| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 604335.544025157 + 52211.4327044027X[t] -10737.0504941598M1[t] -31415.9620245583M2[t] -45812.6252770291M3[t] -40860.6218628332M4[t] -36479.4517819706M5[t] -38801.9483677747M6[t] -45494.7782869121M7[t] -50086.4415393831M8[t] -59034.9381251872M9[t] -54820.2680443246M10[t] -10852.1700808625M11[t] -1504.17008086253t + 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) | 604335.544025157 | 13504.06558 | 44.7521 | 0 | 0 |
| X | 52211.4327044027 | 10825.367641 | 4.8231 | 1e-05 | 5e-06 |
| M1 | -10737.0504941598 | 14061.215256 | -0.7636 | 0.448152 | 0.224076 |
| M2 | -31415.9620245583 | 14623.044119 | -2.1484 | 0.035799 | 0.017899 |
| M3 | -45812.6252770291 | 14615.876218 | -3.1344 | 0.002682 | 0.001341 |
| M4 | -40860.6218628332 | 14610.815998 | -2.7966 | 0.006961 | 0.003481 |
| M5 | -36479.4517819706 | 14607.86565 | -2.4972 | 0.015326 | 0.007663 |
| M6 | -38801.9483677747 | 14607.026451 | -2.6564 | 0.010143 | 0.005071 |
| M7 | -45494.7782869121 | 14608.298766 | -3.1143 | 0.002844 | 0.001422 |
| M8 | -50086.4415393831 | 14611.682042 | -3.4278 | 0.001115 | 0.000557 |
| M9 | -59034.9381251872 | 14617.174815 | -4.0387 | 0.000157 | 7.9e-05 |
| M10 | -54820.2680443246 | 14624.774708 | -3.7485 | 0.000407 | 0.000204 |
| M11 | -10852.1700808625 | 14535.789514 | -0.7466 | 0.45828 | 0.22914 |
| t | -1504.17008086253 | 175.624874 | -8.5647 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.815618618735924 |
| R-squared | 0.665233731228697 |
| Adjusted R-squared | 0.591471672007901 |
| F-TEST (value) | 9.0186437072943 |
| F-TEST (DF numerator) | 13 |
| F-TEST (DF denominator) | 59 |
| p-value | 8.28744184389052e-10 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 25174.8882440813 |
| Sum Squared Residuals | 37392724888.0169 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 577992 | 592094.323450134 | -14102.3234501342 |
| 2 | 565464 | 569911.241838874 | -4447.24183887437 |
| 3 | 547344 | 554010.408505541 | -6666.40850554064 |
| 4 | 554788 | 557458.241838874 | -2670.24183887389 |
| 5 | 562325 | 560335.241838874 | 1989.75816112615 |
| 6 | 560854 | 556508.575172207 | 4345.42482779281 |
| 7 | 555332 | 548311.575172207 | 7020.42482779284 |
| 8 | 543599 | 542215.741838874 | 1383.25816112601 |
| 9 | 536662 | 531763.075172207 | 4898.92482779258 |
| 10 | 542722 | 534473.575172207 | 8248.42482779282 |
| 11 | 593530 | 629148.93575921 | -35618.9357592094 |
| 12 | 610763 | 638496.935759209 | -27733.9357592094 |
| 13 | 612613 | 626255.715184187 | -13642.7151841870 |
| 14 | 611324 | 604072.633572926 | 7251.3664270741 |
| 15 | 594167 | 588171.800239593 | 5995.19976040731 |
| 16 | 595454 | 591619.633572926 | 3834.36642707397 |
| 17 | 590865 | 594496.633572926 | -3631.63357292605 |
| 18 | 589379 | 590669.96690626 | -1290.96690625937 |
| 19 | 584428 | 582472.966906259 | 1955.03309374061 |
| 20 | 573100 | 576377.133572926 | -3277.13357292601 |
| 21 | 567456 | 565924.466906259 | 1531.53309374067 |
| 22 | 569028 | 568634.966906259 | 393.03309374062 |
| 23 | 620735 | 611098.894788859 | 9636.10521114107 |
| 24 | 628884 | 620446.894788859 | 8437.1052111411 |
| 25 | 628232 | 608205.674213837 | 20026.3257861634 |
| 26 | 612117 | 586022.592602576 | 26094.4073974245 |
| 27 | 595404 | 570121.759269242 | 25282.2407307577 |
| 28 | 597141 | 573569.592602576 | 23571.4073974244 |
| 29 | 593408 | 576446.592602576 | 16961.4073974244 |
| 30 | 590072 | 572619.925935909 | 17452.0740640910 |
| 31 | 579799 | 564422.925935909 | 15376.0740640910 |
| 32 | 574205 | 558327.092602576 | 15877.9073974244 |
| 33 | 572775 | 547874.425935909 | 24900.5740640911 |
| 34 | 572942 | 550584.925935909 | 22357.0740640910 |
| 35 | 619567 | 593048.853818509 | 26518.1461814915 |
| 36 | 625809 | 602396.853818509 | 23412.1461814915 |
| 37 | 619916 | 590155.633243486 | 29760.3667565138 |
| 38 | 587625 | 567972.551632225 | 19652.4483677749 |
| 39 | 565742 | 552071.718298892 | 13670.2817011081 |
| 40 | 557274 | 555519.551632225 | 1754.44836777478 |
| 41 | 560576 | 558396.551632225 | 2179.44836777476 |
| 42 | 548854 | 554569.884965559 | -5715.88496555857 |
| 43 | 531673 | 546372.884965559 | -14699.8849655586 |
| 44 | 525919 | 540277.051632225 | -14358.0516322252 |
| 45 | 511038 | 529824.384965559 | -18786.3849655585 |
| 46 | 498662 | 532534.884965559 | -33872.8849655586 |
| 47 | 555362 | 574998.812848158 | -19636.8128481581 |
| 48 | 564591 | 584346.812848158 | -19755.8128481581 |
| 49 | 541657 | 572105.592273136 | -30448.5922731358 |
| 50 | 527070 | 549922.510661875 | -22852.5106618747 |
| 51 | 509846 | 534021.677328541 | -24175.6773285415 |
| 52 | 514258 | 537469.510661875 | -23211.5106618748 |
| 53 | 516922 | 540346.510661875 | -23424.5106618748 |
| 54 | 507561 | 536519.843995208 | -28958.8439952082 |
| 55 | 492622 | 528322.843995208 | -35700.8439952082 |
| 56 | 490243 | 522227.010661875 | -31984.0106618748 |
| 57 | 469357 | 511774.343995208 | -42417.3439952081 |
| 58 | 477580 | 514484.843995208 | -36904.8439952081 |
| 59 | 528379 | 556948.771877808 | -28569.7718778077 |
| 60 | 533590 | 566296.771877808 | -32706.7718778077 |
| 61 | 517945 | 554055.551302785 | -36110.5513027854 |
| 62 | 506174 | 531872.469691524 | -25698.4696915243 |
| 63 | 501866 | 515971.636358191 | -14105.6363581911 |
| 64 | 516141 | 519419.469691524 | -3278.46969152441 |
| 65 | 528222 | 522296.469691524 | 5925.53030847558 |
| 66 | 532638 | 518469.803024858 | 14168.1969751422 |
| 67 | 536322 | 510272.803024858 | 26049.1969751422 |
| 68 | 536535 | 504176.969691524 | 32358.0303084756 |
| 69 | 523597 | 493724.303024858 | 29872.6969751423 |
| 70 | 536214 | 496434.803024858 | 39779.1969751423 |
| 71 | 586570 | 538898.730907457 | 47671.2690925427 |
| 72 | 596594 | 548246.730907457 | 48347.2690925427 |
| 73 | 580523 | 536005.510332435 | 44517.4896675651 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 17 | 0.0149479736485723 | 0.0298959472971445 | 0.985052026351428 |
| 18 | 0.00513693621613692 | 0.0102738724322738 | 0.994863063783863 |
| 19 | 0.00144391983866729 | 0.00288783967733458 | 0.998556080161333 |
| 20 | 0.000358412204707317 | 0.000716824409414634 | 0.999641587795293 |
| 21 | 7.46764115827677e-05 | 0.000149352823165535 | 0.999925323588417 |
| 22 | 2.16714531832214e-05 | 4.33429063664427e-05 | 0.999978328546817 |
| 23 | 3.69890578344136e-06 | 7.39781156688272e-06 | 0.999996301094217 |
| 24 | 8.56005445744122e-07 | 1.71201089148824e-06 | 0.999999143994554 |
| 25 | 1.89173715788026e-07 | 3.78347431576052e-07 | 0.999999810826284 |
| 26 | 1.33817885533315e-07 | 2.67635771066629e-07 | 0.999999866182114 |
| 27 | 4.48930169661696e-08 | 8.97860339323393e-08 | 0.999999955106983 |
| 28 | 1.73324390767128e-08 | 3.46648781534256e-08 | 0.99999998266756 |
| 29 | 1.13972219659738e-08 | 2.27944439319477e-08 | 0.999999988602778 |
| 30 | 7.25307987218253e-09 | 1.45061597443651e-08 | 0.99999999274692 |
| 31 | 8.11454723278488e-09 | 1.62290944655698e-08 | 0.999999991885453 |
| 32 | 2.75193190855175e-09 | 5.5038638171035e-09 | 0.999999997248068 |
| 33 | 8.62349769750184e-10 | 1.72469953950037e-09 | 0.99999999913765 |
| 34 | 3.45208927578017e-10 | 6.90417855156033e-10 | 0.999999999654791 |
| 35 | 1.17657425013385e-10 | 2.35314850026770e-10 | 0.999999999882343 |
| 36 | 4.65328715685841e-11 | 9.30657431371681e-11 | 0.999999999953467 |
| 37 | 5.77777599073358e-11 | 1.15555519814672e-10 | 0.999999999942222 |
| 38 | 9.47722661646543e-09 | 1.89544532329309e-08 | 0.999999990522773 |
| 39 | 4.06517749705112e-07 | 8.13035499410224e-07 | 0.99999959348225 |
| 40 | 1.72359442126052e-05 | 3.44718884252103e-05 | 0.999982764055787 |
| 41 | 0.000112283535831738 | 0.000224567071663476 | 0.999887716464168 |
| 42 | 0.000826027031570898 | 0.00165205406314180 | 0.99917397296843 |
| 43 | 0.00481973740923462 | 0.00963947481846924 | 0.995180262590765 |
| 44 | 0.0112779463897377 | 0.0225558927794755 | 0.988722053610262 |
| 45 | 0.0367445059560468 | 0.0734890119120937 | 0.963255494043953 |
| 46 | 0.082992583990747 | 0.165985167981494 | 0.917007416009253 |
| 47 | 0.093831908348193 | 0.187663816696386 | 0.906168091651807 |
| 48 | 0.126116743485449 | 0.252233486970897 | 0.873883256514551 |
| 49 | 0.207198727543939 | 0.414397455087877 | 0.792801272456061 |
| 50 | 0.430222459594451 | 0.860444919188902 | 0.569777540405549 |
| 51 | 0.649163189754325 | 0.70167362049135 | 0.350836810245675 |
| 52 | 0.829882268627089 | 0.340235462745823 | 0.170117731372911 |
| 53 | 0.952393829075837 | 0.0952123418483266 | 0.0476061709241633 |
| 54 | 0.99257685773841 | 0.0148462845231808 | 0.00742314226159041 |
| 55 | 0.991986515362186 | 0.0160269692756283 | 0.00801348463781416 |
| 56 | 0.995123825288179 | 0.00975234942364287 | 0.00487617471182143 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 26 | 0.65 | NOK |
| 5% type I error level | 31 | 0.775 | NOK |
| 10% type I error level | 33 | 0.825 | NOK |
