| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 13159.5925557422 + 0.373297241848464X[t] -3283.9381552397M1[t] -3305.66197698457M2[t] -3047.64030454197M3[t] -1347.86215250134M4[t] + 471.763379753883M5[t] + 2317.03849281614M6[t] + 2232.07452176467M7[t] + 815.616173691201M8[t] + 881.123473441051M9[t] + 1206.57890403303M10[t] + 861.223542282898M11[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) | 13159.5925557422 | 4215.589279 | 3.1216 | 0.003074 | 0.001537 |
| X | 0.373297241848464 | 0.978075 | 0.3817 | 0.70443 | 0.352215 |
| M1 | -3283.9381552397 | 4371.676915 | -0.7512 | 0.456286 | 0.228143 |
| M2 | -3305.66197698457 | 4024.276034 | -0.8214 | 0.415549 | 0.207774 |
| M3 | -3047.64030454197 | 3679.519981 | -0.8283 | 0.411703 | 0.205852 |
| M4 | -1347.86215250134 | 3555.061961 | -0.3791 | 0.706292 | 0.353146 |
| M5 | 471.763379753883 | 3368.594662 | 0.14 | 0.889221 | 0.44461 |
| M6 | 2317.03849281614 | 3186.219587 | 0.7272 | 0.470707 | 0.235353 |
| M7 | 2232.07452176467 | 3305.84317 | 0.6752 | 0.502863 | 0.251431 |
| M8 | 815.616173691201 | 3231.360754 | 0.2524 | 0.801828 | 0.400914 |
| M9 | 881.123473441051 | 3128.662936 | 0.2816 | 0.779464 | 0.389732 |
| M10 | 1206.57890403303 | 2927.039294 | 0.4122 | 0.682054 | 0.341027 |
| M11 | 861.223542282898 | 2889.945811 | 0.298 | 0.767011 | 0.383506 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.489473303827329 |
| R-squared | 0.239584115159641 |
| Adjusted R-squared | 0.0454353786046553 |
| F-TEST (value) | 1.23402356054883 |
| F-TEST (DF numerator) | 12 |
| F-TEST (DF denominator) | 47 |
| p-value | 0.289347308080491 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 4514.66194796345 |
| Sum Squared Residuals | 957962107.70629 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 10144 | 9917.46369158953 | 226.536308410474 |
| 2 | 10751 | 9967.41294027952 | 783.587059720477 |
| 3 | 11752 | 10408.3502612279 | 1343.64973877213 |
| 4 | 13808 | 12148.0712181463 | 1659.92878185372 |
| 5 | 16203 | 14091.2581374533 | 2111.74186254666 |
| 6 | 17432 | 15939.5196284504 | 1492.48037154961 |
| 7 | 18014 | 15776.9098310944 | 2237.09016890555 |
| 8 | 16956 | 14402.6340713498 | 2553.36592865015 |
| 9 | 17982 | 14633.5120492386 | 3348.48795076144 |
| 10 | 19435 | 15211.3164153201 | 4223.6835846799 |
| 11 | 19990 | 14845.4297052683 | 5144.57029473169 |
| 12 | 20154 | 14248.5006102141 | 5905.49938978588 |
| 13 | 10327 | 9966.36563027163 | 360.634369728369 |
| 14 | 9807 | 10062.2304397090 | -255.230439709031 |
| 15 | 10862 | 10574.0942366086 | 287.905763391415 |
| 16 | 13743 | 12372.4228604972 | 1370.57713950279 |
| 17 | 16458 | 14377.9504191930 | 2080.04958080704 |
| 18 | 18466 | 16277.7269295651 | 2188.27307043490 |
| 19 | 18810 | 16162.8991791658 | 2647.10082083425 |
| 20 | 17361 | 14738.9748862553 | 2622.02511374469 |
| 21 | 17411 | 14769.3922452714 | 2641.60775472859 |
| 22 | 18517 | 15400.5781169373 | 3116.42188306272 |
| 23 | 18525 | 15244.4844568043 | 3280.51554319568 |
| 24 | 17859 | 14652.781523136 | 3206.21847686399 |
| 25 | 9499 | 10028.7062696603 | -529.706269660324 |
| 26 | 9490 | 10267.1706254838 | -777.170625483837 |
| 27 | 9255 | 10717.4403774784 | -1462.44037747840 |
| 28 | 10758 | 12553.0987255519 | -1795.09872555186 |
| 29 | 12375 | 14391.3891198995 | -2016.38911989951 |
| 30 | 14617 | 16372.5444289946 | -1755.54442899461 |
| 31 | 15427 | 16413.0083312042 | -986.008331204222 |
| 32 | 14136 | 15058.1440280357 | -922.144028035748 |
| 33 | 14308 | 15116.9319774323 | -808.931977432325 |
| 34 | 15293 | 15764.9162249814 | -471.916224981375 |
| 35 | 15679 | 15542.0023585575 | 136.997641442459 |
| 36 | 16319 | 15024.5855760171 | 1294.41442398292 |
| 37 | 11196 | 10090.3003145653 | 1105.69968543468 |
| 38 | 11169 | 10226.8545233642 | 942.145476635797 |
| 39 | 12158 | 10638.6746594484 | 1519.32534055163 |
| 40 | 14251 | 12369.0631853206 | 1881.93681467943 |
| 41 | 16237 | 14320.4626439483 | 1916.5373560517 |
| 42 | 19706 | 16558.819752677 | 3147.18024732301 |
| 43 | 18960 | 16277.1281351714 | 2682.87186482862 |
| 44 | 18537 | 15041.3456521526 | 3495.65434784743 |
| 45 | 19103 | 15335.3108639137 | 3767.68913608632 |
| 46 | 19691 | 15931.4067948458 | 3759.59320515421 |
| 47 | 19464 | 15678.2558518322 | 3785.74414816777 |
| 48 | 17264 | 14722.2148101198 | 2541.78518988018 |
| 49 | 8957 | 10120.1640939132 | -1163.16409391320 |
| 50 | 9703 | 10396.3314711634 | -693.331471163406 |
| 51 | 9166 | 10854.4404652368 | -1688.44046523678 |
| 52 | 9519 | 12636.3440104841 | -3117.34401048407 |
| 53 | 10535 | 14626.9396795059 | -4091.93967950589 |
| 54 | 11526 | 16598.3892603129 | -5072.38926031292 |
| 55 | 9630 | 16211.0545233642 | -6581.0545233642 |
| 56 | 7061 | 14809.9013622065 | -7748.90136220652 |
| 57 | 6021 | 14969.8528641440 | -8948.85286414403 |
| 58 | 4728 | 15355.7824479155 | -10627.7824479155 |
| 59 | 2657 | 15004.8276275376 | -12347.8276275376 |
| 60 | 1264 | 14211.9174805130 | -12947.9174805130 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 16 | 0.00103366275599287 | 0.00206732551198574 | 0.998966337244007 |
| 17 | 0.000178397686323817 | 0.000356795372647633 | 0.999821602313676 |
| 18 | 5.79883848532718e-05 | 0.000115976769706544 | 0.999942011615147 |
| 19 | 7.71903337609848e-06 | 1.54380667521970e-05 | 0.999992280966624 |
| 20 | 8.93142023945345e-07 | 1.78628404789069e-06 | 0.999999106857976 |
| 21 | 2.50123982539330e-07 | 5.00247965078659e-07 | 0.999999749876017 |
| 22 | 1.73845984559699e-07 | 3.47691969119398e-07 | 0.999999826154016 |
| 23 | 2.98466520761952e-07 | 5.96933041523904e-07 | 0.99999970153348 |
| 24 | 6.95049547053567e-07 | 1.39009909410713e-06 | 0.999999304950453 |
| 25 | 1.53168588365488e-07 | 3.06337176730976e-07 | 0.999999846831412 |
| 26 | 2.82517266609663e-08 | 5.65034533219326e-08 | 0.999999971748273 |
| 27 | 2.78995018220803e-08 | 5.57990036441606e-08 | 0.999999972100498 |
| 28 | 7.63208124319172e-08 | 1.52641624863834e-07 | 0.999999923679188 |
| 29 | 7.68390189708954e-07 | 1.53678037941791e-06 | 0.99999923160981 |
| 30 | 7.81644607664256e-07 | 1.56328921532851e-06 | 0.999999218355392 |
| 31 | 2.71394374472201e-07 | 5.42788748944403e-07 | 0.999999728605625 |
| 32 | 7.54328461012669e-08 | 1.50865692202534e-07 | 0.999999924567154 |
| 33 | 2.8857189387646e-08 | 5.7714378775292e-08 | 0.99999997114281 |
| 34 | 9.19055057678535e-09 | 1.83811011535707e-08 | 0.99999999080945 |
| 35 | 2.25882142378441e-09 | 4.51764284756882e-09 | 0.999999997741179 |
| 36 | 7.18331622083155e-10 | 1.43666324416631e-09 | 0.999999999281668 |
| 37 | 4.07623712871066e-10 | 8.15247425742133e-10 | 0.999999999592376 |
| 38 | 3.00874112913403e-10 | 6.01748225826806e-10 | 0.999999999699126 |
| 39 | 4.96748352579322e-10 | 9.93496705158644e-10 | 0.999999999503252 |
| 40 | 4.02797482465117e-09 | 8.05594964930234e-09 | 0.999999995972025 |
| 41 | 2.45484616495969e-06 | 4.90969232991938e-06 | 0.999997545153835 |
| 42 | 0.00177377321618241 | 0.00354754643236481 | 0.998226226783818 |
| 43 | 0.0541556301945603 | 0.108311260389121 | 0.94584436980544 |
| 44 | 0.305739012063059 | 0.611478024126118 | 0.694260987936941 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 27 | 0.93103448275862 | NOK |
| 5% type I error level | 27 | 0.93103448275862 | NOK |
| 10% type I error level | 27 | 0.93103448275862 | NOK |
