 | 166.092929539488 |
| 17 | 4107.23 | 3759.17197434758 | 348.058025652417 |
| 18 | 4101.71 | 4120.96709703489 | -19.2570970348935 |
| 19 | 4162.34 | 4170.99625638195 | -8.6562563819518 |
| 20 | 4136.22 | 4101.23918231504 | 34.9808176849629 |
| 21 | 4125.88 | 4238.71290062076 | -112.832900620756 |
| 22 | 4031.48 | 4144.12089743679 | -112.640897436791 |
| 23 | 3761.36 | 3928.70340552247 | -167.343405522471 |
| 24 | 3408.56 | 3665.67236013525 | -257.112360135249 |
| 25 | 3228.47 | 3387.19543615425 | -158.725436154250 |
| 26 | 3090.45 | 3136.85077842823 | -46.4007784282287 |
| 27 | 2741.14 | 2918.1962222011 | -177.056222201099 |
| 28 | 2980.44 | 2755.80637618127 | 224.633623818730 |
| 29 | 3104.33 | 3092.74284813091 | 11.5871518690903 |
| 30 | 3181.57 | 3187.53684003621 | -5.96684003621169 |
| 31 | 2863.86 | 3256.45879863122 | -392.598798631217 |
| 32 | 2898.01 | 2868.82836336585 | 29.1816366341508 |
| 33 | 3112.33 | 2988.50676777422 | 123.823232225784 |
| 34 | 3254.33 | 3201.57098486934 | 52.7590151306578 |
| 35 | 3513.47 | 3250.32957905954 | 263.140420940459 |
| 36 | 3587.61 | 3517.50305670253 | 70.1069432974656 |
| 37 | 3727.45 | 3712.63825252599 | 14.8117474740144 |
| 38 | 3793.34 | 3755.89388164262 | 37.4461183573824 |
| 39 | 3817.58 | 3715.43456101525 | 102.145438984755 |
| 40 | 3845.13 | 3903.01843858982 | -57.8884385898188 |
| 41 | 3931.86 | 4050.32216569016 | -118.462165690162 |
| 42 | 4197.52 | 4002.07331300744 | 195.44668699256 |
| 43 | 4307.13 | 4294.54585333152 | 12.5841466684760 |
| 44 | 4229.43 | 4375.77235615421 | -146.342356154205 |
| 45 | 4362.28 | 4418.32710921413 | -56.0471092141354 |
| 46 | 4217.34 | 4450.18927780526 | -232.849277805261 |
| 47 | 4361.28 | 4217.38674869256 | 143.893251307436 |
| 48 | 4327.74 | 4336.12828612198 | -8.38828612197622 |
| 49 | 4417.65 | 4457.68693390515 | -40.0369339051536 |
| 50 | 4557.68 | 4454.43778121747 | 103.242218782527 |
| 51 | 4650.35 | 4500.65980715702 | 149.690192842980 |
| 52 | 4967.18 | 4778.92452780723 | 188.255472192767 |
| 53 | 5123.42 | 5215.08394422091 | -91.6639442209063 |
| 54 | 5290.85 | 5272.08133642243 | 18.7686635775745 |
| 55 | 5535.66 | 5422.6394712896 | 113.020528710403 |
| 56 | 5514.06 | 5610.64346477198 | -96.5834647719775 |
| 57 | 5493.88 | 5750.7129068573 | -256.832906857296 |
| 58 | 5694.83 | 5612.25372289099 | 82.5762771090105 |
| 59 | 5850.41 | 5691.90881436587 | 158.501185634134 |
| 60 | 6116.64 | 5908.73821733236 | 207.901782667641 |
| 61 | 6175 | 6269.07014147252 | -94.070141472515 |
| 62 | 6513.58 | 6281.69636934747 | 231.883630652532 |
| 63 | 6383.78 | 6466.2215049058 | -82.4415049057986 |
| 64 | 6673.66 | 6559.31690878226 | 114.343091217743 |
| 65 | 6936.61 | 6893.91250830375 | 42.6974916962457 |
| 66 | 7300.68 | 7095.85686887262 | 204.823131127381 |
| 67 | 7392.93 | 7467.35212197099 | -74.4221219709918 |
| 68 | 7497.31 | 7514.24995363125 | -16.9399536312489 |
| 69 | 7584.71 | 7718.81697396314 | -134.106973963144 |
| 70 | 7160.79 | 7738.44190479642 | -577.651904796418 |
| 71 | 7196.19 | 7182.70277073007 | 13.4872292699298 |
| 72 | 7245.63 | 7154.25876134373 | 91.3712386562724 |
| 73 | 7347.51 | 7393.93572628391 | -46.4257262839081 |
| 74 | 7425.75 | 7436.99892972549 | -11.2489297254887 |
| 75 | 7778.51 | 7407.323157697 | 371.186842302995 |
| 76 | 7822.33 | 7935.09289022066 | -112.762890220661 |
| 77 | 8181.22 | 8151.09758454979 | 30.1224154502077 |
| 78 | 8371.47 | 8317.84840510718 | 53.6215948928178 |
| 79 | 8347.71 | 8576.54375274472 | -228.833752744716 |
| 80 | 8672.11 | 8459.57704845609 | 212.532951543911 |
| 81 | 8802.79 | 8899.27041478213 | -96.480414782126 |
| 82 | 9138.46 | 9020.95083026867 | 117.509169731327 |
| 83 | 9123.29 | 9196.22675942976 | -72.9367594297645 |
| 84 | 9023.21 | 8874.26844038391 | 148.941559616092 |
| 85 | 8850.41 | 8811.76546818173 | 38.6445318182745 |
| 86 | 8864.58 | 8562.75483214356 | 301.825167856441 |
| 87 | 9163.74 | 8451.02154940031 | 712.718450599686 |
| 88 | 8516.66 | 8965.89282651934 | -449.232826519343 |
| 89 | 8553.44 | 8488.984462713 | 64.4555372870072 |
| 90 | 7555.2 | 8226.4102156283 | -671.210215628304 |
| 91 | 7851.22 | 7364.33616774957 | 486.883832250433 |
| 92 | 7442 | 7432.58037780123 | 9.41962219877333 |
| 93 | 7992.53 | 7410.29365505514 | 582.23634494486 |
| 94 | 8264.04 | 7772.70160163046 | 491.338398369546 |
| 95 | 7517.39 | 8091.39956900253 | -574.009569002527 |
| 96 | 7200.4 | 7303.44082414884 | -103.040824148837 |
| 97 | 7193.69 | 6912.84119436321 | 280.848805636791 |
| 98 | 6193.58 | 6932.92301098868 | -739.343010988684 |
| 99 | 5104.21 | 5867.81262692919 | -763.602626929185 |
| 100 | 4800.46 | 4783.77844127283 | 16.6815587271750 |
| 101 | 4461.61 | 4612.96491686846 | -151.354916868464 |
| 102 | 4398.59 | 4290.69062490942 | 107.899375090581 |
| 103 | 4243.63 | 4243.67173441287 | -0.0417344128685802 |
| 104 | 4293.82 | 4083.87745989745 | 209.942540102554 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 20 | 0.456487764262263 | 0.912975528524526 | 0.543512235737737 |
| 21 | 0.291422352996407 | 0.582844705992813 | 0.708577647003593 |
| 22 | 0.173320969549334 | 0.346641939098668 | 0.826679030450666 |
| 23 | 0.108075796079291 | 0.216151592158581 | 0.89192420392071 |
| 24 | 0.062561502999662 | 0.125123005999324 | 0.937438497000338 |
| 25 | 0.0322309247106332 | 0.0644618494212664 | 0.967769075289367 |
| 26 | 0.0180759101960211 | 0.0361518203920423 | 0.981924089803979 |
| 27 | 0.00925854958576818 | 0.0185170991715364 | 0.990741450414232 |
| 28 | 0.00479142564165589 | 0.00958285128331178 | 0.995208574358344 |
| 29 | 0.00336221513360233 | 0.00672443026720465 | 0.996637784866398 |
| 30 | 0.00145167290838317 | 0.00290334581676635 | 0.998548327091617 |
| 31 | 0.00485068889305774 | 0.00970137778611547 | 0.995149311106942 |
| 32 | 0.00377256391058799 | 0.00754512782117597 | 0.996227436089412 |
| 33 | 0.00236092720321594 | 0.00472185440643188 | 0.997639072796784 |
| 34 | 0.00115358364838279 | 0.00230716729676558 | 0.998846416351617 |
| 35 | 0.00183716695698327 | 0.00367433391396655 | 0.998162833043017 |
| 36 | 0.00266177200596548 | 0.00532354401193096 | 0.997338227994035 |
| 37 | 0.002027618142755 | 0.00405523628551 | 0.997972381857245 |
| 38 | 0.00112732987902023 | 0.00225465975804045 | 0.99887267012098 |
| 39 | 0.00138825950163486 | 0.00277651900326972 | 0.998611740498365 |
| 40 | 0.00103722274021454 | 0.00207444548042907 | 0.998962777259785 |
| 41 | 0.00053989846196685 | 0.0010797969239337 | 0.999460101538033 |
| 42 | 0.000516859112204057 | 0.00103371822440811 | 0.999483140887796 |
| 43 | 0.000268902482567204 | 0.000537804965134407 | 0.999731097517433 |
| 44 | 0.000153323276909460 | 0.000306646553818921 | 0.99984667672309 |
| 45 | 7.55477790420018e-05 | 0.000151095558084004 | 0.999924452220958 |
| 46 | 6.92759054298304e-05 | 0.000138551810859661 | 0.99993072409457 |
| 47 | 4.54979766963736e-05 | 9.09959533927471e-05 | 0.999954502023304 |
| 48 | 2.36515345451589e-05 | 4.73030690903178e-05 | 0.999976348465455 |
| 49 | 1.14716920525279e-05 | 2.29433841050558e-05 | 0.999988528307947 |
| 50 | 5.48205944314602e-06 | 1.09641188862920e-05 | 0.999994517940557 |
| 51 | 4.31587220125221e-06 | 8.63174440250441e-06 | 0.9999956841278 |
| 52 | 2.14771625802605e-06 | 4.29543251605209e-06 | 0.999997852283742 |
| 53 | 1.10077700015232e-06 | 2.20155400030465e-06 | 0.999998899223 |
| 54 | 4.50160445991516e-07 | 9.00320891983031e-07 | 0.999999549839554 |
| 55 | 2.5823181397344e-07 | 5.1646362794688e-07 | 0.999999741768186 |
| 56 | 1.37922311723677e-07 | 2.75844623447354e-07 | 0.999999862077688 |
| 57 | 1.54505632811504e-07 | 3.09011265623009e-07 | 0.999999845494367 |
| 58 | 9.16343385747625e-08 | 1.83268677149525e-07 | 0.999999908365661 |
| 59 | 3.97702632624459e-08 | 7.95405265248919e-08 | 0.999999960229737 |
| 60 | 4.6070535911162e-08 | 9.2141071822324e-08 | 0.999999953929464 |
| 61 | 2.71130369707650e-08 | 5.42260739415299e-08 | 0.999999972886963 |
| 62 | 2.19039894187291e-08 | 4.38079788374581e-08 | 0.99999997809601 |
| 63 | 1.19248270250692e-08 | 2.38496540501385e-08 | 0.999999988075173 |
| 64 | 5.02990076142499e-09 | 1.00598015228500e-08 | 0.9999999949701 |
| 65 | 1.76251584175015e-09 | 3.52503168350029e-09 | 0.999999998237484 |
| 66 | 1.06802449132289e-09 | 2.13604898264578e-09 | 0.999999998931975 |
| 67 | 4.49446103846945e-10 | 8.9889220769389e-10 | 0.999999999550554 |
| 68 | 1.76704459993446e-10 | 3.53408919986893e-10 | 0.999999999823296 |
| 69 | 1.47227990370749e-10 | 2.94455980741498e-10 | 0.999999999852772 |
| 70 | 2.54015830053602e-07 | 5.08031660107205e-07 | 0.99999974598417 |
| 71 | 1.83538436984950e-07 | 3.67076873969901e-07 | 0.999999816461563 |
| 72 | 1.18684498997847e-07 | 2.37368997995694e-07 | 0.9999998813155 |
| 73 | 3.38572684866247e-07 | 6.77145369732495e-07 | 0.999999661427315 |
| 74 | 3.86943844592037e-07 | 7.73887689184075e-07 | 0.999999613056155 |
| 75 | 9.30987004694379e-07 | 1.86197400938876e-06 | 0.999999069012995 |
| 76 | 9.02001882648798e-07 | 1.80400376529760e-06 | 0.999999097998117 |
| 77 | 4.26422991027671e-07 | 8.52845982055343e-07 | 0.99999957357701 |
| 78 | 2.00195270349507e-07 | 4.00390540699014e-07 | 0.99999979980473 |
| 79 | 1.16391849366838e-07 | 2.32783698733677e-07 | 0.99999988360815 |
| 80 | 7.98080095064588e-08 | 1.59616019012918e-07 | 0.99999992019199 |
| 81 | 5.72677547212754e-08 | 1.14535509442551e-07 | 0.999999942732245 |
| 82 | 1.14939752107190e-07 | 2.29879504214381e-07 | 0.999999885060248 |
| 83 | 3.78977711450038e-08 | 7.57955422900076e-08 | 0.999999962102229 |
| 84 | 2.55721635218840e-08 | 5.11443270437679e-08 | 0.999999974427837 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 57 | 0.876923076923077 | NOK |
| 5% type I error level | 59 | 0.907692307692308 | NOK |
| 10% type I error level | 60 | 0.923076923076923 | NOK |
