| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 2965.25393399467 + 528.345055465305X[t] -0.298382874958045Y1[t] + 0.104830390324839Y2[t] + 0.343772803301765Y3[t] + 0.0254522282235195Y4[t] + 1535.27129445461M1[t] + 2367.41761862446M2[t] + 2113.11253810597M3[t] + 2278.58440522865M4[t] + 1628.66643041343M5[t] -900.645928591427M6[t] -3025.6406474945M7[t] -2570.61346255146M8[t] -2393.54530684769M9[t] -1507.04339002879M10[t] -1056.65250730958M11[t] + 1.80202092207090t + 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) | 2965.25393399467 | 397.59171 | 7.458 | 0 | 0 |
| X | 528.345055465305 | 123.256157 | 4.2866 | 4.2e-05 | 2.1e-05 |
| Y1 | -0.298382874958045 | 0.092271 | -3.2338 | 0.001665 | 0.000833 |
| Y2 | 0.104830390324839 | 0.091343 | 1.1477 | 0.253905 | 0.126953 |
| Y3 | 0.343772803301765 | 0.09124 | 3.7678 | 0.000281 | 0.000141 |
| Y4 | 0.0254522282235195 | 0.092713 | 0.2745 | 0.784259 | 0.392129 |
| M1 | 1535.27129445461 | 211.525132 | 7.2581 | 0 | 0 |
| M2 | 2367.41761862446 | 320.263045 | 7.3921 | 0 | 0 |
| M3 | 2113.11253810597 | 470.469339 | 4.4915 | 1.9e-05 | 1e-05 |
| M4 | 2278.58440522865 | 580.70304 | 3.9238 | 0.000162 | 8.1e-05 |
| M5 | 1628.66643041343 | 674.185732 | 2.4158 | 0.017555 | 0.008778 |
| M6 | -900.645928591427 | 712.944589 | -1.2633 | 0.209487 | 0.104744 |
| M7 | -3025.6406474945 | 686.72077 | -4.4059 | 2.7e-05 | 1.3e-05 |
| M8 | -2570.61346255146 | 616.133527 | -4.1722 | 6.5e-05 | 3.3e-05 |
| M9 | -2393.54530684769 | 399.431255 | -5.9924 | 0 | 0 |
| M10 | -1507.04339002879 | 219.894571 | -6.8535 | 0 | 0 |
| M11 | -1056.65250730958 | 188.321523 | -5.6109 | 0 | 0 |
| t | 1.80202092207090 | 1.044326 | 1.7255 | 0.087583 | 0.043792 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.980496299065626 |
| R-squared | 0.961372992481389 |
| Adjusted R-squared | 0.954672389136324 |
| F-TEST (value) | 143.475586148434 |
| F-TEST (DF numerator) | 17 |
| F-TEST (DF denominator) | 98 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 347.035679883005 |
| Sum Squared Residuals | 11802508.7849622 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 4831 | 4435.82045163164 | 395.179548368358 |
| 2 | 5134 | 5183.12534128784 | -49.1253412878383 |
| 3 | 6250 | 5391.21436457787 | 858.785635422132 |
| 4 | 5760 | 5679.16507438827 | 80.8349256117315 |
| 5 | 6249 | 5427.32433548944 | 821.675664510558 |
| 6 | 2917 | 3093.9003539295 | -176.900353929499 |
| 7 | 1741 | 1876.13746925713 | -135.137469257125 |
| 8 | 2359 | 2490.20338449557 | -131.203384495573 |
| 9 | 1511 | 1756.73261984046 | -245.732619840460 |
| 10 | 2059 | 1945.42172017765 | 113.578279822347 |
| 11 | 2635 | 2327.72440939609 | 307.275590603906 |
| 12 | 2867 | 2995.96759539216 | -128.967595392162 |
| 13 | 4403 | 4691.0023952815 | -288.002395281504 |
| 14 | 5720 | 5302.91625076154 | 417.083749238463 |
| 15 | 4502 | 4912.87819820708 | -410.878198207081 |
| 16 | 5749 | 6115.58399482791 | -366.583994827911 |
| 17 | 5627 | 5459.54458494618 | 167.455415053817 |
| 18 | 2846 | 2713.96576449217 | 132.034235507825 |
| 19 | 1762 | 1805.47040589092 | -43.470405890918 |
| 20 | 2429 | 2284.01197930909 | 144.988020690912 |
| 21 | 1169 | 1191.08729740031 | -22.0872974003102 |
| 22 | 2154 | 2610.18821793167 | -456.188217931672 |
| 23 | 2249 | 2309.74888687266 | -60.7488868726552 |
| 24 | 2687 | 3026.93788051812 | -339.937880518121 |
| 25 | 4359 | 4749.82478743464 | -390.82478743464 |
| 26 | 5382 | 5188.52153767282 | 193.478462327175 |
| 27 | 4459 | 4959.03965914486 | -500.039659144862 |
| 28 | 6398 | 6094.89863316065 | 303.101366839349 |
| 29 | 4596 | 5165.69553782146 | -569.695537821463 |
| 30 | 3024 | 3087.87259927807 | -63.872599278065 |
| 31 | 1887 | 1887.91647631756 | -0.916476317562584 |
| 32 | 2070 | 1949.08691639495 | 120.913083605051 |
| 33 | 1351 | 1367.88511105497 | -16.8851110549693 |
| 34 | 2218 | 2059.02971719874 | 158.970282801261 |
| 35 | 2461 | 2739.46791258723 | -278.467912587227 |
| 36 | 3028 | 3045.44340734133 | -17.4434073413343 |
| 37 | 4784 | 4718.55828583566 | 65.4417141643435 |
| 38 | 4975 | 5193.58900688756 | -218.589006887556 |
| 39 | 4607 | 5269.28105451498 | -662.281054514983 |
| 40 | 6249 | 6184.47890109697 | 64.5210989030287 |
| 41 | 4809 | 5118.19540107432 | -309.195401074316 |
| 42 | 3157 | 3070.84088782014 | 86.15911217986 |
| 43 | 1910 | 1844.72946023730 | 65.2705397626976 |
| 44 | 2228 | 2047.22202834694 | 180.777971653060 |
| 45 | 1594 | 1395.91907430466 | 198.080925695335 |
| 46 | 2467 | 2036.00205214978 | 430.997947850222 |
| 47 | 2222 | 2238.82506134197 | -16.8250613419717 |
| 48 | 3607 | 3780.387231439 | -173.387231438997 |
| 49 | 4685 | 4634.14870849262 | 50.8512915073828 |
| 50 | 4962 | 5229.62586340987 | -267.62586340987 |
| 51 | 5770 | 5477.36744487843 | 292.63255512157 |
| 52 | 5480 | 5838.42440612594 | -358.424406125936 |
| 53 | 5000 | 5484.20500989264 | -484.20500989264 |
| 54 | 3228 | 3354.33633088125 | -126.336330881250 |
| 55 | 1993 | 1630.43078741707 | 362.569212582929 |
| 56 | 2288 | 2097.61130043009 | 190.388699569913 |
| 57 | 1580 | 1437.61051989411 | 142.389480105888 |
| 58 | 2111 | 2098.43373776145 | 12.5662622385519 |
| 59 | 2192 | 2387.94489356800 | -195.944893567997 |
| 60 | 3601 | 3242.01260877882 | 358.987391221176 |
| 61 | 4665 | 5060.02395139222 | -395.023951392222 |
| 62 | 4876 | 5237.21461228531 | -361.214612285307 |
| 63 | 5813 | 5519.72981171666 | 293.27018828334 |
| 64 | 5589 | 5831.17461056428 | -242.174610564277 |
| 65 | 5331 | 5447.73972872261 | -116.739728722610 |
| 66 | 3075 | 3301.21570179515 | -226.215701795149 |
| 67 | 2002 | 1770.97215892153 | 231.027841078471 |
| 68 | 2306 | 2217.07414666986 | 88.9258533301374 |
| 69 | 1507 | 1410.63480135946 | 96.3651986405435 |
| 70 | 1992 | 2142.9266500356 | -150.926650035601 |
| 71 | 2487 | 2443.84106877259 | 43.1589312274148 |
| 72 | 3490 | 3138.50182074939 | 351.498179250611 |
| 73 | 4647 | 4574.58163500471 | 72.4183649952922 |
| 74 | 5594 | 5879.30279905408 | -285.302799054077 |
| 75 | 5611 | 5294.57783769523 | 316.422162304771 |
| 76 | 5788 | 5979.32731483165 | -191.327314831647 |
| 77 | 6204 | 5635.18078148784 | 568.819218512163 |
| 78 | 3013 | 3032.0455442938 | -19.0455442937992 |
| 79 | 1931 | 1965.88251674326 | -34.8825167432633 |
| 80 | 2549 | 2558.56274835552 | -9.56274835551595 |
| 81 | 1504 | 1353.21493753086 | 150.785062469139 |
| 82 | 2090 | 2164.93392738998 | -74.9339273899778 |
| 83 | 2702 | 2517.63898991903 | 184.361010080968 |
| 84 | 2939 | 3111.40070499850 | -172.400704998505 |
| 85 | 4500 | 4816.76676213019 | -316.766762130185 |
| 86 | 6208 | 5435.08820327925 | 772.91179672075 |
| 87 | 6415 | 5461.98340607218 | 953.016593927818 |
| 88 | 5657 | 5760.85881425316 | -103.858814253161 |
| 89 | 5964 | 5987.51184667179 | -23.5118466717879 |
| 90 | 3163 | 3403.56990619989 | -240.569906199886 |
| 91 | 1997 | 1893.01939714562 | 103.980602854376 |
| 92 | 2422 | 2490.37857353216 | -68.3785735321568 |
| 93 | 1376 | 1465.11000519844 | -89.110005198444 |
| 94 | 2202 | 2237.94456612965 | -35.9445661296484 |
| 95 | 2683 | 2450.44677007043 | 232.553229929570 |
| 96 | 3303 | 3103.19988259693 | 199.800117403072 |
| 97 | 5202 | 4763.03253805132 | 438.967461948678 |
| 98 | 5231 | 5281.72490450009 | -50.7249045000937 |
| 99 | 4880 | 5445.02331257937 | -565.023312579367 |
| 100 | 7998 | 6917.01966148775 | 1080.98033851225 |
| 101 | 4977 | 4831.70857369831 | 145.291426301688 |
| 102 | 3531 | 3412.54791855619 | 118.452081443810 |
| 103 | 2025 | 2467.07411718163 | -442.074117181627 |
| 104 | 2205 | 2262.50559715014 | -57.5055971501397 |
| 105 | 1442 | 1655.80563341672 | -213.805633416722 |
| 106 | 2238 | 2236.11941122548 | 1.88058877451727 |
| 107 | 2179 | 2394.36200747201 | -215.362007472007 |
| 108 | 3218 | 3296.14886818574 | -78.1488681857402 |
| 109 | 5139 | 4771.2404847455 | 367.759515254496 |
| 110 | 4990 | 5140.89148086165 | -150.891480861647 |
| 111 | 4914 | 5489.90491061334 | -575.904910613338 |
| 112 | 6084 | 6351.06858926342 | -267.068589263424 |
| 113 | 5672 | 5871.89420019541 | -199.894200195409 |
| 114 | 3548 | 3031.70499275385 | 516.295007246151 |
| 115 | 1793 | 1899.36721088798 | -106.367210887977 |
| 116 | 2086 | 2545.34332531569 | -459.34332531569 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 21 | 0.977996689939066 | 0.0440066201218676 | 0.0220033100609338 |
| 22 | 0.967163269190447 | 0.0656734616191054 | 0.0328367308095527 |
| 23 | 0.936298360044544 | 0.127403279910912 | 0.063701639955456 |
| 24 | 0.894814447927818 | 0.210371104144364 | 0.105185552072182 |
| 25 | 0.841637108456265 | 0.316725783087471 | 0.158362891543735 |
| 26 | 0.818423680070123 | 0.363152639859754 | 0.181576319929877 |
| 27 | 0.795967518174697 | 0.408064963650605 | 0.204032481825303 |
| 28 | 0.852737883669282 | 0.294524232661436 | 0.147262116330718 |
| 29 | 0.847661920947159 | 0.304676158105682 | 0.152338079052841 |
| 30 | 0.790478688272135 | 0.41904262345573 | 0.209521311727865 |
| 31 | 0.792762693917551 | 0.414474612164897 | 0.207237306082449 |
| 32 | 0.81056222024591 | 0.378875559508179 | 0.189437779754090 |
| 33 | 0.762577150068261 | 0.474845699863478 | 0.237422849931739 |
| 34 | 0.740420031670686 | 0.519159936658628 | 0.259579968329314 |
| 35 | 0.728840973975326 | 0.542318052049348 | 0.271159026024674 |
| 36 | 0.702126666933158 | 0.595746666133683 | 0.297873333066842 |
| 37 | 0.655695812579926 | 0.688608374840149 | 0.344304187420074 |
| 38 | 0.606213495404496 | 0.787573009191008 | 0.393786504595504 |
| 39 | 0.6896980484159 | 0.6206039031682 | 0.3103019515841 |
| 40 | 0.640646955269802 | 0.718706089460395 | 0.359353044730198 |
| 41 | 0.601188897381349 | 0.797622205237301 | 0.398811102618651 |
| 42 | 0.551379570235905 | 0.89724085952819 | 0.448620429764095 |
| 43 | 0.531098230846540 | 0.937803538306921 | 0.468901769153460 |
| 44 | 0.497159609765746 | 0.994319219531492 | 0.502840390234254 |
| 45 | 0.447822999735352 | 0.895645999470704 | 0.552177000264648 |
| 46 | 0.462378607057366 | 0.924757214114731 | 0.537621392942634 |
| 47 | 0.400307703445326 | 0.800615406890652 | 0.599692296554674 |
| 48 | 0.388796440133722 | 0.777592880267444 | 0.611203559866278 |
| 49 | 0.334315036793749 | 0.668630073587497 | 0.665684963206251 |
| 50 | 0.315434995450432 | 0.630869990900864 | 0.684565004549568 |
| 51 | 0.298964446870471 | 0.597928893740942 | 0.701035553129529 |
| 52 | 0.279035482166561 | 0.558070964333121 | 0.72096451783344 |
| 53 | 0.345093124502053 | 0.690186249004105 | 0.654906875497947 |
| 54 | 0.305545316270471 | 0.611090632540943 | 0.694454683729529 |
| 55 | 0.328763572654128 | 0.657527145308257 | 0.671236427345872 |
| 56 | 0.289758239699939 | 0.579516479399879 | 0.71024176030006 |
| 57 | 0.240705651492122 | 0.481411302984245 | 0.759294348507878 |
| 58 | 0.196365807942924 | 0.392731615885848 | 0.803634192057076 |
| 59 | 0.171857443373467 | 0.343714886746935 | 0.828142556626533 |
| 60 | 0.168802888341375 | 0.33760577668275 | 0.831197111658625 |
| 61 | 0.2303141410359 | 0.4606282820718 | 0.7696858589641 |
| 62 | 0.225259014926522 | 0.450518029853044 | 0.774740985073478 |
| 63 | 0.20939810612825 | 0.4187962122565 | 0.79060189387175 |
| 64 | 0.195304966520725 | 0.39060993304145 | 0.804695033479275 |
| 65 | 0.167782868098302 | 0.335565736196604 | 0.832217131901698 |
| 66 | 0.175808155728939 | 0.351616311457878 | 0.824191844271061 |
| 67 | 0.143956092380609 | 0.287912184761219 | 0.85604390761939 |
| 68 | 0.111696929495347 | 0.223393858990695 | 0.888303070504653 |
| 69 | 0.0840044195616697 | 0.168008839123339 | 0.91599558043833 |
| 70 | 0.0710833359831426 | 0.142166671966285 | 0.928916664016857 |
| 71 | 0.0537543134473073 | 0.107508626894615 | 0.946245686552693 |
| 72 | 0.0472781239070489 | 0.0945562478140978 | 0.95272187609295 |
| 73 | 0.0379886761693622 | 0.0759773523387244 | 0.962011323830638 |
| 74 | 0.133446867663141 | 0.266893735326283 | 0.866553132336859 |
| 75 | 0.134913161900216 | 0.269826323800433 | 0.865086838099784 |
| 76 | 0.130488013977086 | 0.260976027954172 | 0.869511986022914 |
| 77 | 0.192827234595107 | 0.385654469190214 | 0.807172765404893 |
| 78 | 0.181048796836782 | 0.362097593673564 | 0.818951203163218 |
| 79 | 0.150653757302872 | 0.301307514605745 | 0.849346242697128 |
| 80 | 0.118704120495735 | 0.23740824099147 | 0.881295879504265 |
| 81 | 0.0865197459780516 | 0.173039491956103 | 0.913480254021948 |
| 82 | 0.0711743542110573 | 0.142348708422115 | 0.928825645788943 |
| 83 | 0.04898634617079 | 0.09797269234158 | 0.95101365382921 |
| 84 | 0.047606557394901 | 0.095213114789802 | 0.9523934426051 |
| 85 | 0.214504976801004 | 0.429009953602008 | 0.785495023198996 |
| 86 | 0.304292600561865 | 0.60858520112373 | 0.695707399438135 |
| 87 | 0.478710915609278 | 0.957421831218556 | 0.521289084390722 |
| 88 | 0.752829217873552 | 0.494341564252896 | 0.247170782126448 |
| 89 | 0.951417590403074 | 0.0971648191938516 | 0.0485824095969258 |
| 90 | 0.985029874751647 | 0.0299402504967060 | 0.0149701252483530 |
| 91 | 0.978460949026727 | 0.0430781019465465 | 0.0215390509732733 |
| 92 | 0.952142814777196 | 0.0957143704456076 | 0.0478571852228038 |
| 93 | 0.914126378584064 | 0.171747242831872 | 0.0858736214159358 |
| 94 | 0.8498789023184 | 0.300242195363201 | 0.150121097681600 |
| 95 | 0.950314464901982 | 0.0993710701960357 | 0.0496855350980178 |
| 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 | 0.04 | OK |
| 10% type I error level | 11 | 0.146666666666667 | NOK |
