| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 2294.2 + 482.518518518518X[t] -881.151851851853M1[t] -174.751851851852M2[t] + 84.7481481481482M3[t] + 901.048148148148M4[t] + 2379.04814814815M5[t] + 2964.74814814815M6[t] + 2979.64814814815M7[t] + 3732.74814814815M8[t] + 3100.44814814815M9[t] + 856M10[t] -390.1M11[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) | 2294.2 | 122.104163 | 18.7889 | 0 | 0 |
| X | 482.518518518518 | 135.671292 | 3.5565 | 0.000561 | 0.000281 |
| M1 | -881.151851851853 | 173.213511 | -5.0871 | 2e-06 | 1e-06 |
| M2 | -174.751851851852 | 173.213511 | -1.0089 | 0.315308 | 0.157654 |
| M3 | 84.7481481481482 | 173.213511 | 0.4893 | 0.625652 | 0.312826 |
| M4 | 901.048148148148 | 173.213511 | 5.202 | 1e-06 | 0 |
| M5 | 2379.04814814815 | 173.213511 | 13.7348 | 0 | 0 |
| M6 | 2964.74814814815 | 173.213511 | 17.1161 | 0 | 0 |
| M7 | 2979.64814814815 | 173.213511 | 17.2022 | 0 | 0 |
| M8 | 3732.74814814815 | 173.213511 | 21.55 | 0 | 0 |
| M9 | 3100.44814814815 | 173.213511 | 17.8996 | 0 | 0 |
| M10 | 856 | 172.681364 | 4.9571 | 3e-06 | 1e-06 |
| M11 | -390.1 | 172.681364 | -2.2591 | 0.025906 | 0.012953 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.974222552850857 |
| R-squared | 0.94910958248324 |
| Adjusted R-squared | 0.943402245939304 |
| F-TEST (value) | 166.296410799834 |
| F-TEST (DF numerator) | 12 |
| F-TEST (DF denominator) | 107 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 386.127267313284 |
| Sum Squared Residuals | 15953086.5222222 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 1579 | 1413.04814814815 | 165.951851851848 |
| 2 | 2146 | 2119.44814814815 | 26.5518518518523 |
| 3 | 2462 | 2378.94814814815 | 83.051851851852 |
| 4 | 3695 | 3195.24814814815 | 499.751851851852 |
| 5 | 4831 | 4673.24814814815 | 157.751851851851 |
| 6 | 5134 | 5258.94814814815 | -124.948148148148 |
| 7 | 6250 | 5273.84814814815 | 976.151851851852 |
| 8 | 5760 | 6026.94814814815 | -266.948148148147 |
| 9 | 6249 | 5394.64814814815 | 854.351851851852 |
| 10 | 2917 | 3150.2 | -233.200000000001 |
| 11 | 1741 | 1904.1 | -163.099999999998 |
| 12 | 2359 | 2294.2 | 64.8000000000003 |
| 13 | 1511 | 1895.56666666667 | -384.566666666666 |
| 14 | 2059 | 2119.44814814815 | -60.4481481481483 |
| 15 | 2635 | 2378.94814814815 | 256.051851851852 |
| 16 | 2867 | 3195.24814814815 | -328.248148148148 |
| 17 | 4403 | 4673.24814814815 | -270.248148148148 |
| 18 | 5720 | 5258.94814814815 | 461.051851851852 |
| 19 | 4502 | 5273.84814814815 | -771.848148148148 |
| 20 | 5749 | 6026.94814814815 | -277.948148148148 |
| 21 | 5627 | 5394.64814814815 | 232.351851851852 |
| 22 | 2846 | 3150.2 | -304.2 |
| 23 | 1762 | 1904.1 | -142.1 |
| 24 | 2429 | 2294.2 | 134.8 |
| 25 | 1169 | 1413.04814814815 | -244.048148148148 |
| 26 | 2154 | 2601.96666666667 | -447.966666666666 |
| 27 | 2249 | 2378.94814814815 | -129.948148148148 |
| 28 | 2687 | 3195.24814814815 | -508.248148148148 |
| 29 | 4359 | 4673.24814814815 | -314.248148148148 |
| 30 | 5382 | 5258.94814814815 | 123.051851851852 |
| 31 | 4459 | 5273.84814814815 | -814.848148148148 |
| 32 | 6398 | 6026.94814814815 | 371.051851851852 |
| 33 | 4596 | 5394.64814814815 | -798.648148148148 |
| 34 | 3024 | 3150.2 | -126.2 |
| 35 | 1887 | 1904.1 | -17.1000000000003 |
| 36 | 2070 | 2294.2 | -224.2 |
| 37 | 1351 | 1413.04814814815 | -62.0481481481477 |
| 38 | 2218 | 2119.44814814815 | 98.5518518518517 |
| 39 | 2461 | 2861.46666666667 | -400.466666666667 |
| 40 | 3028 | 3195.24814814815 | -167.248148148148 |
| 41 | 4784 | 4673.24814814815 | 110.751851851852 |
| 42 | 4975 | 5258.94814814815 | -283.948148148148 |
| 43 | 4607 | 5273.84814814815 | -666.848148148148 |
| 44 | 6249 | 6026.94814814815 | 222.051851851852 |
| 45 | 4809 | 5394.64814814815 | -585.648148148148 |
| 46 | 3157 | 3150.2 | 6.80000000000004 |
| 47 | 1910 | 1904.1 | 5.89999999999978 |
| 48 | 2228 | 2294.2 | -66.2000000000002 |
| 49 | 1594 | 1413.04814814815 | 180.951851851852 |
| 50 | 2467 | 2119.44814814815 | 347.551851851852 |
| 51 | 2222 | 2378.94814814815 | -156.948148148148 |
| 52 | 3607 | 3677.76666666667 | -70.7666666666671 |
| 53 | 4685 | 4673.24814814815 | 11.7518518518519 |
| 54 | 4962 | 5258.94814814815 | -296.948148148148 |
| 55 | 5770 | 5273.84814814815 | 496.151851851852 |
| 56 | 5480 | 6026.94814814815 | -546.948148148148 |
| 57 | 5000 | 5394.64814814815 | -394.648148148148 |
| 58 | 3228 | 3150.2 | 77.7999999999999 |
| 59 | 1993 | 1904.1 | 88.8999999999997 |
| 60 | 2288 | 2294.2 | -6.20000000000025 |
| 61 | 1580 | 1413.04814814815 | 166.951851851852 |
| 62 | 2111 | 2119.44814814815 | -8.44814814814824 |
| 63 | 2192 | 2378.94814814815 | -186.948148148148 |
| 64 | 3601 | 3195.24814814815 | 405.751851851852 |
| 65 | 4665 | 5155.76666666667 | -490.766666666667 |
| 66 | 4876 | 5258.94814814815 | -382.948148148148 |
| 67 | 5813 | 5273.84814814815 | 539.151851851852 |
| 68 | 5589 | 6026.94814814815 | -437.948148148148 |
| 69 | 5331 | 5394.64814814815 | -63.6481481481484 |
| 70 | 3075 | 3150.2 | -75.1999999999999 |
| 71 | 2002 | 1904.1 | 97.8999999999997 |
| 72 | 2306 | 2294.2 | 11.8 |
| 73 | 1507 | 1413.04814814815 | 93.9518518518523 |
| 74 | 1992 | 2119.44814814815 | -127.448148148148 |
| 75 | 2487 | 2378.94814814815 | 108.051851851852 |
| 76 | 3490 | 3195.24814814815 | 294.751851851852 |
| 77 | 4647 | 4673.24814814815 | -26.2481481481481 |
| 78 | 5594 | 5741.46666666667 | -147.466666666667 |
| 79 | 5611 | 5273.84814814815 | 337.151851851852 |
| 80 | 5788 | 6026.94814814815 | -238.948148148148 |
| 81 | 6204 | 5394.64814814815 | 809.351851851852 |
| 82 | 3013 | 3150.2 | -137.2 |
| 83 | 1931 | 1904.1 | 26.8999999999998 |
| 84 | 2549 | 2294.2 | 254.8 |
| 85 | 1504 | 1413.04814814815 | 90.9518518518523 |
| 86 | 2090 | 2119.44814814815 | -29.4481481481483 |
| 87 | 2702 | 2378.94814814815 | 323.051851851852 |
| 88 | 2939 | 3195.24814814815 | -256.248148148148 |
| 89 | 4500 | 4673.24814814815 | -173.248148148148 |
| 90 | 6208 | 5258.94814814815 | 949.051851851852 |
| 91 | 6415 | 5756.36666666667 | 658.633333333334 |
| 92 | 5657 | 6026.94814814815 | -369.948148148148 |
| 93 | 5964 | 5394.64814814815 | 569.351851851852 |
| 94 | 3163 | 3150.2 | 12.8 |
| 95 | 1997 | 1904.1 | 92.8999999999997 |
| 96 | 2422 | 2294.2 | 127.8 |
| 97 | 1376 | 1413.04814814815 | -37.0481481481477 |
| 98 | 2202 | 2119.44814814815 | 82.5518518518517 |
| 99 | 2683 | 2378.94814814815 | 304.051851851852 |
| 100 | 3303 | 3195.24814814815 | 107.751851851852 |
| 101 | 5202 | 4673.24814814815 | 528.751851851852 |
| 102 | 5231 | 5258.94814814815 | -27.9481481481483 |
| 103 | 4880 | 5273.84814814815 | -393.848148148148 |
| 104 | 7998 | 6509.46666666667 | 1488.53333333333 |
| 105 | 4977 | 5394.64814814815 | -417.648148148148 |
| 106 | 3531 | 3150.2 | 380.8 |
| 107 | 2025 | 1904.1 | 120.9 |
| 108 | 2205 | 2294.2 | -89.2000000000002 |
| 109 | 1442 | 1413.04814814815 | 28.9518518518523 |
| 110 | 2238 | 2119.44814814815 | 118.551851851852 |
| 111 | 2179 | 2378.94814814815 | -199.948148148148 |
| 112 | 3218 | 3195.24814814815 | 22.7518518518518 |
| 113 | 5139 | 4673.24814814815 | 465.751851851852 |
| 114 | 4990 | 5258.94814814815 | -268.948148148148 |
| 115 | 4914 | 5273.84814814815 | -359.848148148148 |
| 116 | 6084 | 6026.94814814815 | 57.0518518518522 |
| 117 | 5672 | 5877.16666666667 | -205.166666666666 |
| 118 | 3548 | 3150.2 | 397.8 |
| 119 | 1793 | 1904.1 | -111.1 |
| 120 | 2086 | 2294.2 | -208.2 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 16 | 0.520500232492503 | 0.958999535014994 | 0.479499767507497 |
| 17 | 0.457456814445005 | 0.91491362889001 | 0.542543185554995 |
| 18 | 0.491286168166536 | 0.982572336333073 | 0.508713831833464 |
| 19 | 0.974591431624298 | 0.0508171367514047 | 0.0254085683757023 |
| 20 | 0.956007824382729 | 0.087984351234542 | 0.043992175617271 |
| 21 | 0.952822149040614 | 0.0943557019187721 | 0.0471778509593861 |
| 22 | 0.927733439176923 | 0.144533121646155 | 0.0722665608230773 |
| 23 | 0.891290413685482 | 0.217419172629037 | 0.108709586314518 |
| 24 | 0.845139749204356 | 0.309720501591287 | 0.154860250795644 |
| 25 | 0.816066368258028 | 0.367867263483943 | 0.183933631741972 |
| 26 | 0.778391978223602 | 0.443216043552796 | 0.221608021776398 |
| 27 | 0.733235876692563 | 0.533528246614874 | 0.266764123307437 |
| 28 | 0.76149940105456 | 0.47700119789088 | 0.23850059894544 |
| 29 | 0.720412103270093 | 0.559175793459814 | 0.279587896729907 |
| 30 | 0.656423883099852 | 0.687152233800295 | 0.343576116900148 |
| 31 | 0.815536100407802 | 0.368927799184395 | 0.184463899592198 |
| 32 | 0.836008291541466 | 0.327983416917068 | 0.163991708458534 |
| 33 | 0.964296167772983 | 0.0714076644540345 | 0.0357038322270172 |
| 34 | 0.95097462942925 | 0.098050741141501 | 0.0490253705707505 |
| 35 | 0.932496205739957 | 0.135007588520085 | 0.0675037942600426 |
| 36 | 0.917271673948564 | 0.165456652102871 | 0.0827283260514357 |
| 37 | 0.890370870323578 | 0.219258259352843 | 0.109629129676422 |
| 38 | 0.858356144455053 | 0.283287711089894 | 0.141643855544947 |
| 39 | 0.844806705951746 | 0.310386588096509 | 0.155193294048254 |
| 40 | 0.807439663288462 | 0.385120673423076 | 0.192560336711538 |
| 41 | 0.771088198528791 | 0.457823602942418 | 0.228911801471209 |
| 42 | 0.75472668252674 | 0.49054663494652 | 0.24527331747326 |
| 43 | 0.803340547175074 | 0.393318905649852 | 0.196659452824926 |
| 44 | 0.775296543572673 | 0.449406912854654 | 0.224703456427327 |
| 45 | 0.824246598132319 | 0.351506803735363 | 0.175753401867681 |
| 46 | 0.789543408303336 | 0.420913183393327 | 0.210456591696664 |
| 47 | 0.7449891971262 | 0.510021605747601 | 0.255010802873801 |
| 48 | 0.695248539550705 | 0.609502920898591 | 0.304751460449295 |
| 49 | 0.64914258529489 | 0.70171482941022 | 0.35085741470511 |
| 50 | 0.625952648783099 | 0.748094702433802 | 0.374047351216901 |
| 51 | 0.583812340884255 | 0.83237531823149 | 0.416187659115745 |
| 52 | 0.580419118037579 | 0.839161763924842 | 0.419580881962421 |
| 53 | 0.522982025601529 | 0.954035948796942 | 0.477017974398471 |
| 54 | 0.494599714006704 | 0.989199428013409 | 0.505400285993296 |
| 55 | 0.568604920749011 | 0.862790158501978 | 0.431395079250989 |
| 56 | 0.610712530989107 | 0.778574938021786 | 0.389287469010893 |
| 57 | 0.604356923862377 | 0.791286152275245 | 0.395643076137623 |
| 58 | 0.555887298927832 | 0.888225402144336 | 0.444112701072168 |
| 59 | 0.501962381748649 | 0.996075236502702 | 0.498037618251351 |
| 60 | 0.443576505674494 | 0.887153011348987 | 0.556423494325506 |
| 61 | 0.392810557763178 | 0.785621115526355 | 0.607189442236822 |
| 62 | 0.338260357357019 | 0.676520714714039 | 0.66173964264298 |
| 63 | 0.303996858886585 | 0.60799371777317 | 0.696003141113415 |
| 64 | 0.29819326257858 | 0.59638652515716 | 0.70180673742142 |
| 65 | 0.39264115718513 | 0.78528231437026 | 0.60735884281487 |
| 66 | 0.381830148160044 | 0.763660296320088 | 0.618169851839956 |
| 67 | 0.452579468213294 | 0.905158936426588 | 0.547420531786706 |
| 68 | 0.468225295028881 | 0.936450590057761 | 0.531774704971119 |
| 69 | 0.414367106480836 | 0.828734212961672 | 0.585632893519164 |
| 70 | 0.367378360505186 | 0.734756721010371 | 0.632621639494814 |
| 71 | 0.315610035787561 | 0.631220071575122 | 0.684389964212439 |
| 72 | 0.264148757982249 | 0.528297515964497 | 0.735851242017751 |
| 73 | 0.218056589421646 | 0.436113178843293 | 0.781943410578354 |
| 74 | 0.182945397779109 | 0.365890795558217 | 0.817054602220891 |
| 75 | 0.146901774222912 | 0.293803548445823 | 0.853098225777088 |
| 76 | 0.129499130022847 | 0.258998260045693 | 0.870500869977153 |
| 77 | 0.107092382613771 | 0.214184765227543 | 0.892907617386229 |
| 78 | 0.157393485073194 | 0.314786970146389 | 0.842606514926806 |
| 79 | 0.175333669509155 | 0.35066733901831 | 0.824666330490845 |
| 80 | 0.157277319454865 | 0.31455463890973 | 0.842722680545135 |
| 81 | 0.409499627510222 | 0.818999255020445 | 0.590500372489778 |
| 82 | 0.385546680608642 | 0.771093361217284 | 0.614453319391358 |
| 83 | 0.323818272208159 | 0.647636544416319 | 0.67618172779184 |
| 84 | 0.293906123096032 | 0.587812246192064 | 0.706093876903968 |
| 85 | 0.240006082274063 | 0.480012164548127 | 0.759993917725936 |
| 86 | 0.19268235502326 | 0.38536471004652 | 0.80731764497674 |
| 87 | 0.166611573626602 | 0.333223147253205 | 0.833388426373398 |
| 88 | 0.145536515345209 | 0.291073030690419 | 0.85446348465479 |
| 89 | 0.16838044762938 | 0.33676089525876 | 0.83161955237062 |
| 90 | 0.476293492265304 | 0.952586984530607 | 0.523706507734696 |
| 91 | 0.496089677071655 | 0.99217935414331 | 0.503910322928345 |
| 92 | 0.664811690406729 | 0.670376619186542 | 0.335188309593271 |
| 93 | 0.980007747934455 | 0.039984504131091 | 0.0199922520655455 |
| 94 | 0.98110802201777 | 0.0377839559644598 | 0.0188919779822299 |
| 95 | 0.967484828347247 | 0.0650303433055052 | 0.0325151716527526 |
| 96 | 0.958942207293531 | 0.0821155854129375 | 0.0410577927064688 |
| 97 | 0.930363179898495 | 0.13927364020301 | 0.069636820101505 |
| 98 | 0.885816722291157 | 0.228366555417687 | 0.114183277708843 |
| 99 | 0.906491726419531 | 0.187016547160938 | 0.0935082735804692 |
| 100 | 0.846354777840099 | 0.307290444319802 | 0.153645222159901 |
| 101 | 0.770621085965886 | 0.458757828068229 | 0.229378914034114 |
| 102 | 0.685025807869903 | 0.629948384260194 | 0.314974192130097 |
| 103 | 0.549583297954495 | 0.90083340409101 | 0.450416702045505 |
| 104 | 0.975552912021272 | 0.0488941759574557 | 0.0244470879787279 |
| 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 | 3 | 0.0337078651685393 | OK |
| 10% type I error level | 10 | 0.112359550561798 | NOK |
