| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = -118.273578215342 + 298.441154509799X[t] + 1.00180797541842Y1[t] + 4.4709957013409e-06Y2[t] -148.968859133025M1[t] -581.425595573577M2[t] + 150.275891664170M3[t] + 885.158588241026M4[t] + 106.834156822982M5[t] -420.644134187442M6[t] -317.677673527403M7[t] -110.768661010202M8[t] + 220.266999976515M9[t] + 121.178068938109M10[t] + 1151.52013035616M11[t] -0.0921664123525376t + 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) | -118.273578215342 | 201.442387 | -0.5871 | 0.558832 | 0.279416 |
| X | 298.441154509799 | 112.069947 | 2.663 | 0.009427 | 0.004713 |
| Y1 | 1.00180797541842 | 0.119442 | 8.3874 | 0 | 0 |
| Y2 | 4.4709957013409e-06 | 0.122257 | 0 | 0.999971 | 0.499985 |
| M1 | -148.968859133025 | 197.182234 | -0.7555 | 0.452261 | 0.22613 |
| M2 | -581.425595573577 | 208.723488 | -2.7856 | 0.006722 | 0.003361 |
| M3 | 150.275891664170 | 249.464086 | 0.6024 | 0.548681 | 0.274341 |
| M4 | 885.158588241026 | 181.710113 | 4.8713 | 6e-06 | 3e-06 |
| M5 | 106.834156822982 | 140.33494 | 0.7613 | 0.448815 | 0.224408 |
| M6 | -420.644134187442 | 189.998481 | -2.2139 | 0.029793 | 0.014896 |
| M7 | -317.677673527403 | 234.405891 | -1.3552 | 0.179302 | 0.089651 |
| M8 | -110.768661010202 | 223.617533 | -0.4953 | 0.621765 | 0.310882 |
| M9 | 220.266999976515 | 204.060755 | 1.0794 | 0.283771 | 0.141885 |
| M10 | 121.178068938109 | 173.437906 | 0.6987 | 0.486855 | 0.243428 |
| M11 | 1151.52013035616 | 186.867397 | 6.1622 | 0 | 0 |
| t | -0.0921664123525376 | 1.683467 | -0.0547 | 0.956481 | 0.478241 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.99412317923994 |
| R-squared | 0.988280895502124 |
| Adjusted R-squared | 0.985997953067473 |
| F-TEST (value) | 432.897860454874 |
| F-TEST (DF numerator) | 15 |
| F-TEST (DF denominator) | 77 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 263.319472494806 |
| Sum Squared Residuals | 5338960.13381062 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 8776 | 8571.65763033812 | 204.342369661884 |
| 2 | 8255 | 8092.0227332535 | 162.977266746493 |
| 3 | 7969 | 8301.6898887491 | -332.689888749102 |
| 4 | 8758 | 8749.96100855518 | 8.03899144482334 |
| 5 | 8693 | 8761.96962462514 | -68.969624625143 |
| 6 | 8271 | 8169.28517641578 | 101.714823584222 |
| 7 | 7790 | 7849.39621442217 | -59.3962144221709 |
| 8 | 7769 | 7574.34153759057 | 194.658462409425 |
| 9 | 8170 | 7884.24491413222 | 285.755085867781 |
| 10 | 8209 | 8186.78872093334 | 22.2112790666617 |
| 11 | 9395 | 9256.11091984963 | 138.889080150372 |
| 12 | 9260 | 9292.6430562962 | -32.6430562961964 |
| 13 | 9018 | 9008.34325667023 | 9.65674332976637 |
| 14 | 8501 | 8333.35622018165 | 167.643779818348 |
| 15 | 8500 | 8547.02973573476 | -47.0297357347634 |
| 16 | 9649 | 9280.81614641907 | 368.183853580930 |
| 17 | 9319 | 9653.47690787344 | -334.476907873443 |
| 18 | 8830 | 8795.31495573665 | 34.6850442633516 |
| 19 | 8436 | 8408.30367457615 | 27.6963254238532 |
| 20 | 8169 | 8220.40599204924 | -51.4059920492399 |
| 21 | 8269 | 8283.86499561458 | -14.8649956145794 |
| 22 | 7945 | 8284.86350194981 | -339.863501949811 |
| 23 | 9144 | 8990.5280600195 | 153.471939980491 |
| 24 | 8770 | 9040.08207717508 | -270.082077175078 |
| 25 | 8834 | 8516.35022954706 | 317.649770452944 |
| 26 | 7837 | 8147.91536496854 | -310.915364968539 |
| 27 | 7792 | 7880.7224204455 | -88.7224204454935 |
| 28 | 8616 | 8570.42713413345 | 45.5728658665474 |
| 29 | 8518 | 8617.50010685303 | -99.500106853028 |
| 30 | 7940 | 7991.7561519397 | -51.7561519397043 |
| 31 | 7545 | 7515.58499823797 | 29.4150017620344 |
| 32 | 7531 | 7326.68510981702 | 204.314890182977 |
| 33 | 7665 | 7643.60152669223 | 21.3984733077729 |
| 34 | 7599 | 7678.6626353536 | -79.6626353535975 |
| 35 | 8444 | 8642.7938030951 | -198.793803095101 |
| 36 | 8549 | 8337.70895046944 | 211.291049530560 |
| 37 | 7986 | 8293.84154033436 | -307.841540334364 |
| 38 | 7335 | 7297.27521677544 | 37.7247832245617 |
| 39 | 7287 | 7376.70502843286 | -89.7050284328615 |
| 40 | 7870 | 8063.40586515908 | -193.405865159078 |
| 41 | 7839 | 7869.04310238983 | -30.043102389827 |
| 42 | 7327 | 7310.41920431957 | 16.5807956804267 |
| 43 | 7259 | 6900.36767655216 | 358.632323447837 |
| 44 | 6964 | 7039.05929117876 | -75.0592911787596 |
| 45 | 7271 | 7074.46912897698 | 196.530871023018 |
| 46 | 6956 | 7282.84176103595 | -326.841761035947 |
| 47 | 7608 | 7997.52351638052 | -389.52351638052 |
| 48 | 7692 | 7499.08861122117 | 192.911388778825 |
| 49 | 7255 | 7434.18237070014 | -179.182370700141 |
| 50 | 6804 | 6563.84375815303 | 240.156241846973 |
| 51 | 6655 | 6843.6357282396 | -188.635728239592 |
| 52 | 7341 | 7429.15485364769 | -88.1548536476886 |
| 53 | 7602 | 7337.97786077597 | 264.022139224031 |
| 54 | 7086 | 7071.88235204045 | 14.1176479595488 |
| 55 | 6625 | 6657.82489790211 | -32.8248979021116 |
| 56 | 6272 | 6402.80596030529 | -130.805960305287 |
| 57 | 6576 | 6380.10917842793 | 195.890821572070 |
| 58 | 6491 | 6585.47612724289 | -94.476127242889 |
| 59 | 7649 | 7530.57370352071 | 118.426296479288 |
| 60 | 7400 | 7539.0546622521 | -139.054662252098 |
| 61 | 6913 | 7140.54862824056 | -227.548628240556 |
| 62 | 6532 | 6220.11812808095 | 311.881871919048 |
| 63 | 6486 | 6570.03643289702 | -84.036432897022 |
| 64 | 7295 | 7258.74209274291 | 36.2579072570855 |
| 65 | 7556 | 7290.78794136022 | 265.212058639782 |
| 66 | 7088 | 7323.13413706697 | -235.13413706697 |
| 67 | 6952 | 6957.16346574871 | -5.16346574871477 |
| 68 | 6773 | 7027.73233477067 | -254.732334770670 |
| 69 | 6917 | 7179.35159368972 | -262.351593689721 |
| 70 | 7371 | 7224.43004439099 | 146.569955609014 |
| 71 | 8221 | 8709.50140406003 | -488.501404060024 |
| 72 | 7953 | 8409.42791622922 | -456.427916229221 |
| 73 | 8027 | 7991.88615361805 | 35.1138463819479 |
| 74 | 7287 | 7633.46984271926 | -346.469842719263 |
| 75 | 8076 | 7623.74159258871 | 452.258407411291 |
| 76 | 8933 | 9148.95530682152 | -215.955306821525 |
| 77 | 9433 | 9229.09167154032 | 203.908328459676 |
| 78 | 9479 | 9202.42903347007 | 276.570966529927 |
| 79 | 9199 | 9351.38873008486 | -152.388730084858 |
| 80 | 9469 | 9277.69954873835 | 191.300451261648 |
| 81 | 10015 | 9879.1299447969 | 135.870055203107 |
| 82 | 10999 | 10326.9372090934 | 672.062790906569 |
| 83 | 13009 | 12342.9685930745 | 666.031406925494 |
| 84 | 13699 | 13204.9947263568 | 494.00527364321 |
| 85 | 13895 | 13747.1901905515 | 147.809809448519 |
| 86 | 13248 | 13510.9987358676 | -262.998735867622 |
| 87 | 13973 | 13594.4391729125 | 378.560827087544 |
| 88 | 15095 | 15055.5375925211 | 39.4624074789058 |
| 89 | 15201 | 15401.1527845820 | -200.152784582048 |
| 90 | 14823 | 14979.7789890108 | -156.778989010801 |
| 91 | 14538 | 14703.9703424759 | -165.970342475870 |
| 92 | 14547 | 14625.2702255501 | -78.2702255500941 |
| 93 | 14407 | 14965.2287176694 | -558.228717669449 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 19 | 0.299635102465501 | 0.599270204931003 | 0.700364897534499 |
| 20 | 0.194084207320224 | 0.388168414640448 | 0.805915792679776 |
| 21 | 0.152473954387757 | 0.304947908775515 | 0.847526045612243 |
| 22 | 0.180442661136544 | 0.360885322273089 | 0.819557338863456 |
| 23 | 0.109793568593438 | 0.219587137186876 | 0.890206431406562 |
| 24 | 0.111545533822162 | 0.223091067644324 | 0.888454466177838 |
| 25 | 0.100169081615200 | 0.200338163230399 | 0.8998309183848 |
| 26 | 0.179174978890243 | 0.358349957780486 | 0.820825021109757 |
| 27 | 0.127959814686716 | 0.255919629373432 | 0.872040185313284 |
| 28 | 0.0858777441237858 | 0.171755488247572 | 0.914122255876214 |
| 29 | 0.0602859511891754 | 0.120571902378351 | 0.939714048810825 |
| 30 | 0.0368083686930114 | 0.0736167373860229 | 0.963191631306989 |
| 31 | 0.0223349986461251 | 0.0446699972922502 | 0.977665001353875 |
| 32 | 0.0174874888852450 | 0.0349749777704900 | 0.982512511114755 |
| 33 | 0.0103109705600909 | 0.0206219411201817 | 0.98968902943991 |
| 34 | 0.00589831985561707 | 0.0117966397112341 | 0.994101680144383 |
| 35 | 0.00588569635015595 | 0.0117713927003119 | 0.994114303649844 |
| 36 | 0.00644007721961358 | 0.0128801544392272 | 0.993559922780386 |
| 37 | 0.00612477746145415 | 0.0122495549229083 | 0.993875222538546 |
| 38 | 0.003812182543617 | 0.007624365087234 | 0.996187817456383 |
| 39 | 0.00246256071244176 | 0.00492512142488353 | 0.997537439287558 |
| 40 | 0.00194205175394190 | 0.00388410350788379 | 0.998057948246058 |
| 41 | 0.00104868535085329 | 0.00209737070170658 | 0.998951314649147 |
| 42 | 0.000600320364227534 | 0.00120064072845507 | 0.999399679635772 |
| 43 | 0.00166835962637618 | 0.00333671925275236 | 0.998331640373624 |
| 44 | 0.000895125456363203 | 0.00179025091272641 | 0.999104874543637 |
| 45 | 0.000852182595419215 | 0.00170436519083843 | 0.99914781740458 |
| 46 | 0.000658275724126272 | 0.00131655144825254 | 0.999341724275874 |
| 47 | 0.00166536248944694 | 0.00333072497889388 | 0.998334637510553 |
| 48 | 0.00136739981115318 | 0.00273479962230636 | 0.998632600188847 |
| 49 | 0.000766507777499719 | 0.00153301555499944 | 0.9992334922225 |
| 50 | 0.00103623844555915 | 0.00207247689111831 | 0.99896376155444 |
| 51 | 0.000746158644872515 | 0.00149231728974503 | 0.999253841355128 |
| 52 | 0.000492915176868759 | 0.000985830353737519 | 0.999507084823131 |
| 53 | 0.000947489143841888 | 0.00189497828768378 | 0.999052510856158 |
| 54 | 0.000647798985551475 | 0.00129559797110295 | 0.999352201014449 |
| 55 | 0.000415281296107953 | 0.000830562592215905 | 0.999584718703892 |
| 56 | 0.000283435237137404 | 0.000566870474274808 | 0.999716564762863 |
| 57 | 0.0006690299769646 | 0.0013380599539292 | 0.999330970023035 |
| 58 | 0.000545738262984044 | 0.00109147652596809 | 0.999454261737016 |
| 59 | 0.000521220584946034 | 0.00104244116989207 | 0.999478779415054 |
| 60 | 0.000270589354793919 | 0.000541178709587838 | 0.999729410645206 |
| 61 | 0.000233924768352102 | 0.000467849536704204 | 0.999766075231648 |
| 62 | 0.00109662084339246 | 0.00219324168678491 | 0.998903379156608 |
| 63 | 0.0104353566094947 | 0.0208707132189895 | 0.989564643390505 |
| 64 | 0.00706783622460844 | 0.0141356724492169 | 0.992932163775392 |
| 65 | 0.0066221938041856 | 0.0132443876083712 | 0.993377806195814 |
| 66 | 0.00370314515277530 | 0.00740629030555059 | 0.996296854847225 |
| 67 | 0.00986919126715436 | 0.0197383825343087 | 0.990130808732846 |
| 68 | 0.00568940932784329 | 0.0113788186556866 | 0.994310590672157 |
| 69 | 0.0203485741362743 | 0.0406971482725487 | 0.979651425863726 |
| 70 | 0.0379147853216333 | 0.0758295706432666 | 0.962085214678367 |
| 71 | 0.0362354258309453 | 0.0724708516618906 | 0.963764574169055 |
| 72 | 0.109086546221593 | 0.218173092443185 | 0.890913453778407 |
| 73 | 0.0781665886749354 | 0.156333177349871 | 0.921833411325065 |
| 74 | 0.057065818982896 | 0.114131637965792 | 0.942934181017104 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 26 | 0.464285714285714 | NOK |
| 5% type I error level | 39 | 0.696428571428571 | NOK |
| 10% type I error level | 42 | 0.75 | NOK |
