| Multiple Linear Regression - Estimated Regression Equation |
| Yt-5[t] = + 7020.47641726063 + 0.250863300117026`Yt-6`[t] -679.47273995534M1[t] -63.2724898724251M2[t] + 72.1050849430458M3[t] -877.017102218858M4[t] + 302.088829651828M5[t] -322.230497226616M6[t] -56.5172825314797M7[t] -153.698715001137M8[t] + 425.146565088753M9[t] + 95.456109910176M10[t] -136.157685669757M11[t] + 7.52661398200408t + 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) | 7020.47641726063 | 1206.106206 | 5.8208 | 0 | 0 |
| `Yt-6` | 0.250863300117026 | 0.129066 | 1.9437 | 0.057057 | 0.028528 |
| M1 | -679.47273995534 | 166.985747 | -4.069 | 0.000152 | 7.6e-05 |
| M2 | -63.2724898724251 | 182.470663 | -0.3468 | 0.730099 | 0.36505 |
| M3 | 72.1050849430458 | 167.15312 | 0.4314 | 0.667884 | 0.333942 |
| M4 | -877.017102218858 | 166.567529 | -5.2652 | 2e-06 | 1e-06 |
| M5 | 302.088829651828 | 194.598402 | 1.5524 | 0.126309 | 0.063155 |
| M6 | -322.230497226616 | 167.476942 | -1.924 | 0.059532 | 0.029766 |
| M7 | -56.5172825314797 | 168.305294 | -0.3358 | 0.738298 | 0.369149 |
| M8 | -153.698715001137 | 166.155366 | -0.925 | 0.358991 | 0.179496 |
| M9 | 425.146565088753 | 166.583286 | 2.5522 | 0.013514 | 0.006757 |
| M10 | 95.456109910176 | 184.141959 | 0.5184 | 0.60627 | 0.303135 |
| M11 | -136.157685669757 | 177.169138 | -0.7685 | 0.445467 | 0.222733 |
| t | 7.52661398200408 | 2.082157 | 3.6148 | 0.000653 | 0.000326 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.855889471630712 |
| R-squared | 0.7325467876483 |
| Adjusted R-squared | 0.669330573819716 |
| F-TEST (value) | 11.5879573179543 |
| F-TEST (DF numerator) | 13 |
| F-TEST (DF denominator) | 55 |
| p-value | 1.81126225129447e-11 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 274.182074467497 |
| Sum Squared Residuals | 4134669.5477615 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 9081 | 8781.90430242245 | 299.095697577554 |
| 2 | 9084 | 9250.34678371493 | -166.346783714931 |
| 3 | 9743 | 9394.00356241276 | 348.996437587244 |
| 4 | 8587 | 8617.72690400998 | -30.7269040099772 |
| 5 | 9731 | 9514.36147492739 | 216.638525072615 |
| 6 | 9563 | 9184.55637736483 | 378.443622635174 |
| 7 | 9998 | 9415.6511716223 | 582.348828377696 |
| 8 | 9437 | 9435.12188868556 | 1.87811131444258 |
| 9 | 10038 | 9880.7594713918 | 157.240528608201 |
| 10 | 9918 | 9709.36447356556 | 208.635526434441 |
| 11 | 9252 | 9455.1736959536 | -203.173695953588 |
| 12 | 9737 | 9431.7830377274 | 305.216962272592 |
| 13 | 9035 | 8881.50561231083 | 153.49438768917 |
| 14 | 9133 | 9329.1264396936 | -196.126439693597 |
| 15 | 9487 | 9496.61523190254 | -9.61523190254031 |
| 16 | 8700 | 8643.82526696407 | 56.1747330359326 |
| 17 | 9627 | 9633.02839562466 | -6.02839562465827 |
| 18 | 8947 | 9248.7859619367 | -301.785961936702 |
| 19 | 9283 | 9351.43874653426 | -68.4387465342645 |
| 20 | 8829 | 9346.07399688593 | -517.073996885932 |
| 21 | 9947 | 9818.5539527047 | 128.446047295304 |
| 22 | 9628 | 9776.85528103896 | -148.855281038959 |
| 23 | 9318 | 9472.7427067037 | -154.742706703698 |
| 24 | 9605 | 9538.65938331918 | 66.3406166808187 |
| 25 | 8640 | 8938.71102447943 | -298.711024479432 |
| 26 | 9214 | 9320.35480393142 | -106.354803931420 |
| 27 | 9567 | 9607.25452699607 | -40.2545269960684 |
| 28 | 8547 | 8754.21369875748 | -207.213698757478 |
| 29 | 9185 | 9684.9656784908 | -499.965678490802 |
| 30 | 9470 | 9228.22375106902 | 241.776248930975 |
| 31 | 9123 | 9572.95962027952 | -449.959620279518 |
| 32 | 9278 | 9396.25523665126 | -118.255236651257 |
| 33 | 10170 | 10021.5109422413 | 148.489057758711 |
| 34 | 9434 | 9923.1171647491 | -489.117164749105 |
| 35 | 9655 | 9514.39459426504 | 140.605405734956 |
| 36 | 9429 | 9713.51968324267 | -284.519683242668 |
| 37 | 8739 | 8984.87845144288 | -245.878451442884 |
| 38 | 9552 | 9435.50963842705 | 116.490361572945 |
| 39 | 9687 | 9782.36569021967 | -95.3656902196723 |
| 40 | 9019 | 8874.63666255557 | 144.363337444430 |
| 41 | 9672 | 9893.69252393009 | -221.692523930088 |
| 42 | 9206 | 9440.71354601007 | -234.713546010066 |
| 43 | 9069 | 9597.05107683267 | -528.051076832672 |
| 44 | 9788 | 9473.02798622899 | 314.972013771014 |
| 45 | 10312 | 10239.7705930850 | 72.229406914978 |
| 46 | 10105 | 10049.0591211498 | 55.9408788502284 |
| 47 | 9863 | 9773.04323642762 | 89.956763572382 |
| 48 | 9656 | 9856.01861745106 | -200.018617451059 |
| 49 | 9295 | 9132.1437883535 | 162.856211646502 |
| 50 | 9946 | 9665.30900107617 | 280.690998923829 |
| 51 | 9701 | 9971.52519824983 | -270.52519824983 |
| 52 | 9049 | 8968.46811654126 | 80.5318834587424 |
| 53 | 10190 | 9991.53779071765 | 198.462209282353 |
| 54 | 9706 | 9660.98010325473 | 45.0198967452653 |
| 55 | 9765 | 9812.80209467523 | -47.8020946752344 |
| 56 | 9893 | 9737.94821089448 | 155.051789105514 |
| 57 | 9994 | 10356.4306073814 | -362.430607381359 |
| 58 | 10433 | 10059.6039594966 | 373.396040503394 |
| 59 | 10073 | 9945.64576665005 | 127.354233349948 |
| 60 | 10112 | 9999.01927825968 | 112.980721740317 |
| 61 | 9266 | 9336.8568209909 | -70.8568209909108 |
| 62 | 9820 | 9748.35333315683 | 71.6466668431742 |
| 63 | 10097 | 10030.2357902191 | 66.7642097808667 |
| 64 | 9115 | 9158.12935117165 | -43.129351171649 |
| 65 | 10411 | 10098.4141363094 | 312.58586369058 |
| 66 | 9678 | 9806.74026036465 | -128.740260364646 |
| 67 | 10408 | 9896.097290056 | 511.902709943993 |
| 68 | 10153 | 9989.57268065378 | 163.427319346218 |
| 69 | 10368 | 10511.9744331958 | -143.974433195834 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 17 | 0.056504302788464 | 0.113008605576928 | 0.943495697211536 |
| 18 | 0.541618437956419 | 0.916763124087162 | 0.458381562043581 |
| 19 | 0.554558275205689 | 0.890883449588623 | 0.445441724794311 |
| 20 | 0.440854208102566 | 0.881708416205132 | 0.559145791897434 |
| 21 | 0.514010457693492 | 0.971979084613017 | 0.485989542306508 |
| 22 | 0.415800622900055 | 0.831601245800111 | 0.584199377099945 |
| 23 | 0.418875094957492 | 0.837750189914985 | 0.581124905042508 |
| 24 | 0.354658928560669 | 0.709317857121339 | 0.64534107143933 |
| 25 | 0.291730699564732 | 0.583461399129465 | 0.708269300435268 |
| 26 | 0.424691667180891 | 0.849383334361782 | 0.575308332819109 |
| 27 | 0.357332958348975 | 0.71466591669795 | 0.642667041651025 |
| 28 | 0.276820039233162 | 0.553640078466324 | 0.723179960766838 |
| 29 | 0.339184293539972 | 0.678368587079944 | 0.660815706460028 |
| 30 | 0.523535319804669 | 0.95292936039066 | 0.47646468019533 |
| 31 | 0.517930757554188 | 0.964138484891624 | 0.482069242445812 |
| 32 | 0.536436645007689 | 0.927126709984621 | 0.463563354992311 |
| 33 | 0.635677050822106 | 0.728645898355789 | 0.364322949177894 |
| 34 | 0.660964092878909 | 0.678071814242183 | 0.339035907121091 |
| 35 | 0.713933549816912 | 0.572132900366175 | 0.286066450183088 |
| 36 | 0.638141390442139 | 0.723717219115722 | 0.361858609557861 |
| 37 | 0.57322552397043 | 0.85354895205914 | 0.42677447602957 |
| 38 | 0.643488572121076 | 0.713022855757847 | 0.356511427878924 |
| 39 | 0.592852013745946 | 0.814295972508108 | 0.407147986254054 |
| 40 | 0.671282583456328 | 0.657434833087344 | 0.328717416543672 |
| 41 | 0.624604240133178 | 0.750791519733644 | 0.375395759866822 |
| 42 | 0.545267198325276 | 0.909465603349448 | 0.454732801674724 |
| 43 | 0.881478407423037 | 0.237043185153925 | 0.118521592576963 |
| 44 | 0.898133991538457 | 0.203732016923086 | 0.101866008461543 |
| 45 | 0.953242268643902 | 0.0935154627121968 | 0.0467577313560984 |
| 46 | 0.929938999223243 | 0.140122001553514 | 0.0700610007767572 |
| 47 | 0.89104483164016 | 0.217910336719681 | 0.108955168359841 |
| 48 | 0.861411332492943 | 0.277177335014114 | 0.138588667507057 |
| 49 | 0.815995637529766 | 0.368008724940467 | 0.184004362470234 |
| 50 | 0.909134833055171 | 0.181730333889658 | 0.0908651669448288 |
| 51 | 0.819259906989893 | 0.361480186020214 | 0.180740093010107 |
| 52 | 0.708094131189167 | 0.583811737621667 | 0.291905868810833 |
| 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 | 1 | 0.0277777777777778 | OK |
