| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 9377.3192435779 + 0.194844740786332X[t] + 319.219351869687M1[t] -694.785640883456M2[t] + 97.740582935755M3[t] -364.920329651367M4[t] -481.046525992848M5[t] -605.987816434113M6[t] + 16.6244363891546M7[t] -310.219838948932M8[t] -295.757655712276M9[t] + 171.852236023613M10[t] -400.19652387905M11[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) | 9377.3192435779 | 369.47296 | 25.3803 | 0 | 0 |
| X | 0.194844740786332 | 0.137895 | 1.413 | 0.162025 | 0.081013 |
| M1 | 319.219351869687 | 294.195856 | 1.0851 | 0.281567 | 0.140783 |
| M2 | -694.785640883456 | 270.021184 | -2.5731 | 0.01217 | 0.006085 |
| M3 | 97.740582935755 | 270.140174 | 0.3618 | 0.718565 | 0.359283 |
| M4 | -364.920329651367 | 299.130205 | -1.2199 | 0.226525 | 0.113263 |
| M5 | -481.046525992848 | 426.413834 | -1.1281 | 0.263066 | 0.131533 |
| M6 | -605.987816434113 | 496.380465 | -1.2208 | 0.226196 | 0.113098 |
| M7 | 16.6244363891546 | 501.802032 | 0.0331 | 0.973664 | 0.486832 |
| M8 | -310.219838948932 | 597.868895 | -0.5189 | 0.605461 | 0.30273 |
| M9 | -295.757655712276 | 490.654276 | -0.6028 | 0.548574 | 0.274287 |
| M10 | 171.852236023613 | 295.280072 | 0.582 | 0.562412 | 0.281206 |
| M11 | -400.19652387905 | 273.378164 | -1.4639 | 0.147637 | 0.073818 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.621383931711173 |
| R-squared | 0.386117990588836 |
| Adjusted R-squared | 0.282363284772864 |
| F-TEST (value) | 3.72145039159659 |
| F-TEST (DF numerator) | 12 |
| F-TEST (DF denominator) | 71 |
| p-value | 0.000227788697980236 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 504.227458280158 |
| Sum Squared Residuals | 18051418.4075405 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 9487 | 9924.31209742676 | -437.312097426764 |
| 2 | 8700 | 9102.22917434819 | -402.22917434819 |
| 3 | 9627 | 9913.2656485421 | -286.265648542104 |
| 4 | 8947 | 9535.9467324194 | -588.946732419396 |
| 5 | 9283 | 9745.60094267266 | -462.600942672662 |
| 6 | 8829 | 9819.98582205581 | -990.985822055815 |
| 7 | 9947 | 10262.7563791333 | -315.756379133297 |
| 8 | 9628 | 10313.7160561799 | -685.716056179909 |
| 9 | 9318 | 9977.0680165196 | -659.068016519594 |
| 10 | 9605 | 10138.3819757394 | -533.381975739369 |
| 11 | 8640 | 9344.79474556265 | -704.794745562646 |
| 12 | 9214 | 9780.6478570056 | -566.647857005595 |
| 13 | 9567 | 9959.7738402499 | -392.773840249909 |
| 14 | 8547 | 9114.69923775852 | -567.699237758516 |
| 15 | 9185 | 9954.5727335888 | -769.572733588806 |
| 16 | 9470 | 9602.38878902753 | -132.388789027535 |
| 17 | 9123 | 9828.40995750685 | -705.409957506853 |
| 18 | 9278 | 9740.68401255578 | -462.684012555777 |
| 19 | 10170 | 10291.5934007697 | -121.593400769674 |
| 20 | 9434 | 10284.6841898027 | -850.684189802746 |
| 21 | 9655 | 10018.5699463071 | -363.569946307083 |
| 22 | 9429 | 10164.2963262640 | -735.296326263951 |
| 23 | 8739 | 9349.27617460073 | -610.276174600732 |
| 24 | 9552 | 9811.43332604984 | -259.433326049836 |
| 25 | 9784 | 10007.1211122610 | -223.121112260987 |
| 26 | 9089 | 9163.21557821431 | -74.2155782143124 |
| 27 | 9763 | 9908.00484054087 | -145.004840540873 |
| 28 | 9330 | 9715.20389394282 | -385.203893942821 |
| 29 | 9144 | 9809.120328169 | -665.120328169006 |
| 30 | 9895 | 9738.15103092556 | 156.848969074445 |
| 31 | 10404 | 10518.1978343042 | -114.197834304179 |
| 32 | 10195 | 10134.8485841381 | 60.1514158619441 |
| 33 | 9987 | 10055.7852917973 | -68.7852917972726 |
| 34 | 9789 | 10178.1303028598 | -389.130302859781 |
| 35 | 9437 | 9365.448288086 | 71.5517119140023 |
| 36 | 10096 | 9823.12401049701 | 272.875989502984 |
| 37 | 9776 | 10004.3932858900 | -228.393285889979 |
| 38 | 9106 | 9093.85085049438 | 12.1491495056219 |
| 39 | 10258 | 9902.15949831728 | 355.840501682718 |
| 40 | 9766 | 9714.0348254981 | 51.9651745018972 |
| 41 | 9826 | 9805.22343335328 | 20.7765666467205 |
| 42 | 9957 | 9721.39438321793 | 235.605616782070 |
| 43 | 10036 | 10526.576158158 | -490.576158157991 |
| 44 | 10508 | 10156.0866608838 | 351.913339116234 |
| 45 | 10146 | 10120.2789009975 | 25.7210990024515 |
| 46 | 10166 | 10148.3190575195 | 17.6809424805280 |
| 47 | 9365 | 9367.20189075307 | -2.20189075307489 |
| 48 | 9968 | 9826.63121583117 | 141.368784168831 |
| 49 | 10123 | 9990.16961981258 | 132.830380187424 |
| 50 | 9144 | 9070.6643263408 | 73.3356736591955 |
| 51 | 10447 | 9959.63869684925 | 487.361303150749 |
| 52 | 9699 | 9692.40705927082 | 6.59294072918005 |
| 53 | 10451 | 9801.71622801913 | 649.283771980874 |
| 54 | 10192 | 9861.29290710252 | 330.707092897483 |
| 55 | 10404 | 10487.2175205192 | -83.2175205191521 |
| 56 | 10597 | 10194.8607643002 | 402.139235699754 |
| 57 | 10633 | 10290.3783597040 | 342.621640295983 |
| 58 | 10727 | 10136.2386835907 | 590.761316409281 |
| 59 | 9784 | 9353.36791415724 | 430.632085842755 |
| 60 | 9667 | 9873.97848784225 | -206.978487842248 |
| 61 | 10297 | 9989.58508559022 | 307.414914409783 |
| 62 | 9426 | 9089.75911093786 | 336.240889062135 |
| 63 | 10274 | 10001.5303161183 | 272.469683881688 |
| 64 | 9598 | 9585.04760709755 | 12.9523929024491 |
| 65 | 10400 | 9773.07405112353 | 626.925948876466 |
| 66 | 9985 | 9980.92757794533 | 4.07242205467463 |
| 67 | 10761 | 10643.8726921114 | 117.127307888637 |
| 68 | 11081 | 10169.3361032572 | 911.663896742763 |
| 69 | 10297 | 10243.6156219153 | 53.3843780847029 |
| 70 | 10751 | 10165.4653947087 | 585.534605291331 |
| 71 | 9760 | 9366.22766704914 | 393.772332950857 |
| 72 | 10133 | 9849.23320576238 | 283.766794237616 |
| 73 | 10806 | 9964.64495876957 | 841.355041230433 |
| 74 | 9734 | 9111.58172190593 | 622.418278094066 |
| 75 | 10083 | 9997.82826604337 | 85.1717339566282 |
| 76 | 10691 | 9655.97109274378 | 1035.02890725622 |
| 77 | 10446 | 9909.85505915554 | 536.14494084446 |
| 78 | 10517 | 9790.56426619708 | 726.435733802922 |
| 79 | 11353 | 10344.7860150043 | 1008.21398499566 |
| 80 | 10436 | 10625.4676414380 | -189.467641438041 |
| 81 | 10721 | 10051.3038627592 | 669.696137240813 |
| 82 | 10701 | 10237.1682593180 | 463.83174068196 |
| 83 | 9793 | 9371.68331979116 | 421.316680208839 |
| 84 | 10142 | 9806.95189701175 | 335.04810298825 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 16 | 0.224370961433045 | 0.448741922866091 | 0.775629038566955 |
| 17 | 0.144159698320091 | 0.288319396640182 | 0.85584030167991 |
| 18 | 0.123781286366600 | 0.247562572733200 | 0.8762187136334 |
| 19 | 0.0792444379636867 | 0.158488875927373 | 0.920755562036313 |
| 20 | 0.0615474457181716 | 0.123094891436343 | 0.938452554281828 |
| 21 | 0.0550326798015203 | 0.110065359603041 | 0.94496732019848 |
| 22 | 0.0434507295669407 | 0.0869014591338814 | 0.95654927043306 |
| 23 | 0.0322296084500884 | 0.0644592169001768 | 0.967770391549912 |
| 24 | 0.0285384206549975 | 0.0570768413099951 | 0.971461579345003 |
| 25 | 0.0215867810755321 | 0.0431735621510643 | 0.978413218924468 |
| 26 | 0.0244749734421714 | 0.0489499468843427 | 0.975525026557829 |
| 27 | 0.0291890036925535 | 0.058378007385107 | 0.970810996307446 |
| 28 | 0.0205365239358798 | 0.0410730478717596 | 0.97946347606412 |
| 29 | 0.0294409096483986 | 0.0588818192967971 | 0.970559090351601 |
| 30 | 0.153610025903611 | 0.307220051807223 | 0.846389974096389 |
| 31 | 0.120170000578354 | 0.240340001156708 | 0.879829999421646 |
| 32 | 0.237369902341412 | 0.474739804682824 | 0.762630097658588 |
| 33 | 0.287661852868500 | 0.575323705736999 | 0.7123381471315 |
| 34 | 0.34606487556097 | 0.69212975112194 | 0.65393512443903 |
| 35 | 0.457172564392254 | 0.914345128784508 | 0.542827435607746 |
| 36 | 0.523819401080113 | 0.952361197839774 | 0.476180598919887 |
| 37 | 0.533321919433508 | 0.933356161132985 | 0.466678080566492 |
| 38 | 0.51564397927494 | 0.96871204145012 | 0.48435602072506 |
| 39 | 0.590891998311507 | 0.818216003376987 | 0.409108001688493 |
| 40 | 0.580257711117693 | 0.839484577764613 | 0.419742288882307 |
| 41 | 0.68549325883416 | 0.629013482331681 | 0.314506741165841 |
| 42 | 0.732737038462757 | 0.534525923074486 | 0.267262961537243 |
| 43 | 0.80752468027829 | 0.384950639443422 | 0.192475319721711 |
| 44 | 0.852773941577609 | 0.294452116844783 | 0.147226058422392 |
| 45 | 0.875111110206413 | 0.249777779587173 | 0.124888889793587 |
| 46 | 0.9182999301688 | 0.163400139662399 | 0.0817000698311994 |
| 47 | 0.923080910165946 | 0.153838179668107 | 0.0769190898340536 |
| 48 | 0.898966473992785 | 0.202067052014429 | 0.101033526007215 |
| 49 | 0.904792781672414 | 0.190414436655172 | 0.095207218327586 |
| 50 | 0.910040141136665 | 0.179919717726671 | 0.0899598588633354 |
| 51 | 0.914681124672247 | 0.170637750655507 | 0.0853188753277533 |
| 52 | 0.906747760064105 | 0.186504479871790 | 0.0932522399358952 |
| 53 | 0.928964585188937 | 0.142070829622126 | 0.0710354148110631 |
| 54 | 0.91394726573387 | 0.172105468532262 | 0.0860527342661309 |
| 55 | 0.9441760811217 | 0.111647837756599 | 0.0558239188782993 |
| 56 | 0.950597591699709 | 0.0988048166005817 | 0.0494024083002909 |
| 57 | 0.94637069796032 | 0.107258604079360 | 0.0536293020396799 |
| 58 | 0.941928769172605 | 0.116142461654790 | 0.0580712308273949 |
| 59 | 0.921546306936948 | 0.156907386126105 | 0.0784536930630525 |
| 60 | 0.910894242894332 | 0.178211514211336 | 0.0891057571056679 |
| 61 | 0.90799417899126 | 0.184011642017481 | 0.0920058210087406 |
| 62 | 0.884776339821227 | 0.230447320357545 | 0.115223660178773 |
| 63 | 0.830560709651137 | 0.338878580697725 | 0.169439290348863 |
| 64 | 0.99959394890197 | 0.000812102196059899 | 0.000406051098029949 |
| 65 | 0.999768531648946 | 0.000462936702108012 | 0.000231468351054006 |
| 66 | 0.999778064677923 | 0.000443870644154239 | 0.000221935322077120 |
| 67 | 0.999323475529247 | 0.00135304894150632 | 0.000676524470753158 |
| 68 | 0.99759091401496 | 0.00481817197008008 | 0.00240908598504004 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 5 | 0.0943396226415094 | NOK |
| 5% type I error level | 8 | 0.150943396226415 | NOK |
| 10% type I error level | 14 | 0.264150943396226 | NOK |
