| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 8100.42455233596 + 3072.40963029376X[t] -6.22802678073278t + 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) | 8100.42455233596 | 436.359319 | 18.5637 | 0 | 0 |
| X | 3072.40963029376 | 665.087204 | 4.6196 | 1.2e-05 | 6e-06 |
| t | -6.22802678073278 | 11.057641 | -0.5632 | 0.574646 | 0.287323 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.57996515606376 |
| R-squared | 0.336359582248061 |
| Adjusted R-squared | 0.321932616644758 |
| F-TEST (value) | 23.3146450540544 |
| F-TEST (DF numerator) | 2 |
| F-TEST (DF denominator) | 92 |
| p-value | 6.44035913488494e-09 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 1813.08224263671 |
| Sum Squared Residuals | 302428584.10794 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 9051 | 8094.1965255552 | 956.80347444479 |
| 2 | 8823 | 8087.9684987745 | 735.031501225507 |
| 3 | 8776 | 8081.74047199376 | 694.259528006238 |
| 4 | 8255 | 8075.51244521303 | 179.487554786972 |
| 5 | 7969 | 8069.2844184323 | -100.284418432296 |
| 6 | 8758 | 8063.05639165156 | 694.943608348437 |
| 7 | 8693 | 8056.82836487083 | 636.17163512917 |
| 8 | 8271 | 8050.6003380901 | 220.399661909903 |
| 9 | 7790 | 8044.37231130936 | -254.372311309365 |
| 10 | 7769 | 8038.14428452863 | -269.144284528632 |
| 11 | 8170 | 8031.9162577479 | 138.083742252101 |
| 12 | 8209 | 8025.68823096717 | 183.311769032834 |
| 13 | 9395 | 8019.46020418643 | 1375.53979581357 |
| 14 | 9260 | 8013.2321774057 | 1246.7678225943 |
| 15 | 9018 | 8007.00415062497 | 1010.99584937503 |
| 16 | 8501 | 8000.77612384424 | 500.223876155765 |
| 17 | 8500 | 7994.5480970635 | 505.451902936498 |
| 18 | 9649 | 7988.32007028277 | 1660.67992971723 |
| 19 | 9319 | 7982.09204350204 | 1336.90795649796 |
| 20 | 8830 | 7975.8640167213 | 854.135983278696 |
| 21 | 8436 | 7969.63598994057 | 466.364010059429 |
| 22 | 8169 | 7963.40796315984 | 205.592036840162 |
| 23 | 8269 | 7957.1799363791 | 311.820063620894 |
| 24 | 7945 | 7950.95190959837 | -5.95190959837275 |
| 25 | 9144 | 7944.72388281764 | 1199.27611718236 |
| 26 | 8770 | 7938.4958560369 | 831.504143963093 |
| 27 | 8834 | 7932.26782925617 | 901.732170743825 |
| 28 | 7837 | 7926.03980247544 | -89.0398024754416 |
| 29 | 7792 | 7919.8117756947 | -127.811775694709 |
| 30 | 8616 | 7913.58374891398 | 702.416251086024 |
| 31 | 8518 | 7907.35572213324 | 610.644277866757 |
| 32 | 7940 | 7901.12769535251 | 38.8723046474895 |
| 33 | 7545 | 7894.89966857178 | -349.899668571778 |
| 34 | 7531 | 7888.67164179104 | -357.671641791045 |
| 35 | 7665 | 7882.44361501031 | -217.443615010312 |
| 36 | 7599 | 7876.21558822958 | -277.215588229579 |
| 37 | 8444 | 7869.98756144885 | 574.012438551153 |
| 38 | 8549 | 7863.75953466811 | 685.240465331886 |
| 39 | 7986 | 7857.53150788738 | 128.468492112619 |
| 40 | 7335 | 7851.30348110665 | -516.303481106648 |
| 41 | 7287 | 7845.07545432592 | -558.075454325916 |
| 42 | 7870 | 7838.84742754518 | 31.1525724548173 |
| 43 | 7839 | 7832.61940076445 | 6.3805992355501 |
| 44 | 7327 | 7826.39137398372 | -499.391373983717 |
| 45 | 7259 | 7820.16334720298 | -561.163347202984 |
| 46 | 6964 | 7813.93532042225 | -849.935320422252 |
| 47 | 7271 | 7807.70729364152 | -536.707293641519 |
| 48 | 6956 | 7801.47926686079 | -845.479266860786 |
| 49 | 7608 | 7795.25124008005 | -187.251240080053 |
| 50 | 7692 | 7789.02321329932 | -97.0232132993204 |
| 51 | 7255 | 7782.79518651859 | -527.795186518588 |
| 52 | 6804 | 7776.56715973786 | -972.567159737855 |
| 53 | 6655 | 7770.33913295712 | -1115.33913295712 |
| 54 | 7341 | 7764.11110617639 | -423.111106176389 |
| 55 | 7602 | 7757.88307939566 | -155.883079395657 |
| 56 | 7086 | 7751.65505261492 | -665.655052614924 |
| 57 | 6625 | 7745.42702583419 | -1120.42702583419 |
| 58 | 6272 | 7739.19899905346 | -1467.19899905346 |
| 59 | 6576 | 7732.97097227273 | -1156.97097227273 |
| 60 | 6491 | 7726.74294549199 | -1235.74294549199 |
| 61 | 7649 | 7720.51491871126 | -71.5149187112598 |
| 62 | 7400 | 7714.28689193053 | -314.286891930527 |
| 63 | 6913 | 7708.0588651498 | -795.058865149794 |
| 64 | 6532 | 7701.83083836906 | -1169.83083836906 |
| 65 | 6486 | 7695.60281158833 | -1209.60281158833 |
| 66 | 7295 | 7689.3747848076 | -394.374784807596 |
| 67 | 7556 | 7683.14675802686 | -127.146758026863 |
| 68 | 7088 | 10749.3283615399 | -3661.32836153989 |
| 69 | 6952 | 10743.1003347592 | -3791.10033475916 |
| 70 | 6773 | 10736.8723079784 | -3963.87230797843 |
| 71 | 6917 | 10730.6442811977 | -3813.64428119769 |
| 72 | 7371 | 10724.4162544170 | -3353.41625441696 |
| 73 | 8221 | 10718.1882276362 | -2497.18822763623 |
| 74 | 7953 | 10711.9602008555 | -2758.96020085550 |
| 75 | 8027 | 10705.7321740748 | -2678.73217407476 |
| 76 | 7287 | 10699.5041472940 | -3412.50414729403 |
| 77 | 8076 | 10693.2761205133 | -2617.2761205133 |
| 78 | 8933 | 10687.0480937326 | -1754.04809373256 |
| 79 | 9433 | 10680.8200669518 | -1247.82006695183 |
| 80 | 9479 | 10674.5920401711 | -1195.5920401711 |
| 81 | 9199 | 10668.3640133904 | -1469.36401339037 |
| 82 | 9469 | 10662.1359866096 | -1193.13598660963 |
| 83 | 10015 | 10655.9079598289 | -640.9079598289 |
| 84 | 10999 | 10649.6799330482 | 349.320066951832 |
| 85 | 13009 | 10643.4519062674 | 2365.54809373256 |
| 86 | 13699 | 10637.2238794867 | 3061.7761205133 |
| 87 | 13895 | 10630.9958527060 | 3264.00414729403 |
| 88 | 13248 | 10624.7678259252 | 2623.23217407476 |
| 89 | 13973 | 10618.5397991445 | 3354.46020085550 |
| 90 | 15095 | 10612.3117723638 | 4482.68822763623 |
| 91 | 15201 | 10606.0837455830 | 4594.91625441696 |
| 92 | 14823 | 10599.8557188023 | 4223.14428119769 |
| 93 | 14538 | 10593.6276920216 | 3944.37230797843 |
| 94 | 14547 | 10587.3996652408 | 3959.60033475916 |
| 95 | 14407 | 10581.1716384601 | 3825.82836153989 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 6 | 0.0152400832962651 | 0.0304801665925301 | 0.984759916703735 |
| 7 | 0.00459133932060204 | 0.00918267864120409 | 0.995408660679398 |
| 8 | 0.000861016075447155 | 0.00172203215089431 | 0.999138983924553 |
| 9 | 0.000234234850517527 | 0.000468469701035055 | 0.999765765149482 |
| 10 | 4.41000920688087e-05 | 8.82001841376173e-05 | 0.999955899907931 |
| 11 | 1.14187154927883e-05 | 2.28374309855766e-05 | 0.999988581284507 |
| 12 | 3.09248942198712e-06 | 6.18497884397423e-06 | 0.999996907510578 |
| 13 | 5.66760875860673e-05 | 0.000113352175172135 | 0.999943323912414 |
| 14 | 5.2378818436127e-05 | 0.000104757636872254 | 0.999947621181564 |
| 15 | 2.03736113583785e-05 | 4.0747222716757e-05 | 0.999979626388642 |
| 16 | 5.75733584987185e-06 | 1.15146716997437e-05 | 0.99999424266415 |
| 17 | 1.56855421723328e-06 | 3.13710843446656e-06 | 0.999998431445783 |
| 18 | 1.93542067172423e-06 | 3.87084134344845e-06 | 0.999998064579328 |
| 19 | 8.02807486677303e-07 | 1.60561497335461e-06 | 0.999999197192513 |
| 20 | 2.44863904515184e-07 | 4.89727809030368e-07 | 0.999999755136096 |
| 21 | 1.01608723441908e-07 | 2.03217446883816e-07 | 0.999999898391277 |
| 22 | 5.76438604762046e-08 | 1.15287720952409e-07 | 0.99999994235614 |
| 23 | 2.3849316806935e-08 | 4.769863361387e-08 | 0.999999976150683 |
| 24 | 1.46598065737051e-08 | 2.93196131474101e-08 | 0.999999985340193 |
| 25 | 7.71855427291519e-09 | 1.54371085458304e-08 | 0.999999992281446 |
| 26 | 2.68329386673462e-09 | 5.36658773346923e-09 | 0.999999997316706 |
| 27 | 9.96454786358733e-10 | 1.99290957271747e-09 | 0.999999999003545 |
| 28 | 9.31352448223389e-10 | 1.86270489644678e-09 | 0.999999999068648 |
| 29 | 7.2432908162088e-10 | 1.44865816324176e-09 | 0.999999999275671 |
| 30 | 3.01092403092351e-10 | 6.02184806184701e-10 | 0.999999999698908 |
| 31 | 1.27504891397803e-10 | 2.55009782795607e-10 | 0.999999999872495 |
| 32 | 7.60692079812584e-11 | 1.52138415962517e-10 | 0.999999999923931 |
| 33 | 8.0822823247571e-11 | 1.61645646495142e-10 | 0.999999999919177 |
| 34 | 6.92797311046796e-11 | 1.38559462209359e-10 | 0.99999999993072 |
| 35 | 4.25429197232622e-11 | 8.50858394465245e-11 | 0.999999999957457 |
| 36 | 2.65041834052225e-11 | 5.3008366810445e-11 | 0.999999999973496 |
| 37 | 2.17731838560015e-11 | 4.35463677120031e-11 | 0.999999999978227 |
| 38 | 2.52989059418776e-11 | 5.05978118837553e-11 | 0.9999999999747 |
| 39 | 1.93765499263936e-11 | 3.87530998527871e-11 | 0.999999999980623 |
| 40 | 2.42046559033218e-11 | 4.84093118066436e-11 | 0.999999999975795 |
| 41 | 2.91829157100462e-11 | 5.83658314200924e-11 | 0.999999999970817 |
| 42 | 3.08161338130817e-11 | 6.16322676261633e-11 | 0.999999999969184 |
| 43 | 3.936135483189e-11 | 7.872270966378e-11 | 0.999999999960639 |
| 44 | 5.7417751275504e-11 | 1.14835502551008e-10 | 0.999999999942582 |
| 45 | 9.0589802801297e-11 | 1.81179605602594e-10 | 0.99999999990941 |
| 46 | 1.79356867989256e-10 | 3.58713735978513e-10 | 0.999999999820643 |
| 47 | 2.97140150866394e-10 | 5.94280301732788e-10 | 0.99999999970286 |
| 48 | 5.51310641766996e-10 | 1.10262128353399e-09 | 0.99999999944869 |
| 49 | 1.59131876718285e-09 | 3.1826375343657e-09 | 0.999999998408681 |
| 50 | 7.41528441648192e-09 | 1.48305688329638e-08 | 0.999999992584716 |
| 51 | 2.33051164277520e-08 | 4.66102328555040e-08 | 0.999999976694883 |
| 52 | 6.31995357892066e-08 | 1.26399071578413e-07 | 0.999999936800464 |
| 53 | 1.51426139160157e-07 | 3.02852278320314e-07 | 0.99999984857386 |
| 54 | 6.03562723134238e-07 | 1.20712544626848e-06 | 0.999999396437277 |
| 55 | 5.52118504879695e-06 | 1.10423700975939e-05 | 0.999994478814951 |
| 56 | 1.87545504059333e-05 | 3.75091008118667e-05 | 0.999981245449594 |
| 57 | 3.65766268202646e-05 | 7.31532536405291e-05 | 0.99996342337318 |
| 58 | 5.51557518443365e-05 | 0.000110311503688673 | 0.999944844248156 |
| 59 | 5.83800449889991e-05 | 0.000116760089977998 | 0.999941619955011 |
| 60 | 4.83345956117284e-05 | 9.66691912234569e-05 | 0.999951665404388 |
| 61 | 0.000186165504700086 | 0.000372331009400171 | 0.9998138344953 |
| 62 | 0.000343284408219095 | 0.000686568816438191 | 0.99965671559178 |
| 63 | 0.000264939982423 | 0.000529879964846 | 0.999735060017577 |
| 64 | 0.000160998018454701 | 0.000321996036909403 | 0.999839001981545 |
| 65 | 0.000100811452401330 | 0.000201622904802660 | 0.999899188547599 |
| 66 | 6.73755909427882e-05 | 0.000134751181885576 | 0.999932624409057 |
| 67 | 5.77299034565234e-05 | 0.000115459806913047 | 0.999942270096543 |
| 68 | 0.000102334295999245 | 0.00020466859199849 | 0.999897665704 |
| 69 | 0.000115305913570740 | 0.000230611827141481 | 0.99988469408643 |
| 70 | 8.16865735954318e-05 | 0.000163373147190864 | 0.999918313426405 |
| 71 | 4.97001889223254e-05 | 9.94003778446507e-05 | 0.999950299811078 |
| 72 | 4.02249273909967e-05 | 8.04498547819934e-05 | 0.99995977507261 |
| 73 | 0.000184341531282795 | 0.000368683062565590 | 0.999815658468717 |
| 74 | 0.000219674129220574 | 0.000439348258441149 | 0.99978032587078 |
| 75 | 0.000204866261566980 | 0.000409732523133960 | 0.999795133738433 |
| 76 | 0.000146614978204057 | 0.000293229956408114 | 0.999853385021796 |
| 77 | 0.000121834560674017 | 0.000243669121348035 | 0.999878165439326 |
| 78 | 0.000230259787039446 | 0.000460519574078891 | 0.99976974021296 |
| 79 | 0.000614267526291938 | 0.00122853505258388 | 0.999385732473708 |
| 80 | 0.00112779634753602 | 0.00225559269507205 | 0.998872203652464 |
| 81 | 0.00270467511957741 | 0.00540935023915482 | 0.997295324880423 |
| 82 | 0.0162885882479345 | 0.032577176495869 | 0.983711411752066 |
| 83 | 0.181862438963686 | 0.363724877927372 | 0.818137561036314 |
| 84 | 0.809265163540811 | 0.381469672918378 | 0.190734836459189 |
| 85 | 0.906384652759437 | 0.187230694481126 | 0.0936153472405632 |
| 86 | 0.918905529607947 | 0.162188940784106 | 0.081094470392053 |
| 87 | 0.902110731923369 | 0.195778536153262 | 0.097889268076631 |
| 88 | 0.958146491177433 | 0.0837070176451333 | 0.0418535088225666 |
| 89 | 0.998239895817243 | 0.0035202083655135 | 0.00176010418275675 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 76 | 0.904761904761905 | NOK |
| 5% type I error level | 78 | 0.928571428571429 | NOK |
| 10% type I error level | 79 | 0.94047619047619 | NOK |
