| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 2187.30135021097 + 471.720675105485X[t] -862.255625879044M1[t] -157.475302390999M2[t] + 100.405021097046M3[t] + 915.085344585091M4[t] + 2391.46566807314M5[t] + 2975.54599156118M6[t] + 2988.82631504923M7[t] + 3740.30663853727M8[t] + 3106.38696202532M9[t] + 859.23935302391M10[t] -388.480323488046M11[t] + 1.61967651195499t + 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) | 2187.30135021097 | 138.566337 | 15.7852 | 0 | 0 |
| X | 471.720675105485 | 134.877022 | 3.4974 | 0.000688 | 0.000344 |
| M1 | -862.255625879044 | 172.390428 | -5.0018 | 2e-06 | 1e-06 |
| M2 | -157.475302390999 | 172.323461 | -0.9138 | 0.362877 | 0.181439 |
| M3 | 100.405021097046 | 172.262469 | 0.5829 | 0.561225 | 0.280613 |
| M4 | 915.085344585091 | 172.207458 | 5.3139 | 1e-06 | 0 |
| M5 | 2391.46566807314 | 172.158433 | 13.8911 | 0 | 0 |
| M6 | 2975.54599156118 | 172.115399 | 17.2881 | 0 | 0 |
| M7 | 2988.82631504923 | 172.078362 | 17.369 | 0 | 0 |
| M8 | 3740.30663853727 | 172.047324 | 21.74 | 0 | 0 |
| M9 | 3106.38696202532 | 172.02229 | 18.058 | 0 | 0 |
| M10 | 859.23935302391 | 171.465587 | 5.0111 | 2e-06 | 1e-06 |
| M11 | -388.480323488046 | 171.456544 | -2.2658 | 0.025498 | 0.012749 |
| t | 1.61967651195499 | 1.016674 | 1.5931 | 0.114112 | 0.057056 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.974833105636288 |
| R-squared | 0.95029958384449 |
| Adjusted R-squared | 0.944204249787683 |
| F-TEST (value) | 155.906070936853 |
| F-TEST (DF numerator) | 13 |
| F-TEST (DF denominator) | 106 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 383.381748113083 |
| Sum Squared Residuals | 15580045.8673418 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 1579 | 1326.66540084389 | 252.334599156115 |
| 2 | 2146 | 2033.06540084388 | 112.934599156119 |
| 3 | 2462 | 2292.56540084388 | 169.434599156118 |
| 4 | 3695 | 3108.86540084388 | 586.134599156118 |
| 5 | 4831 | 4586.86540084388 | 244.134599156118 |
| 6 | 5134 | 5172.56540084388 | -38.5654008438817 |
| 7 | 6250 | 5187.46540084388 | 1062.53459915612 |
| 8 | 5760 | 5940.56540084388 | -180.565400843881 |
| 9 | 6249 | 5308.26540084388 | 940.734599156118 |
| 10 | 2917 | 3062.73746835443 | -145.737468354431 |
| 11 | 1741 | 1816.63746835443 | -75.6374683544286 |
| 12 | 2359 | 2206.73746835443 | 152.26253164557 |
| 13 | 1511 | 1817.82219409283 | -306.822194092826 |
| 14 | 2059 | 2052.50151898734 | 6.49848101265803 |
| 15 | 2635 | 2312.00151898734 | 322.998481012658 |
| 16 | 2867 | 3128.30151898734 | -261.301518987342 |
| 17 | 4403 | 4606.30151898734 | -203.301518987342 |
| 18 | 5720 | 5192.00151898734 | 527.998481012658 |
| 19 | 4502 | 5206.90151898734 | -704.901518987342 |
| 20 | 5749 | 5960.00151898734 | -211.001518987342 |
| 21 | 5627 | 5327.70151898734 | 299.298481012658 |
| 22 | 2846 | 3082.17358649789 | -236.17358649789 |
| 23 | 1762 | 1836.07358649789 | -74.0735864978905 |
| 24 | 2429 | 2226.17358649789 | 202.82641350211 |
| 25 | 1169 | 1365.53763713080 | -196.537637130801 |
| 26 | 2154 | 2543.65831223629 | -389.658312236287 |
| 27 | 2249 | 2331.4376371308 | -82.4376371308018 |
| 28 | 2687 | 3147.7376371308 | -460.737637130801 |
| 29 | 4359 | 4625.7376371308 | -266.737637130802 |
| 30 | 5382 | 5211.4376371308 | 170.562362869198 |
| 31 | 4459 | 5226.3376371308 | -767.337637130802 |
| 32 | 6398 | 5979.4376371308 | 418.562362869198 |
| 33 | 4596 | 5347.1376371308 | -751.137637130802 |
| 34 | 3024 | 3101.60970464135 | -77.60970464135 |
| 35 | 1887 | 1855.50970464135 | 31.4902953586496 |
| 36 | 2070 | 2245.60970464135 | -175.609704641351 |
| 37 | 1351 | 1384.97375527426 | -33.9737552742612 |
| 38 | 2218 | 2091.37375527426 | 126.626244725738 |
| 39 | 2461 | 2822.59443037975 | -361.594430379747 |
| 40 | 3028 | 3167.17375527426 | -139.173755274262 |
| 41 | 4784 | 4645.17375527426 | 138.826244725738 |
| 42 | 4975 | 5230.87375527426 | -255.873755274262 |
| 43 | 4607 | 5245.77375527426 | -638.773755274262 |
| 44 | 6249 | 5998.87375527426 | 250.126244725738 |
| 45 | 4809 | 5366.57375527426 | -557.573755274262 |
| 46 | 3157 | 3121.04582278481 | 35.9541772151900 |
| 47 | 1910 | 1874.94582278481 | 35.0541772151897 |
| 48 | 2228 | 2265.04582278481 | -37.0458227848103 |
| 49 | 1594 | 1404.40987341772 | 189.590126582279 |
| 50 | 2467 | 2110.80987341772 | 356.190126582279 |
| 51 | 2222 | 2370.30987341772 | -148.309873417722 |
| 52 | 3607 | 3658.33054852321 | -51.3305485232071 |
| 53 | 4685 | 4664.60987341772 | 20.3901265822786 |
| 54 | 4962 | 5250.30987341772 | -288.309873417722 |
| 55 | 5770 | 5265.20987341772 | 504.790126582279 |
| 56 | 5480 | 6018.30987341772 | -538.309873417722 |
| 57 | 5000 | 5386.00987341772 | -386.009873417722 |
| 58 | 3228 | 3140.48194092827 | 87.51805907173 |
| 59 | 1993 | 1894.38194092827 | 98.6180590717298 |
| 60 | 2288 | 2284.48194092827 | 3.51805907172975 |
| 61 | 1580 | 1423.84599156118 | 156.154008438819 |
| 62 | 2111 | 2130.24599156118 | -19.2459915611815 |
| 63 | 2192 | 2389.74599156118 | -197.745991561182 |
| 64 | 3601 | 3206.04599156118 | 394.954008438818 |
| 65 | 4665 | 5155.76666666667 | -490.766666666667 |
| 66 | 4876 | 5269.74599156118 | -393.745991561182 |
| 67 | 5813 | 5284.64599156118 | 528.354008438819 |
| 68 | 5589 | 6037.74599156118 | -448.745991561182 |
| 69 | 5331 | 5405.44599156118 | -74.4459915611815 |
| 70 | 3075 | 3159.91805907173 | -84.9180590717297 |
| 71 | 2002 | 1913.81805907173 | 88.1819409282699 |
| 72 | 2306 | 2303.91805907173 | 2.0819409282701 |
| 73 | 1507 | 1443.28210970464 | 63.7178902953591 |
| 74 | 1992 | 2149.68210970464 | -157.682109704641 |
| 75 | 2487 | 2409.18210970464 | 77.8178902953588 |
| 76 | 3490 | 3225.48210970464 | 264.517890295359 |
| 77 | 4647 | 4703.48210970464 | -56.4821097046412 |
| 78 | 5594 | 5760.90278481013 | -166.902784810127 |
| 79 | 5611 | 5304.08210970464 | 306.917890295359 |
| 80 | 5788 | 6057.18210970464 | -269.182109704641 |
| 81 | 6204 | 5424.88210970464 | 779.117890295359 |
| 82 | 3013 | 3179.35417721519 | -166.354177215190 |
| 83 | 1931 | 1933.25417721519 | -2.25417721519004 |
| 84 | 2549 | 2323.35417721519 | 225.645822784810 |
| 85 | 1504 | 1462.7182278481 | 41.2817721518992 |
| 86 | 2090 | 2169.1182278481 | -79.1182278481013 |
| 87 | 2702 | 2428.6182278481 | 273.381772151899 |
| 88 | 2939 | 3244.9182278481 | -305.918227848101 |
| 89 | 4500 | 4722.9182278481 | -222.918227848101 |
| 90 | 6208 | 5308.6182278481 | 899.3817721519 |
| 91 | 6415 | 5795.23890295359 | 619.761097046414 |
| 92 | 5657 | 6076.6182278481 | -419.618227848101 |
| 93 | 5964 | 5444.3182278481 | 519.681772151899 |
| 94 | 3163 | 3198.79029535865 | -35.7902953586497 |
| 95 | 1997 | 1952.69029535865 | 44.30970464135 |
| 96 | 2422 | 2342.79029535865 | 79.2097046413504 |
| 97 | 1376 | 1482.15434599156 | -106.154345991561 |
| 98 | 2202 | 2188.55434599156 | 13.4456540084387 |
| 99 | 2683 | 2448.05434599156 | 234.945654008439 |
| 100 | 3303 | 3264.35434599156 | 38.6456540084388 |
| 101 | 5202 | 4742.35434599156 | 459.645654008439 |
| 102 | 5231 | 5328.05434599156 | -97.0543459915613 |
| 103 | 4880 | 5342.95434599156 | -462.954345991562 |
| 104 | 7998 | 6567.77502109705 | 1430.22497890295 |
| 105 | 4977 | 5463.75434599156 | -486.754345991561 |
| 106 | 3531 | 3218.22641350211 | 312.77358649789 |
| 107 | 2025 | 1972.12641350211 | 52.8735864978902 |
| 108 | 2205 | 2362.22641350211 | -157.22641350211 |
| 109 | 1442 | 1501.59046413502 | -59.5904641350206 |
| 110 | 2238 | 2207.99046413502 | 30.0095358649788 |
| 111 | 2179 | 2467.49046413502 | -288.490464135021 |
| 112 | 3218 | 3283.79046413502 | -65.790464135021 |
| 113 | 5139 | 4761.79046413502 | 377.209535864979 |
| 114 | 4990 | 5347.49046413502 | -357.490464135021 |
| 115 | 4914 | 5362.39046413502 | -448.390464135022 |
| 116 | 6084 | 6115.49046413502 | -31.4904641350208 |
| 117 | 5672 | 5954.9111392405 | -282.911139240506 |
| 118 | 3548 | 3237.66253164557 | 310.337468354430 |
| 119 | 1793 | 1991.56253164557 | -198.562531645570 |
| 120 | 2086 | 2381.66253164557 | -295.66253164557 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 17 | 0.443024576432498 | 0.886049152864996 | 0.556975423567502 |
| 18 | 0.648999851226522 | 0.702000297546955 | 0.351000148773478 |
| 19 | 0.970014206300081 | 0.0599715873998378 | 0.0299857936999189 |
| 20 | 0.95258516882444 | 0.09482966235112 | 0.04741483117556 |
| 21 | 0.933117010759867 | 0.133765978480267 | 0.0668829892401333 |
| 22 | 0.902521128519988 | 0.194957742960024 | 0.097478871480012 |
| 23 | 0.86859800449697 | 0.262803991006059 | 0.131401995503029 |
| 24 | 0.837252512334933 | 0.325494975330135 | 0.162747487665067 |
| 25 | 0.777806270471462 | 0.444387459057076 | 0.222193729528538 |
| 26 | 0.729919159699901 | 0.540161680600197 | 0.270080840300099 |
| 27 | 0.655570596145894 | 0.688858807708213 | 0.344429403854107 |
| 28 | 0.603122741748647 | 0.793754516502706 | 0.396877258251353 |
| 29 | 0.529302422797248 | 0.941395154405503 | 0.470697577202752 |
| 30 | 0.48962076276346 | 0.97924152552692 | 0.51037923723654 |
| 31 | 0.555642056298079 | 0.888715887403841 | 0.444357943701921 |
| 32 | 0.752963366224755 | 0.49407326755049 | 0.247036633775245 |
| 33 | 0.881016246037458 | 0.237967507925084 | 0.118983753962542 |
| 34 | 0.872581882552799 | 0.254836234894402 | 0.127418117447201 |
| 35 | 0.858788099900733 | 0.282423800198535 | 0.141211900099267 |
| 36 | 0.817326914674931 | 0.365346170650138 | 0.182673085325069 |
| 37 | 0.793786710969723 | 0.412426578060553 | 0.206213289030277 |
| 38 | 0.783090001931405 | 0.43381999613719 | 0.216909998068595 |
| 39 | 0.758454533825266 | 0.483090932349469 | 0.241545466174734 |
| 40 | 0.71539097425275 | 0.5692180514945 | 0.28460902574725 |
| 41 | 0.7105548564248 | 0.578890287150401 | 0.289445143575201 |
| 42 | 0.661942361487671 | 0.676115277024658 | 0.338057638512329 |
| 43 | 0.675636356072574 | 0.648727287854853 | 0.324363643927427 |
| 44 | 0.68354029977541 | 0.632919400449179 | 0.316459700224589 |
| 45 | 0.694449810533577 | 0.611100378932847 | 0.305550189466423 |
| 46 | 0.677531425197789 | 0.644937149604421 | 0.322468574802211 |
| 47 | 0.640126622228259 | 0.719746755543483 | 0.359873377771741 |
| 48 | 0.585109465662682 | 0.829781068674637 | 0.414890534337318 |
| 49 | 0.568474796633989 | 0.863050406732023 | 0.431525203366011 |
| 50 | 0.58427182563981 | 0.831456348720379 | 0.415728174360190 |
| 51 | 0.527721548527181 | 0.944556902945638 | 0.472278451472819 |
| 52 | 0.543974027274959 | 0.912051945450082 | 0.456025972725041 |
| 53 | 0.493823320730366 | 0.987646641460731 | 0.506176679269634 |
| 54 | 0.44812478027621 | 0.89624956055242 | 0.55187521972379 |
| 55 | 0.565774468878252 | 0.868451062243495 | 0.434225531121748 |
| 56 | 0.581772772842267 | 0.836454454315466 | 0.418227227157733 |
| 57 | 0.559888238580053 | 0.880223522839893 | 0.440111761419947 |
| 58 | 0.520887236985997 | 0.958225526028005 | 0.479112763014002 |
| 59 | 0.473564937248844 | 0.947129874497688 | 0.526435062751156 |
| 60 | 0.416651682848209 | 0.833303365696418 | 0.583348317151791 |
| 61 | 0.374102620725668 | 0.748205241451335 | 0.625897379274332 |
| 62 | 0.319344899611905 | 0.63868979922381 | 0.680655100388095 |
| 63 | 0.28005520257129 | 0.56011040514258 | 0.71994479742871 |
| 64 | 0.287011666546647 | 0.574023333093294 | 0.712988333453353 |
| 65 | 0.374994589809749 | 0.749989179619497 | 0.625005410190251 |
| 66 | 0.360857044323079 | 0.721714088646158 | 0.639142955676921 |
| 67 | 0.437548833663188 | 0.875097667326376 | 0.562451166336812 |
| 68 | 0.453667447853034 | 0.907334895706068 | 0.546332552146966 |
| 69 | 0.404650948456199 | 0.809301896912398 | 0.595349051543801 |
| 70 | 0.365359943144178 | 0.730719886288357 | 0.634640056855822 |
| 71 | 0.314317630712232 | 0.628635261424464 | 0.685682369287768 |
| 72 | 0.264344657971422 | 0.528689315942845 | 0.735655342028578 |
| 73 | 0.217928322530693 | 0.435856645061386 | 0.782071677469307 |
| 74 | 0.185337896231835 | 0.370675792463669 | 0.814662103768165 |
| 75 | 0.151238220034319 | 0.302476440068638 | 0.84876177996568 |
| 76 | 0.129474217743623 | 0.258948435487247 | 0.870525782256377 |
| 77 | 0.112470190417367 | 0.224940380834733 | 0.887529809582633 |
| 78 | 0.211606916296705 | 0.423213832593411 | 0.788393083703295 |
| 79 | 0.208791527766089 | 0.417583055532178 | 0.791208472233911 |
| 80 | 0.215245998362681 | 0.430491996725362 | 0.784754001637319 |
| 81 | 0.422602950832748 | 0.845205901665497 | 0.577397049167252 |
| 82 | 0.436859299923177 | 0.873718599846355 | 0.563140700076823 |
| 83 | 0.381155297882831 | 0.762310595765661 | 0.61884470211717 |
| 84 | 0.326395737031003 | 0.652791474062006 | 0.673604262968997 |
| 85 | 0.266771032358745 | 0.53354206471749 | 0.733228967641255 |
| 86 | 0.227281441172124 | 0.454562882344249 | 0.772718558827876 |
| 87 | 0.185359857064269 | 0.370719714128537 | 0.814640142935732 |
| 88 | 0.186952302305534 | 0.373904604611068 | 0.813047697694466 |
| 89 | 0.301678936713896 | 0.603357873427791 | 0.698321063286104 |
| 90 | 0.533651154455584 | 0.932697691088831 | 0.466348845544416 |
| 91 | 0.514002840654945 | 0.97199431869011 | 0.485997159345055 |
| 92 | 0.817406295603407 | 0.365187408793186 | 0.182593704396593 |
| 93 | 0.984769524386675 | 0.0304609512266500 | 0.0152304756133250 |
| 94 | 0.99662538091856 | 0.00674923816288166 | 0.00337461908144083 |
| 95 | 0.99429218550515 | 0.0114156289896999 | 0.00570781449484997 |
| 96 | 0.987667353063601 | 0.0246652938727971 | 0.0123326469363985 |
| 97 | 0.982750145224322 | 0.0344997095513566 | 0.0172498547756783 |
| 98 | 0.975265200314984 | 0.0494695993700329 | 0.0247347996850164 |
| 99 | 0.966159772443998 | 0.0676804551120045 | 0.0338402275560022 |
| 100 | 0.935473244145092 | 0.129053511709816 | 0.064526755854908 |
| 101 | 0.892276882229258 | 0.215446235541484 | 0.107723117770742 |
| 102 | 0.795049941459592 | 0.409900117080817 | 0.204950058540408 |
| 103 | 0.738603123706794 | 0.522793752586411 | 0.261396876293206 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 1 | 0.0114942528735632 | NOK |
| 5% type I error level | 6 | 0.0689655172413793 | NOK |
| 10% type I error level | 9 | 0.103448275862069 | NOK |
