| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 15281.0179858574 + 639.031849385553X[t] + 1.21329152111263Y1[t] -0.258949144967362Y2[t] -30.8517960553214M1[t] + 18948.0579225308M2[t] + 13586.0496020729M3[t] + 7223.28254784197M4[t] + 4475.86728372419M5[t] + 7396.19831256279M6[t] + 2278.67422706786M7[t] + 16154.5210622411M8[t] + 61280.2391484256M9[t] + 9312.77487688442M10[t] + 1391.16702241957M11[t] -61.7258250201235t + 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) | 15281.0179858574 | 22689.40533 | 0.6735 | 0.503458 | 0.251729 |
| X | 639.031849385553 | 3843.731993 | 0.1663 | 0.868568 | 0.434284 |
| Y1 | 1.21329152111263 | 0.131046 | 9.2585 | 0 | 0 |
| Y2 | -0.258949144967362 | 0.132899 | -1.9485 | 0.056468 | 0.028234 |
| M1 | -30.8517960553214 | 4396.580505 | -0.007 | 0.994427 | 0.497213 |
| M2 | 18948.0579225308 | 4502.965195 | 4.2079 | 9.6e-05 | 4.8e-05 |
| M3 | 13586.0496020729 | 4723.01371 | 2.8766 | 0.005711 | 0.002855 |
| M4 | 7223.28254784197 | 4657.365051 | 1.5509 | 0.126652 | 0.063326 |
| M5 | 4475.86728372419 | 4445.350881 | 1.0069 | 0.318409 | 0.159205 |
| M6 | 7396.19831256279 | 4442.406881 | 1.6649 | 0.101618 | 0.050809 |
| M7 | 2278.67422706786 | 4514.840106 | 0.5047 | 0.61578 | 0.30789 |
| M8 | 16154.5210622411 | 4589.936171 | 3.5196 | 0.000876 | 0.000438 |
| M9 | 61280.2391484256 | 4964.276187 | 12.3442 | 0 | 0 |
| M10 | 9312.77487688442 | 8984.857863 | 1.0365 | 0.304506 | 0.152253 |
| M11 | 1391.16702241957 | 4880.973129 | 0.285 | 0.776701 | 0.38835 |
| t | -61.7258250201235 | 75.912614 | -0.8131 | 0.419657 | 0.209829 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.98761175325378 |
| R-squared | 0.975376975165005 |
| Adjusted R-squared | 0.968661604755461 |
| F-TEST (value) | 145.245446740925 |
| F-TEST (DF numerator) | 15 |
| F-TEST (DF denominator) | 55 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 7057.9828257733 |
| Sum Squared Residuals | 2739831686.2901 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 547344 | 551590.582861239 | -4246.5828612385 |
| 2 | 554788 | 551767.039280395 | 3020.96071960472 |
| 3 | 562325 | 560067.205724888 | 2257.79427511161 |
| 4 | 560854 | 560859.673605126 | -5.67360512606075 |
| 5 | 555332 | 554314.080982812 | 1017.91901718752 |
| 6 | 543599 | 550853.804599294 | -7254.80459929401 |
| 7 | 536662 | 532868.922450074 | 3793.07754992579 |
| 8 | 542722 | 541304.690496171 | 1417.30950382899 |
| 9 | 593530 | 596156.591443302 | -2626.59144330212 |
| 10 | 610763 | 604203.085132929 | 6559.91486707082 |
| 11 | 612613 | 603971.716079276 | 8641.2839207236 |
| 12 | 611324 | 600300.941930673 | 11023.0580693274 |
| 13 | 594167 | 598165.375620693 | -3998.37562069333 |
| 14 | 595454 | 596599.902334393 | -1145.90233439286 |
| 15 | 590865 | 597180.464856792 | -6315.4648567918 |
| 16 | 589379 | 584854.909637582 | 4524.09036241811 |
| 17 | 584428 | 581431.134974326 | 2996.86502567415 |
| 18 | 573100 | 578667.532286537 | -5567.53228653717 |
| 19 | 567456 | 561026.173241592 | 6429.82675840836 |
| 20 | 569028 | 570925.852820775 | -1897.85282077531 |
| 21 | 620735 | 619358.648327325 | 1376.35167267541 |
| 22 | 628884 | 629658.054857045 | -774.054857045401 |
| 23 | 628232 | 618172.35034428 | 10059.6496557201 |
| 24 | 612117 | 613818.214842736 | -1701.21484273570 |
| 25 | 595404 | 594342.279201449 | 1061.72079855107 |
| 26 | 597141 | 597154.687373809 | -13.6873738085848 |
| 27 | 593408 | 598166.257660343 | -4758.2576603427 |
| 28 | 590072 | 586762.75286797 | 3309.24713203011 |
| 29 | 579799 | 580872.728422563 | -1073.72842256341 |
| 30 | 574205 | 572131.044177603 | 2073.95582239707 |
| 31 | 572775 | 562824.826064234 | 9950.17393576647 |
| 32 | 572942 | 576352.501716143 | -3410.50171614299 |
| 33 | 619567 | 621989.410938637 | -2422.41093863658 |
| 34 | 625809 | 626486.693506742 | -677.693506742114 |
| 35 | 619916 | 614003.221617939 | 5912.77838206108 |
| 36 | 587625 | 603784.041273696 | -16159.0412736962 |
| 37 | 565742 | 566039.054455665 | -297.054455665445 |
| 38 | 557274 | 566767.506832865 | -9493.50683286486 |
| 39 | 560576 | 556736.204225926 | 3839.79577407417 |
| 40 | 548854 | 556510.781308972 | -7656.78130897231 |
| 41 | 531673 | 538624.38693267 | -6951.38693266992 |
| 42 | 525919 | 523672.83238956 | 2246.16761044032 |
| 43 | 511038 | 515961.308326247 | -4923.3083262468 |
| 44 | 498662 | 513210.431590865 | -14548.4315908650 |
| 45 | 555362 | 547112.150212999 | 8249.84978700113 |
| 46 | 564591 | 567081.34398164 | -2490.34398163978 |
| 47 | 541657 | 555613.061230854 | -13956.0612308538 |
| 48 | 527070 | 523944.698979313 | 3125.30102068672 |
| 49 | 509846 | 512092.57763045 | -2246.57763044937 |
| 50 | 514258 | 513889.31954201 | 368.68045798966 |
| 51 | 516922 | 518278.767660599 | -1356.76766059908 |
| 52 | 507561 | 513943.999765996 | -6382.99976599607 |
| 53 | 492622 | 499087.39622553 | -6465.39622552979 |
| 54 | 490243 | 486244.662341486 | 3998.33765851388 |
| 55 | 469357 | 482047.433178912 | -12690.4331789115 |
| 56 | 477580 | 471136.787494984 | 6443.21250501644 |
| 57 | 528379 | 531586.087776046 | -3207.08777604549 |
| 58 | 533590 | 539061.554841418 | -5471.55484141809 |
| 59 | 517945 | 524246.325663254 | -6301.325663254 |
| 60 | 506174 | 502462.102973582 | 3711.89702641773 |
| 61 | 501866 | 492139.130230504 | 9726.86976949558 |
| 62 | 516141 | 508877.544636528 | 7263.45536347194 |
| 63 | 528222 | 521889.099871452 | 6332.90012854778 |
| 64 | 532638 | 526425.882814354 | 6212.11718564623 |
| 65 | 536322 | 525846.272462099 | 10475.7275379014 |
| 66 | 536535 | 532031.12420552 | 4503.8757944799 |
| 67 | 523597 | 526156.336738942 | -2559.33673894227 |
| 68 | 536214 | 524217.735881062 | 11996.2641189379 |
| 69 | 586570 | 587940.111301692 | -1370.11130169234 |
| 70 | 596594 | 593740.267680225 | 2853.73231977456 |
| 71 | 580523 | 584879.325064397 | -4356.32506439698 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 19 | 0.0704426446334585 | 0.140885289266917 | 0.929557355366541 |
| 20 | 0.0469136868021406 | 0.093827373604281 | 0.95308631319786 |
| 21 | 0.0159081342475844 | 0.0318162684951688 | 0.984091865752416 |
| 22 | 0.0260358698229200 | 0.0520717396458401 | 0.97396413017708 |
| 23 | 0.0155310005033157 | 0.0310620010066314 | 0.984468999496684 |
| 24 | 0.0559424734626664 | 0.111884946925333 | 0.944057526537334 |
| 25 | 0.0383243941379119 | 0.0766487882758238 | 0.961675605862088 |
| 26 | 0.0195773618003229 | 0.0391547236006459 | 0.980422638199677 |
| 27 | 0.0111834329186336 | 0.0223668658372673 | 0.988816567081366 |
| 28 | 0.00573549842303096 | 0.0114709968460619 | 0.99426450157697 |
| 29 | 0.00321032234895991 | 0.00642064469791983 | 0.99678967765104 |
| 30 | 0.00285390440372860 | 0.00570780880745719 | 0.997146095596271 |
| 31 | 0.00628100111570191 | 0.0125620022314038 | 0.993718998884298 |
| 32 | 0.00385497065459460 | 0.00770994130918921 | 0.996145029345405 |
| 33 | 0.00184316080489719 | 0.00368632160979438 | 0.998156839195103 |
| 34 | 0.00122758206163809 | 0.00245516412327619 | 0.998772417938362 |
| 35 | 0.0159188454208922 | 0.0318376908417844 | 0.984081154579108 |
| 36 | 0.228540009195388 | 0.457080018390776 | 0.771459990804612 |
| 37 | 0.167330897210627 | 0.334661794421253 | 0.832669102789373 |
| 38 | 0.195246544931806 | 0.390493089863613 | 0.804753455068194 |
| 39 | 0.185484585098708 | 0.370969170197416 | 0.814515414901292 |
| 40 | 0.151885856340917 | 0.303771712681834 | 0.848114143659083 |
| 41 | 0.123555267746533 | 0.247110535493067 | 0.876444732253467 |
| 42 | 0.107754519356311 | 0.215509038712621 | 0.89224548064369 |
| 43 | 0.136235213514960 | 0.272470427029921 | 0.86376478648504 |
| 44 | 0.301452464051464 | 0.602904928102928 | 0.698547535948536 |
| 45 | 0.815967030043305 | 0.368065939913391 | 0.184032969956695 |
| 46 | 0.83280000057082 | 0.334399998858359 | 0.167199999429180 |
| 47 | 0.843694592047082 | 0.312610815905836 | 0.156305407952918 |
| 48 | 0.9130334093079 | 0.173933181384202 | 0.086966590692101 |
| 49 | 0.86526813522931 | 0.269463729541381 | 0.134731864770690 |
| 50 | 0.847845654884616 | 0.304308690230768 | 0.152154345115384 |
| 51 | 0.899644030835822 | 0.200711938328356 | 0.100355969164178 |
| 52 | 0.974054843719595 | 0.0518903125608097 | 0.0259451562804048 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 5 | 0.147058823529412 | NOK |
| 5% type I error level | 12 | 0.352941176470588 | NOK |
| 10% type I error level | 16 | 0.470588235294118 | NOK |
