| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 72515.1331006383 + 0.548453531164433X[t] + 3444.62240244408M1[t] + 5252.44902743883M2[t] + 6444.18114239702M3[t] + 7655.64877227978M4[t] + 9291.3039631184M5[t] + 9145.69561028996M6[t] -3397.38353593821M7[t] -10003.1470243896M8[t] -9464.2835414011M9[t] -5046.2793650683M10[t] -2975.32673037337M11[t] -213.238635508375t + 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) | 72515.1331006383 | 12756.933278 | 5.6844 | 0 | 0 |
| X | 0.548453531164433 | 0.029096 | 18.8496 | 0 | 0 |
| M1 | 3444.62240244408 | 2219.682776 | 1.5519 | 0.126137 | 0.063069 |
| M2 | 5252.44902743883 | 2195.918196 | 2.3919 | 0.020023 | 0.010011 |
| M3 | 6444.18114239702 | 2195.152478 | 2.9356 | 0.004765 | 0.002382 |
| M4 | 7655.64877227978 | 2232.349855 | 3.4294 | 0.00112 | 0.00056 |
| M5 | 9291.3039631184 | 2311.339667 | 4.0199 | 0.00017 | 8.5e-05 |
| M6 | 9145.69561028996 | 2321.142191 | 3.9402 | 0.000221 | 0.000111 |
| M7 | -3397.38353593821 | 2302.920102 | -1.4753 | 0.145553 | 0.072777 |
| M8 | -10003.1470243896 | 2472.023054 | -4.0465 | 0.000156 | 7.8e-05 |
| M9 | -9464.2835414011 | 2401.19951 | -3.9415 | 0.00022 | 0.00011 |
| M10 | -5046.2793650683 | 2272.792059 | -2.2203 | 0.03032 | 0.01516 |
| M11 | -2975.32673037337 | 2179.989875 | -1.3648 | 0.177576 | 0.088788 |
| t | -213.238635508375 | 71.089081 | -2.9996 | 0.003979 | 0.001989 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.990415764972113 |
| R-squared | 0.980923387505297 |
| Adjusted R-squared | 0.976647595049587 |
| F-TEST (value) | 229.413236883256 |
| F-TEST (DF numerator) | 13 |
| F-TEST (DF denominator) | 58 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 3775.4821923672 |
| Sum Squared Residuals | 826747415.523148 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 344744 | 346060.066504933 | -1316.06650493254 |
| 2 | 338653 | 341125.863659437 | -2472.86365943729 |
| 3 | 327532 | 331669.480254953 | -4137.48025495261 |
| 4 | 326225 | 329746.097288814 | -3521.09728881405 |
| 5 | 318672 | 323144.090229678 | -4472.0902296775 |
| 6 | 317756 | 321233.668201677 | -3477.66820167649 |
| 7 | 337302 | 335369.123959994 | 1932.87604000558 |
| 8 | 349420 | 346311.240989264 | 3108.75901073634 |
| 9 | 336923 | 336176.760090376 | 746.239909624273 |
| 10 | 330758 | 331350.141333515 | -592.141333515424 |
| 11 | 321002 | 321784.116732078 | -782.116732078 |
| 12 | 320820 | 322338.130910475 | -1518.13091047498 |
| 13 | 327032 | 329335.745075917 | -2303.74507591685 |
| 14 | 324047 | 327109.257313781 | -3062.25731378062 |
| 15 | 316735 | 321461.335229702 | -4726.33522970174 |
| 16 | 315710 | 319650.933690983 | -3940.93369098307 |
| 17 | 313427 | 317354.835305018 | -3927.83530501847 |
| 18 | 310527 | 314385.89796187 | -3858.89796187012 |
| 19 | 330962 | 330525.951376594 | 436.04862340595 |
| 20 | 339015 | 337779.169955251 | 1235.83004474867 |
| 21 | 341332 | 339889.462593140 | 1442.53740685949 |
| 22 | 339092 | 338557.041283329 | 534.958716671184 |
| 23 | 323308 | 322948.155675522 | 359.844324478328 |
| 24 | 325849 | 325755.765413473 | 93.2345865266907 |
| 25 | 330675 | 331719.54467267 | -1044.54467267022 |
| 26 | 332225 | 332522.165763155 | -297.165763155156 |
| 27 | 331735 | 331215.801831774 | 519.198168226073 |
| 28 | 328047 | 327174.839781809 | 872.160218190492 |
| 29 | 326165 | 325017.500139230 | 1147.49986077049 |
| 30 | 327081 | 325153.358236003 | 1927.64176399699 |
| 31 | 346764 | 345973.914085684 | 790.085914315782 |
| 32 | 344190 | 343731.756679292 | 458.243320708333 |
| 33 | 343333 | 342841.46004818 | 491.539951819767 |
| 34 | 345777 | 344638.514587193 | 1138.48541280721 |
| 35 | 344094 | 341370.381884117 | 2723.61811588344 |
| 36 | 348609 | 345777.282118944 | 2831.71788105631 |
| 37 | 354846 | 352807.255042724 | 2038.74495727574 |
| 38 | 356427 | 353219.925672551 | 3207.07432744872 |
| 39 | 353467 | 350317.561965482 | 3149.43803451844 |
| 40 | 355996 | 350873.737413737 | 5122.26258626258 |
| 41 | 352487 | 347760.443266338 | 4726.5567336622 |
| 42 | 355178 | 350754.84116754 | 4423.15883245967 |
| 43 | 374556 | 372195.697960969 | 2360.30203903149 |
| 44 | 375021 | 371075.676479338 | 3945.32352066161 |
| 45 | 375787 | 370456.864346153 | 5330.13565384664 |
| 46 | 372720 | 367790.60404855 | 4929.39595145024 |
| 47 | 364431 | 359710.340063037 | 4720.65993696321 |
| 48 | 370490 | 366555.11624389 | 3934.88375611019 |
| 49 | 376974 | 373920.194275212 | 3053.80572478814 |
| 50 | 377632 | 374708.007120355 | 2923.99287964465 |
| 51 | 378205 | 372657.940200715 | 5547.05979928484 |
| 52 | 370861 | 367221.163913937 | 3639.83608606275 |
| 53 | 369167 | 364838.95832358 | 4328.04167642017 |
| 54 | 371551 | 367803.739734099 | 3747.26026590051 |
| 55 | 382842 | 382913.248963765 | -71.2489637654439 |
| 56 | 381903 | 385545.746542362 | -3642.74654236238 |
| 57 | 384502 | 386886.010422497 | -2384.0104224967 |
| 58 | 392058 | 390383.81936165 | 1674.18063834984 |
| 59 | 384359 | 382831.716126649 | 1527.28387335146 |
| 60 | 388884 | 386299.663916122 | 2584.33608387784 |
| 61 | 386586 | 387014.194428544 | -428.194428544277 |
| 62 | 387495 | 387793.78047072 | -298.780470720308 |
| 63 | 385705 | 386056.880517375 | -351.880517375007 |
| 64 | 378670 | 380842.227910719 | -2172.22791071870 |
| 65 | 377367 | 379169.172736157 | -1802.17273615689 |
| 66 | 376911 | 379672.494698811 | -2761.49469881056 |
| 67 | 389827 | 395275.063652993 | -5448.06365299336 |
| 68 | 387820 | 392925.409354493 | -5105.40935449257 |
| 69 | 387267 | 392893.442499653 | -5626.44249965347 |
| 70 | 380575 | 388259.879385763 | -7684.87938576305 |
| 71 | 372402 | 380951.289518598 | -8549.28951859844 |
| 72 | 376740 | 384666.041397096 | -7926.04139709605 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 17 | 0.000715244630606708 | 0.00143048926121342 | 0.999284755369393 |
| 18 | 0.000256446628734183 | 0.000512893257468366 | 0.999743553371266 |
| 19 | 0.00136604566100699 | 0.00273209132201399 | 0.998633954338993 |
| 20 | 0.00135259579626021 | 0.00270519159252042 | 0.99864740420374 |
| 21 | 0.000733076101352404 | 0.00146615220270481 | 0.999266923898648 |
| 22 | 0.00061054369279736 | 0.00122108738559472 | 0.999389456307203 |
| 23 | 0.00035166344861589 | 0.00070332689723178 | 0.999648336551384 |
| 24 | 0.000227566479395257 | 0.000455132958790514 | 0.999772433520605 |
| 25 | 0.000141415055394137 | 0.000282830110788275 | 0.999858584944606 |
| 26 | 0.000528592904969662 | 0.00105718580993932 | 0.99947140709503 |
| 27 | 0.00925994561397192 | 0.0185198912279438 | 0.990740054386028 |
| 28 | 0.0205767321429387 | 0.0411534642858774 | 0.979423267857061 |
| 29 | 0.0392326677074898 | 0.0784653354149796 | 0.96076733229251 |
| 30 | 0.0323537396924909 | 0.0647074793849819 | 0.96764626030751 |
| 31 | 0.363550013792811 | 0.727100027585623 | 0.636449986207189 |
| 32 | 0.508563535344978 | 0.982872929310043 | 0.491436464655022 |
| 33 | 0.532583598310036 | 0.934832803379928 | 0.467416401689964 |
| 34 | 0.499729116670677 | 0.999458233341353 | 0.500270883329323 |
| 35 | 0.447567802943103 | 0.895135605886206 | 0.552432197056897 |
| 36 | 0.407860773670209 | 0.815721547340418 | 0.592139226329791 |
| 37 | 0.391910658881617 | 0.783821317763233 | 0.608089341118383 |
| 38 | 0.34962322353403 | 0.69924644706806 | 0.65037677646597 |
| 39 | 0.393577743415675 | 0.78715548683135 | 0.606422256584325 |
| 40 | 0.379986770788135 | 0.75997354157627 | 0.620013229211865 |
| 41 | 0.385414909535114 | 0.770829819070229 | 0.614585090464886 |
| 42 | 0.39162253587892 | 0.78324507175784 | 0.60837746412108 |
| 43 | 0.709390312355814 | 0.581219375288373 | 0.290609687644186 |
| 44 | 0.678977254194079 | 0.642045491611842 | 0.321022745805921 |
| 45 | 0.642027778694131 | 0.715944442611739 | 0.357972221305869 |
| 46 | 0.56854840896203 | 0.86290318207594 | 0.43145159103797 |
| 47 | 0.548172197061764 | 0.903655605876471 | 0.451827802938236 |
| 48 | 0.468697527360517 | 0.937395054721035 | 0.531302472639483 |
| 49 | 0.404039106979094 | 0.808078213958188 | 0.595960893020906 |
| 50 | 0.358217182804715 | 0.71643436560943 | 0.641782817195285 |
| 51 | 0.279974679103702 | 0.559949358207404 | 0.720025320896298 |
| 52 | 0.215627874055253 | 0.431255748110506 | 0.784372125944747 |
| 53 | 0.201374910461055 | 0.402749820922109 | 0.798625089538945 |
| 54 | 0.256857622584289 | 0.513715245168578 | 0.743142377415711 |
| 55 | 0.973738457607703 | 0.0525230847845944 | 0.0262615423922972 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 10 | 0.256410256410256 | NOK |
| 5% type I error level | 12 | 0.307692307692308 | NOK |
| 10% type I error level | 15 | 0.384615384615385 | NOK |
