| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 59313.335440879 -345.279769827803X[t] + 0.213894954464884Y1[t] + 0.507550237696988Y2[t] -0.215173320358447Y3[t] + 0.325595448772870Y4[t] -11107.3359434972M1[t] -7270.12175937004M2[t] + 1809.7233257425M3[t] -456.589776813249M4[t] -11681.9631328455M5[t] -5738.79009446743M6[t] + 2125.90512822115M7[t] -236.514315406094M8[t] -11095.5021540931M9[t] -6801.7209454567M10[t] + 2587.76554077346M11[t] + 625.751505986009t + 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) | 59313.335440879 | 11944.30533 | 4.9658 | 4e-06 | 2e-06 |
| X | -345.279769827803 | 79.207601 | -4.3592 | 4.3e-05 | 2.1e-05 |
| Y1 | 0.213894954464884 | 0.159533 | 1.3408 | 0.184215 | 0.092108 |
| Y2 | 0.507550237696988 | 0.193956 | 2.6168 | 0.010808 | 0.005404 |
| Y3 | -0.215173320358447 | 0.188576 | -1.141 | 0.257633 | 0.128816 |
| Y4 | 0.325595448772870 | 0.166636 | 1.9539 | 0.054594 | 0.027297 |
| M1 | -11107.3359434972 | 2849.885156 | -3.8975 | 0.000216 | 0.000108 |
| M2 | -7270.12175937004 | 4646.259177 | -1.5647 | 0.122032 | 0.061016 |
| M3 | 1809.7233257425 | 3337.080962 | 0.5423 | 0.589281 | 0.294641 |
| M4 | -456.589776813249 | 1158.548292 | -0.3941 | 0.694668 | 0.347334 |
| M5 | -11681.9631328455 | 2756.939703 | -4.2373 | 6.6e-05 | 3.3e-05 |
| M6 | -5738.79009446743 | 4554.875333 | -1.2599 | 0.211766 | 0.105883 |
| M7 | 2125.90512822115 | 3348.765179 | 0.6348 | 0.52755 | 0.263775 |
| M8 | -236.514315406094 | 1191.153196 | -0.1986 | 0.843167 | 0.421584 |
| M9 | -11095.5021540931 | 2810.4122 | -3.948 | 0.000182 | 9.1e-05 |
| M10 | -6801.7209454567 | 4565.700972 | -1.4897 | 0.14066 | 0.07033 |
| M11 | 2587.76554077346 | 3264.589379 | 0.7927 | 0.43057 | 0.215285 |
| t | 625.751505986009 | 129.810358 | 4.8205 | 8e-06 | 4e-06 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.997952047794552 |
| R-squared | 0.99590828969734 |
| Adjusted R-squared | 0.994942191431434 |
| F-TEST (value) | 1030.85609905699 |
| F-TEST (DF numerator) | 17 |
| F-TEST (DF denominator) | 72 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 2217.37818625887 |
| Sum Squared Residuals | 354007153.504561 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 106370 | 110789.223748055 | -4419.22374805503 |
| 2 | 109375 | 113991.610659245 | -4616.6106592452 |
| 3 | 116476 | 116523.958824619 | -47.9588246193766 |
| 4 | 123297 | 123410.771366961 | -113.771366960822 |
| 5 | 114813 | 111543.651365237 | 3269.34863476347 |
| 6 | 117925 | 118347.160438379 | -422.160438379289 |
| 7 | 126466 | 123523.628457557 | 2942.37154244318 |
| 8 | 131235 | 128480.135178093 | 2754.86482190718 |
| 9 | 120546 | 119548.475717370 | 997.524282629702 |
| 10 | 123791 | 122672.754791245 | 1118.24520875481 |
| 11 | 129813 | 129331.818836326 | 481.181163674124 |
| 12 | 133463 | 133363.489584558 | 99.5104154420338 |
| 13 | 122987 | 121815.47456912 | 1171.52543087991 |
| 14 | 125418 | 123717.451868887 | 1700.54813111313 |
| 15 | 130199 | 129076.196460739 | 1122.80353926059 |
| 16 | 133016 | 132444.140821748 | 571.85917825189 |
| 17 | 121454 | 120697.938642843 | 756.061357156643 |
| 18 | 122044 | 125019.574279092 | -2975.57427909211 |
| 19 | 128313 | 128511.283917885 | -198.283917885046 |
| 20 | 131556 | 131371.150698427 | 184.849301573219 |
| 21 | 120027 | 120880.225466575 | -853.225466574991 |
| 22 | 123001 | 122821.617108971 | 179.382891028670 |
| 23 | 130111 | 128999.310772775 | 1111.68922722507 |
| 24 | 132524 | 133397.01566003 | -873.015660029913 |
| 25 | 123742 | 122957.278346865 | 784.721653135353 |
| 26 | 124931 | 125445.360333711 | -514.360333710849 |
| 27 | 133646 | 132605.630349032 | 1040.36965096777 |
| 28 | 136557 | 135935.314545609 | 621.685454391414 |
| 29 | 127509 | 127197.364966544 | 311.635033456173 |
| 30 | 128945 | 130957.144781943 | -2012.14478194311 |
| 31 | 137191 | 137339.096938056 | -148.096938056247 |
| 32 | 139716 | 140678.993697401 | -962.99369740135 |
| 33 | 129083 | 131467.261175466 | -2384.26117546578 |
| 34 | 131604 | 133154.993675675 | -1550.99367567498 |
| 35 | 139413 | 140316.11469941 | -903.114699409919 |
| 36 | 143125 | 144344.95098283 | -1219.95098283015 |
| 37 | 133948 | 134340.072259181 | -392.072259180559 |
| 38 | 137116 | 137208.656539505 | -92.656539505202 |
| 39 | 144864 | 144574.351378352 | 289.648621648318 |
| 40 | 149277 | 149071.471115929 | 205.528884070750 |
| 41 | 138796 | 139367.856636484 | -571.856636483645 |
| 42 | 143258 | 144608.531317978 | -1350.53131797765 |
| 43 | 150034 | 149788.977311781 | 245.022688218931 |
| 44 | 154708 | 155009.571331533 | -301.571331533269 |
| 45 | 144888 | 144669.931287694 | 218.068712305775 |
| 46 | 148762 | 148820.258524659 | -58.2585246594785 |
| 47 | 156500 | 155707.857012904 | 792.142987096144 |
| 48 | 161088 | 160760.351051209 | 327.648948791323 |
| 49 | 152772 | 151398.307492943 | 1373.69250705708 |
| 50 | 158011 | 155386.005262202 | 2624.99473779769 |
| 51 | 163318 | 163489.124154871 | -171.12415487135 |
| 52 | 169969 | 168511.636304219 | 1457.36369578133 |
| 53 | 162269 | 157951.558291544 | 4317.44170845621 |
| 54 | 165765 | 165742.710775963 | 22.2892240365053 |
| 55 | 170600 | 171266.030797166 | -666.030797165741 |
| 56 | 174681 | 175780.502745089 | -1099.50274508871 |
| 57 | 166364 | 165683.902191265 | 680.097808734801 |
| 58 | 170240 | 170268.614257983 | -28.6142579830335 |
| 59 | 176150 | 177553.217464230 | -1403.21746423047 |
| 60 | 182056 | 182009.994817473 | 46.0051825271638 |
| 61 | 172218 | 172214.778771684 | 3.22122831564263 |
| 62 | 177856 | 176836.283723097 | 1019.71627690272 |
| 63 | 182253 | 183200.82843932 | -947.828439319855 |
| 64 | 188090 | 188849.725412082 | -759.725412082309 |
| 65 | 176863 | 176968.671831365 | -105.671831365079 |
| 66 | 183273 | 184263.270993316 | -990.270993316145 |
| 67 | 187969 | 188429.554493895 | -460.554493894696 |
| 68 | 194650 | 194887.178041399 | -237.178041399191 |
| 69 | 183036 | 183120.956935987 | -84.956935987502 |
| 70 | 189516 | 189160.670277170 | 355.329722830374 |
| 71 | 193805 | 194378.874641017 | -573.874641017446 |
| 72 | 200499 | 200676.004156411 | -177.004156410861 |
| 73 | 188142 | 188454.686970685 | -312.686970685221 |
| 74 | 193732 | 194099.458643029 | -367.458643029133 |
| 75 | 197126 | 198443.342576793 | -1317.34257679263 |
| 76 | 205140 | 204824.571191347 | 315.428808652804 |
| 77 | 191751 | 192262.887306922 | -511.887306922197 |
| 78 | 196700 | 199951.309002789 | -3251.30900278881 |
| 79 | 199784 | 201498.428083660 | -1714.42808366038 |
| 80 | 207360 | 207698.468308058 | -338.468308057885 |
| 81 | 196101 | 194674.247225642 | 1426.75277435799 |
| 82 | 200824 | 200839.091364296 | -15.0913642963660 |
| 83 | 205743 | 205247.806573337 | 495.193426662506 |
| 84 | 212489 | 210692.193747490 | 1796.80625251040 |
| 85 | 200810 | 199019.177841467 | 1790.82215853283 |
| 86 | 203683 | 203437.172970323 | 245.827029676841 |
| 87 | 207286 | 207254.567816273 | 31.4321837265343 |
| 88 | 210910 | 213208.369242105 | -2298.36924210505 |
| 89 | 194915 | 202380.070959062 | -7465.07095906157 |
| 90 | 217920 | 206940.298410539 | 10979.7015894606 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 21 | 0.00373156064466383 | 0.00746312128932767 | 0.996268439355336 |
| 22 | 0.00067902338990544 | 0.00135804677981088 | 0.999320976610095 |
| 23 | 0.000113433925108827 | 0.000226867850217653 | 0.999886566074891 |
| 24 | 0.0165692479386536 | 0.0331384958773071 | 0.983430752061346 |
| 25 | 0.0159420301413825 | 0.0318840602827649 | 0.984057969858618 |
| 26 | 0.193316254295535 | 0.38663250859107 | 0.806683745704465 |
| 27 | 0.178941192711826 | 0.357882385423653 | 0.821058807288173 |
| 28 | 0.216027420947 | 0.432054841894 | 0.783972579053 |
| 29 | 0.262602890040785 | 0.52520578008157 | 0.737397109959215 |
| 30 | 0.213259936718751 | 0.426519873437502 | 0.786740063281249 |
| 31 | 0.193155950906202 | 0.386311901812404 | 0.806844049093798 |
| 32 | 0.197184877815873 | 0.394369755631746 | 0.802815122184127 |
| 33 | 0.156425731497479 | 0.312851462994959 | 0.84357426850252 |
| 34 | 0.1203320682098 | 0.2406641364196 | 0.8796679317902 |
| 35 | 0.0821555715002832 | 0.164311143000566 | 0.917844428499717 |
| 36 | 0.0553309186406516 | 0.110661837281303 | 0.944669081359348 |
| 37 | 0.0415807653514012 | 0.0831615307028024 | 0.958419234648599 |
| 38 | 0.0285219327149492 | 0.0570438654298984 | 0.97147806728505 |
| 39 | 0.0182185632492281 | 0.0364371264984561 | 0.981781436750772 |
| 40 | 0.0109497925238979 | 0.0218995850477957 | 0.989050207476102 |
| 41 | 0.00810407519849312 | 0.0162081503969862 | 0.991895924801507 |
| 42 | 0.0093439972396913 | 0.0186879944793826 | 0.990656002760309 |
| 43 | 0.00586051022678071 | 0.0117210204535614 | 0.99413948977322 |
| 44 | 0.00337138529567505 | 0.0067427705913501 | 0.996628614704325 |
| 45 | 0.00225374328942397 | 0.00450748657884795 | 0.997746256710576 |
| 46 | 0.00155809736228122 | 0.00311619472456244 | 0.998441902637719 |
| 47 | 0.000807636306405668 | 0.00161527261281134 | 0.999192363693594 |
| 48 | 0.000507302834898848 | 0.00101460566979770 | 0.999492697165101 |
| 49 | 0.000399861918192597 | 0.000799723836385194 | 0.999600138081807 |
| 50 | 0.000293294699989456 | 0.000586589399978912 | 0.99970670530001 |
| 51 | 0.000381260370033930 | 0.000762520740067861 | 0.999618739629966 |
| 52 | 0.000190058284843804 | 0.000380116569687607 | 0.999809941715156 |
| 53 | 0.00094942913698783 | 0.00189885827397566 | 0.999050570863012 |
| 54 | 0.000478087519433957 | 0.000956175038867914 | 0.999521912480566 |
| 55 | 0.000787404301887814 | 0.00157480860377563 | 0.999212595698112 |
| 56 | 0.000579510158167696 | 0.00115902031633539 | 0.999420489841832 |
| 57 | 0.000309955275186735 | 0.00061991055037347 | 0.999690044724813 |
| 58 | 0.000164944482550861 | 0.000329888965101723 | 0.99983505551745 |
| 59 | 0.000129577636116032 | 0.000259155272232065 | 0.999870422363884 |
| 60 | 0.000192708336390849 | 0.000385416672781698 | 0.99980729166361 |
| 61 | 8.71757165820747e-05 | 0.000174351433164149 | 0.999912824283418 |
| 62 | 6.34612230998622e-05 | 0.000126922446199724 | 0.9999365387769 |
| 63 | 5.35502984946583e-05 | 0.000107100596989317 | 0.999946449701505 |
| 64 | 3.04144292267508e-05 | 6.08288584535015e-05 | 0.999969585570773 |
| 65 | 0.000116116822090649 | 0.000232233644181299 | 0.99988388317791 |
| 66 | 0.000158035352877228 | 0.000316070705754457 | 0.999841964647123 |
| 67 | 0.000102752640265982 | 0.000205505280531964 | 0.999897247359734 |
| 68 | 7.98057807163835e-05 | 0.000159611561432767 | 0.999920194219284 |
| 69 | 0.000128664537644598 | 0.000257329075289196 | 0.999871335462355 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 29 | 0.591836734693878 | NOK |
| 5% type I error level | 36 | 0.73469387755102 | NOK |
| 10% type I error level | 38 | 0.775510204081633 | NOK |
