| Multiple Linear Regression - Estimated Regression Equation |
| X[t] = + 15528.2166014861 + 0.283174803792777Y_1[t] + 0.298954678015929Y_2[t] -0.0123849708445849Y_3[t] -3780.91761340949M1[t] -8590.0139987651M2[t] -4995.57765924133M3[t] -9992.05694547716M4[t] -10063.8242839980M5[t] -6319.54201284951M6[t] -3551.14205129836M7[t] -9582.68297879728M8[t] -14587.2298411741M9[t] + 5113.37309057484M10[t] -64.3210395853369M11[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) | 15528.2166014861 | 3489.29975 | 4.4502 | 2.9e-05 | 1.4e-05 |
| Y_1 | 0.283174803792777 | 0.113263 | 2.5002 | 0.014569 | 0.007284 |
| Y_2 | 0.298954678015929 | 0.114488 | 2.6112 | 0.010865 | 0.005432 |
| Y_3 | -0.0123849708445849 | 0.114838 | -0.1078 | 0.914401 | 0.4572 |
| M1 | -3780.91761340949 | 2225.513895 | -1.6989 | 0.093429 | 0.046715 |
| M2 | -8590.0139987651 | 1879.994129 | -4.5692 | 1.9e-05 | 9e-06 |
| M3 | -4995.57765924133 | 2534.664761 | -1.9709 | 0.052376 | 0.026188 |
| M4 | -9992.05694547716 | 2348.815557 | -4.2541 | 5.9e-05 | 3e-05 |
| M5 | -10063.8242839980 | 2108.647425 | -4.7726 | 9e-06 | 4e-06 |
| M6 | -6319.54201284951 | 2569.088047 | -2.4598 | 0.016172 | 0.008086 |
| M7 | -3551.14205129836 | 2071.511517 | -1.7143 | 0.090554 | 0.045277 |
| M8 | -9582.68297879728 | 1758.231334 | -5.4502 | 1e-06 | 0 |
| M9 | -14587.2298411741 | 1964.628892 | -7.4249 | 0 | 0 |
| M10 | 5113.37309057484 | 2739.961795 | 1.8662 | 0.065868 | 0.032934 |
| M11 | -64.3210395853369 | 2471.396257 | -0.026 | 0.979305 | 0.489652 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.949610283391202 |
| R-squared | 0.901759690322319 |
| Adjusted R-squared | 0.883662791171167 |
| F-TEST (value) | 49.8295140394219 |
| F-TEST (DF numerator) | 14 |
| F-TEST (DF denominator) | 76 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 1935.56350504491 |
| Sum Squared Residuals | 284726862.236691 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 26105 | 27792.8971747924 | -1687.89717479238 |
| 2 | 22397 | 22803.0100337030 | -406.010033703028 |
| 3 | 23843 | 24314.2308813743 | -471.2308813743 |
| 4 | 21705 | 18660.2747624650 | 3044.72523753496 |
| 5 | 18089 | 18461.2916297380 | -372.291629737961 |
| 6 | 20764 | 20524.5400409325 | 239.459959067528 |
| 7 | 25316 | 22995.8915545894 | 2320.10844541058 |
| 8 | 17704 | 19097.8501522218 | -1393.85015222184 |
| 9 | 15548 | 13265.4885806936 | 2282.51141930637 |
| 10 | 28029 | 30023.5472391236 | -1994.54723912357 |
| 11 | 29383 | 27829.8859473677 | 1553.11405263233 |
| 12 | 36438 | 32035.5810047462 | 4402.41899525382 |
| 13 | 32034 | 30502.6694450170 | 1531.33055498297 |
| 14 | 22679 | 26538.8272266368 | -3859.82722663684 |
| 15 | 24319 | 26080.1909053885 | -1761.19090538848 |
| 16 | 18004 | 18805.9406961333 | -801.940696133347 |
| 17 | 17537 | 17552.0715458583 | -15.0715458583007 |
| 18 | 20366 | 19255.9010397799 | 1110.09896022013 |
| 19 | 22782 | 22764.0017775109 | 17.9982224890889 |
| 20 | 19169 | 18268.1377414668 | 900.86225853318 |
| 21 | 13807 | 12927.7177325538 | 879.282267446175 |
| 22 | 29743 | 29999.8920251339 | -256.892025133856 |
| 23 | 25591 | 27776.6234843554 | -2185.62348435545 |
| 24 | 29096 | 31495.7527011237 | -2399.75270112368 |
| 25 | 26482 | 27268.7360565064 | -786.73605650644 |
| 26 | 22405 | 22818.6792794291 | -413.679279429058 |
| 27 | 27044 | 24433.7350927458 | 2610.26490725424 |
| 28 | 17970 | 19564.4398128214 | -1594.43981282143 |
| 29 | 18730 | 18360.4885821342 | 369.511417865829 |
| 30 | 19684 | 19549.8150761006 | 134.184923899377 |
| 31 | 19785 | 22927.9505812060 | -3142.95058120596 |
| 32 | 18479 | 17200.8004938754 | 1278.19950612459 |
| 33 | 10698 | 11844.8064980391 | -1146.80649803908 |
| 34 | 31956 | 28950.3405899323 | 3005.65941006766 |
| 35 | 29506 | 27482.3848610801 | 2023.61513891990 |
| 36 | 34506 | 33304.4736347775 | 1201.52636522253 |
| 37 | 27165 | 29943.7113689787 | -2778.71136897866 |
| 38 | 26736 | 24580.9453176292 | 2155.05468237085 |
| 39 | 23691 | 25797.3485207880 | -2106.34852078796 |
| 40 | 18157 | 19901.2684711044 | -1744.26847110439 |
| 41 | 17328 | 17357.4079263281 | -29.4079263281101 |
| 42 | 18205 | 19250.2353332140 | -1045.23533321402 |
| 43 | 20995 | 22087.6845982702 | -1092.68459827017 |
| 44 | 17382 | 17118.6517668032 | 263.348233196776 |
| 45 | 9367 | 11914.2162705568 | -2547.21627055681 |
| 46 | 31124 | 28230.4958295787 | 2893.50417042127 |
| 47 | 26551 | 26862.4610609018 | -311.461060901819 |
| 48 | 30651 | 32235.4461936547 | -1584.4461936547 |
| 49 | 25859 | 27978.9657225631 | -2119.96572256313 |
| 50 | 25100 | 23095.2463289701 | 2004.75367102987 |
| 51 | 25778 | 24991.3837949000 | 786.616205099955 |
| 52 | 20418 | 20019.3392053089 | 398.66079469112 |
| 53 | 18688 | 18641.8463830246 | 46.1536169754334 |
| 54 | 20424 | 20285.4421592136 | 138.557840786435 |
| 55 | 24776 | 23094.6254309084 | 1681.3745690916 |
| 56 | 19814 | 18835.8725701124 | 978.127429887575 |
| 57 | 12738 | 13705.7627806549 | -967.762780654945 |
| 58 | 31566 | 29865.3082953355 | 1700.69170466445 |
| 59 | 30111 | 27965.2802946759 | 2145.71970532411 |
| 60 | 30019 | 33333.9367261229 | -3314.93672612293 |
| 61 | 31934 | 28858.8037431895 | 3075.19625681051 |
| 62 | 25826 | 24582.5034092985 | 1243.49659070154 |
| 63 | 26835 | 27020.9456729742 | -185.945672974149 |
| 64 | 20205 | 20460.4573712766 | -255.457371276559 |
| 65 | 17789 | 18888.5337556464 | -1099.53375564637 |
| 66 | 20520 | 19954.0997500037 | 565.90024999626 |
| 67 | 22518 | 22855.6879553261 | -337.687955326084 |
| 68 | 15572 | 18236.2976010271 | -2664.29760102714 |
| 69 | 11509 | 11828.3066428049 | -319.306642804933 |
| 70 | 25447 | 28277.0859814977 | -2830.08598149773 |
| 71 | 24090 | 25917.6554173090 | -1827.65541730904 |
| 72 | 27786 | 29814.8586868751 | -2028.85868687515 |
| 73 | 26195 | 26502.2519265843 | -307.251926584328 |
| 74 | 20516 | 22364.3673237774 | -1848.36732377739 |
| 75 | 22759 | 23829.2422075970 | -1070.24220759704 |
| 76 | 19028 | 17789.8648784297 | 1238.13512157031 |
| 77 | 16971 | 17402.4619391741 | -431.461939174095 |
| 78 | 20036 | 19421.0742456390 | 614.925754360975 |
| 79 | 22485 | 22488.6635343574 | -3.66353435742568 |
| 80 | 18730 | 18092.3896744931 | 637.610325506859 |
| 81 | 14538 | 12718.7014946968 | 1819.29850530322 |
| 82 | 27561 | 30079.3300393982 | -2518.33003939823 |
| 83 | 25985 | 27382.7089343100 | -1397.70893431002 |
| 84 | 34670 | 30945.9510526999 | 3724.04894730011 |
| 85 | 32066 | 28991.9645623685 | 3074.03543763146 |
| 86 | 27186 | 26061.4210805559 | 1124.57891944405 |
| 87 | 29586 | 27387.9229242323 | 2198.07707576774 |
| 88 | 21359 | 21644.4148024607 | -285.414802460667 |
| 89 | 21553 | 20020.8982380964 | 1532.10176190358 |
| 90 | 19573 | 21330.8923551167 | -1757.89235511668 |
| 91 | 24256 | 23698.4945678316 | 557.50543216837 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 18 | 0.441396375022166 | 0.882792750044332 | 0.558603624977834 |
| 19 | 0.600318068217923 | 0.799363863564154 | 0.399681931782077 |
| 20 | 0.537086816887232 | 0.925826366225535 | 0.462913183112768 |
| 21 | 0.448098021551798 | 0.896196043103596 | 0.551901978448202 |
| 22 | 0.332048430678689 | 0.664096861357379 | 0.66795156932131 |
| 23 | 0.343963323986153 | 0.687926647972306 | 0.656036676013847 |
| 24 | 0.840588087839614 | 0.318823824320772 | 0.159411912160386 |
| 25 | 0.779671048016554 | 0.440657903966891 | 0.220328951983446 |
| 26 | 0.711823983774338 | 0.576352032451324 | 0.288176016225662 |
| 27 | 0.702103713406819 | 0.595792573186362 | 0.297896286593181 |
| 28 | 0.762690795892442 | 0.474618408215116 | 0.237309204107558 |
| 29 | 0.702469702624331 | 0.595060594751338 | 0.297530297375669 |
| 30 | 0.625294990562958 | 0.749410018874084 | 0.374705009437042 |
| 31 | 0.761130745191144 | 0.477738509617712 | 0.238869254808856 |
| 32 | 0.722237771639335 | 0.555524456721329 | 0.277762228360665 |
| 33 | 0.743374407344538 | 0.513251185310924 | 0.256625592655462 |
| 34 | 0.775399573621534 | 0.449200852756931 | 0.224600426378466 |
| 35 | 0.770630355020125 | 0.45873928995975 | 0.229369644979875 |
| 36 | 0.731557534383313 | 0.536884931233374 | 0.268442465616687 |
| 37 | 0.76529354528691 | 0.469412909426179 | 0.234706454713090 |
| 38 | 0.82279419022098 | 0.354411619558042 | 0.177205809779021 |
| 39 | 0.821528088740679 | 0.356943822518642 | 0.178471911259321 |
| 40 | 0.806281562557162 | 0.387436874885676 | 0.193718437442838 |
| 41 | 0.754837022425662 | 0.490325955148675 | 0.245162977574338 |
| 42 | 0.719078766851162 | 0.561842466297676 | 0.280921233148838 |
| 43 | 0.674834009747382 | 0.650331980505236 | 0.325165990252618 |
| 44 | 0.61085354955047 | 0.778292900899059 | 0.389146450449529 |
| 45 | 0.665462908028117 | 0.669074183943766 | 0.334537091971883 |
| 46 | 0.752680056624289 | 0.494639886751421 | 0.247319943375711 |
| 47 | 0.696599106193974 | 0.606801787612051 | 0.303400893806025 |
| 48 | 0.688048764184126 | 0.623902471631748 | 0.311951235815874 |
| 49 | 0.796404689374823 | 0.407190621250355 | 0.203595310625177 |
| 50 | 0.789668153582554 | 0.420663692834891 | 0.210331846417445 |
| 51 | 0.736306166786221 | 0.527387666427557 | 0.263693833213779 |
| 52 | 0.694388200276487 | 0.611223599447026 | 0.305611799723513 |
| 53 | 0.626838288925003 | 0.746323422149993 | 0.373161711074997 |
| 54 | 0.556561797352774 | 0.886876405294453 | 0.443438202647226 |
| 55 | 0.53496144955604 | 0.93007710088792 | 0.46503855044396 |
| 56 | 0.482584874616921 | 0.965169749233843 | 0.517415125383079 |
| 57 | 0.430028626046065 | 0.86005725209213 | 0.569971373953935 |
| 58 | 0.520675232888065 | 0.95864953422387 | 0.479324767111935 |
| 59 | 0.536803826427483 | 0.926392347145033 | 0.463196173572517 |
| 60 | 0.749918166183122 | 0.500163667633756 | 0.250081833816878 |
| 61 | 0.76743751394201 | 0.465124972115979 | 0.232562486057989 |
| 62 | 0.732566275179782 | 0.534867449640436 | 0.267433724820218 |
| 63 | 0.708930713588155 | 0.582138572823689 | 0.291069286411845 |
| 64 | 0.63049459485146 | 0.739010810297081 | 0.369505405148540 |
| 65 | 0.565364287765549 | 0.869271424468902 | 0.434635712234451 |
| 66 | 0.50818798402215 | 0.9836240319557 | 0.49181201597785 |
| 67 | 0.409211889894579 | 0.818423779789158 | 0.590788110105421 |
| 68 | 0.455129500334603 | 0.910259000669205 | 0.544870499665397 |
| 69 | 0.366768469503080 | 0.733536939006159 | 0.633231530496920 |
| 70 | 0.318832163880075 | 0.63766432776015 | 0.681167836119925 |
| 71 | 0.232479720560809 | 0.464959441121619 | 0.76752027943919 |
| 72 | 0.54544978404701 | 0.90910043190598 | 0.45455021595299 |
| 73 | 0.503492250011608 | 0.993015499976783 | 0.496507749988392 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 0 | 0 | OK |
| 5% type I error level | 0 | 0 | OK |
| 10% type I error level | 0 | 0 | OK |
