| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 107756.349835734 + 0.465346280212279X[t] + 4646.78857839405M1[t] + 5889.18188955366M2[t] + 6136.0129828292M3[t] + 6531.672854175M4[t] + 7278.30279838781M5[t] + 7017.24534200469M6[t] -1198.54933758642M7[t] -6602.51200200083M8[t] -6533.95173292422M9[t] -3172.51702113678M10[t] -2894.00700454304M11[t] + 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) | 107756.349835734 | 5296.972888 | 20.343 | 0 | 0 |
| X | 0.465346280212279 | 0.009469 | 49.1424 | 0 | 0 |
| M1 | 4646.78857839405 | 2326.470037 | 1.9974 | 0.050405 | 0.025202 |
| M2 | 5889.18188955366 | 2329.062027 | 2.5286 | 0.014148 | 0.007074 |
| M3 | 6136.0129828292 | 2336.641606 | 2.626 | 0.010988 | 0.005494 |
| M4 | 6531.672854175 | 2345.091911 | 2.7853 | 0.00718 | 0.00359 |
| M5 | 7278.30279838781 | 2356.913429 | 3.0881 | 0.003069 | 0.001535 |
| M6 | 7017.24534200469 | 2355.050683 | 2.9797 | 0.004185 | 0.002093 |
| M7 | -1198.54933758642 | 2326.401335 | -0.5152 | 0.608342 | 0.304171 |
| M8 | -6602.51200200083 | 2340.887441 | -2.8205 | 0.006521 | 0.00326 |
| M9 | -6533.95173292422 | 2337.435952 | -2.7954 | 0.006985 | 0.003492 |
| M10 | -3172.51702113678 | 2328.665265 | -1.3624 | 0.178258 | 0.089129 |
| M11 | -2894.00700454304 | 2322.86763 | -1.2459 | 0.217734 | 0.108867 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.988920632601208 |
| R-squared | 0.977964017584373 |
| Adjusted R-squared | 0.973482122855771 |
| F-TEST (value) | 218.203254829554 |
| F-TEST (DF numerator) | 12 |
| F-TEST (DF denominator) | 59 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 4023.24052128466 |
| Sum Squared Residuals | 955001393.234303 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 344744 | 341756.032810954 | 2987.96718904641 |
| 2 | 338653 | 337458.944002466 | 1194.05599753383 |
| 3 | 327532 | 328852.096768423 | -1320.09676842291 |
| 4 | 326225 | 326768.857005078 | -543.857005077890 |
| 5 | 318672 | 320707.005523505 | -2035.00552350486 |
| 6 | 317756 | 319129.483440401 | -1373.48344040119 |
| 7 | 337302 | 333730.547572179 | 3571.45242782144 |
| 8 | 349420 | 343396.358846159 | 6023.64115384141 |
| 9 | 336923 | 334589.834859027 | 2333.16514097337 |
| 10 | 330758 | 330288.412374558 | 469.587625441537 |
| 11 | 321002 | 320874.224720611 | 127.775279389375 |
| 12 | 320820 | 321894.747601019 | -1074.74760101903 |
| 13 | 327032 | 329737.069085631 | -2705.06908563080 |
| 14 | 324047 | 327737.394862551 | -3690.39486255146 |
| 15 | 316735 | 322361.912198302 | -5626.91219830224 |
| 16 | 315710 | 320374.533768681 | -4664.53376868096 |
| 17 | 313427 | 317966.115933055 | -4539.11593305452 |
| 18 | 310527 | 315490.475529141 | -4963.47552914117 |
| 19 | 330962 | 331792.380315094 | -830.380315094416 |
| 20 | 339015 | 338328.272508367 | 686.727491633325 |
| 21 | 341332 | 339911.069573254 | 1420.93042674596 |
| 22 | 339092 | 338574.368240018 | 517.631759981688 |
| 23 | 323308 | 324032.995270692 | -724.995270691583 |
| 24 | 325849 | 326965.626016492 | -1116.62601649224 |
| 25 | 330675 | 333930.769762904 | -3255.76976290386 |
| 26 | 332225 | 334501.203045437 | -2276.20304543695 |
| 27 | 331735 | 332809.401535348 | -1074.40153534812 |
| 28 | 328047 | 328929.459784103 | -882.459784103503 |
| 29 | 326165 | 326638.774557371 | -473.77455737077 |
| 30 | 327081 | 326797.459445739 | 283.54055426087 |
| 31 | 346764 | 347070.629387024 | -306.629387023978 |
| 32 | 344190 | 345549.981430981 | -1359.98143098104 |
| 33 | 343333 | 344586.868996827 | -1253.86899682703 |
| 34 | 345777 | 345905.433538483 | -128.433538482564 |
| 35 | 344094 | 341834.817220212 | 2259.18277978766 |
| 36 | 348609 | 346124.397719112 | 2484.602280888 |
| 37 | 354846 | 353994.174634256 | 851.825365743703 |
| 38 | 356427 | 354233.746711558 | 2193.25328844155 |
| 39 | 353467 | 351187.787526052 | 2279.21247394811 |
| 40 | 355996 | 351208.378295547 | 4787.6217044534 |
| 41 | 352487 | 348106.594502404 | 4380.40549759614 |
| 42 | 355178 | 350690.664203239 | 4487.33579676138 |
| 43 | 374556 | 371490.140787444 | 3065.85921255644 |
| 44 | 375021 | 370921.591320715 | 4099.40867928505 |
| 45 | 375787 | 370188.825295266 | 5598.17470473399 |
| 46 | 372720 | 367720.401808554 | 4999.59819144598 |
| 47 | 364431 | 359566.837227701 | 4864.16277229875 |
| 48 | 370490 | 365924.881942144 | 4565.11805785551 |
| 49 | 376974 | 374078.985434499 | 2895.01456550151 |
| 50 | 377632 | 374636.854367466 | 2995.14563253415 |
| 51 | 378205 | 372314.043301409 | 5890.95669859082 |
| 52 | 370861 | 367249.795267024 | 3611.20473297570 |
| 53 | 369167 | 364768.318065405 | 4398.68193459547 |
| 54 | 371551 | 367327.259067108 | 4223.74093289217 |
| 55 | 382842 | 382754.778192542 | 87.2218074577937 |
| 56 | 381903 | 385370.127975026 | -3467.12797502602 |
| 57 | 384502 | 386299.578862495 | -1797.57886249534 |
| 58 | 392058 | 389061.182219089 | 2996.81778091084 |
| 59 | 384359 | 381355.746106081 | 3003.25389391919 |
| 60 | 388884 | 384848.653773257 | 4035.34622674295 |
| 61 | 386586 | 387359.968271757 | -773.96827175695 |
| 62 | 387495 | 387910.857010521 | -415.857010521121 |
| 63 | 385705 | 385853.758670466 | -148.75867046566 |
| 64 | 378670 | 380977.975879567 | -2307.97587956675 |
| 65 | 377367 | 379098.191418261 | -1731.19141826147 |
| 66 | 376911 | 379568.658314372 | -2657.65831437206 |
| 67 | 389827 | 395414.523745717 | -5587.52374571728 |
| 68 | 387820 | 393802.667918753 | -5982.66791875273 |
| 69 | 387267 | 393567.822413131 | -6300.82241313094 |
| 70 | 380575 | 389430.201819298 | -8855.20181929749 |
| 71 | 372402 | 381931.379454703 | -9529.3794547034 |
| 72 | 376740 | 385633.692947975 | -8893.69294797517 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 16 | 0.00304819391745426 | 0.00609638783490853 | 0.996951806082546 |
| 17 | 0.00088281379700344 | 0.00176562759400688 | 0.999117186202997 |
| 18 | 0.00058986871609564 | 0.00117973743219128 | 0.999410131283904 |
| 19 | 0.00217219252978077 | 0.00434438505956154 | 0.99782780747022 |
| 20 | 0.00137770432856784 | 0.00275540865713568 | 0.998622295671432 |
| 21 | 0.00264268213814901 | 0.00528536427629802 | 0.99735731786185 |
| 22 | 0.00373631210848664 | 0.00747262421697328 | 0.996263687891513 |
| 23 | 0.00206786847422759 | 0.00413573694845518 | 0.997932131525772 |
| 24 | 0.00116703587295805 | 0.00233407174591610 | 0.998832964127042 |
| 25 | 0.000976561032553229 | 0.00195312206510646 | 0.999023438967447 |
| 26 | 0.00062734241856427 | 0.00125468483712854 | 0.999372657581436 |
| 27 | 0.000322325048177439 | 0.000644650096354878 | 0.999677674951823 |
| 28 | 0.000159920423282380 | 0.000319840846564759 | 0.999840079576718 |
| 29 | 8.21240665046418e-05 | 0.000164248133009284 | 0.999917875933495 |
| 30 | 4.21951197615399e-05 | 8.43902395230798e-05 | 0.999957804880238 |
| 31 | 0.000685316619325973 | 0.00137063323865195 | 0.999314683380674 |
| 32 | 0.00255843782114721 | 0.00511687564229443 | 0.997441562178853 |
| 33 | 0.00491040374545432 | 0.00982080749090863 | 0.995089596254546 |
| 34 | 0.00515098341891328 | 0.0103019668378266 | 0.994849016581087 |
| 35 | 0.00314921620258725 | 0.0062984324051745 | 0.996850783797413 |
| 36 | 0.00204495387539322 | 0.00408990775078644 | 0.997955046124607 |
| 37 | 0.00183487642336095 | 0.00366975284672191 | 0.998165123576639 |
| 38 | 0.00158243047203305 | 0.0031648609440661 | 0.998417569527967 |
| 39 | 0.00298661334725444 | 0.00597322669450889 | 0.997013386652746 |
| 40 | 0.00241349133481990 | 0.00482698266963981 | 0.99758650866518 |
| 41 | 0.00243982749497725 | 0.00487965498995449 | 0.997560172505023 |
| 42 | 0.00212938581193953 | 0.00425877162387906 | 0.99787061418806 |
| 43 | 0.00229487562186315 | 0.0045897512437263 | 0.997705124378137 |
| 44 | 0.00153562632701370 | 0.00307125265402739 | 0.998464373672986 |
| 45 | 0.000797286310377515 | 0.00159457262075503 | 0.999202713689622 |
| 46 | 0.000368893060013302 | 0.000737786120026603 | 0.999631106939987 |
| 47 | 0.000166064279037451 | 0.000332128558074902 | 0.999833935720963 |
| 48 | 7.37272943460321e-05 | 0.000147454588692064 | 0.999926272705654 |
| 49 | 3.80917532514781e-05 | 7.61835065029563e-05 | 0.999961908246749 |
| 50 | 1.95832797848147e-05 | 3.91665595696293e-05 | 0.999980416720215 |
| 51 | 7.89805379748756e-06 | 1.57961075949751e-05 | 0.999992101946203 |
| 52 | 2.87932402917856e-06 | 5.75864805835713e-06 | 0.99999712067597 |
| 53 | 8.8582979110376e-07 | 1.77165958220752e-06 | 0.999999114170209 |
| 54 | 2.54582050721663e-07 | 5.09164101443326e-07 | 0.99999974541795 |
| 55 | 6.2274978379137e-07 | 1.24549956758274e-06 | 0.999999377250216 |
| 56 | 1.05832552454630e-05 | 2.11665104909261e-05 | 0.999989416744755 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 40 | 0.97560975609756 | NOK |
| 5% type I error level | 41 | 1 | NOK |
| 10% type I error level | 41 | 1 | NOK |
