| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 293474.404040404 + 14540.1515151515x[t] -7702.2207792208M1[t] -12230.6226551226M2[t] -17885.1911976912M3[t] -14697.9264069264M4[t] -11813.4949494950M5[t] -12045.0634920635M6[t] -14989.7987012987M7[t] -16747.7005772006M8[t] -21823.7691197691M9[t] -23024.5043290043M10[t] -1199.73953823954M11[t] -466.098124098123t + 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) | 293474.404040404 | 7110.322051 | 41.2744 | 0 | 0 |
| x | 14540.1515151515 | 6151.315239 | 2.3637 | 0.021462 | 0.010731 |
| M1 | -7702.2207792208 | 8587.549656 | -0.8969 | 0.373477 | 0.186739 |
| M2 | -12230.6226551226 | 8580.662167 | -1.4254 | 0.15941 | 0.079705 |
| M3 | -17885.1911976912 | 8575.301406 | -2.0857 | 0.041419 | 0.020709 |
| M4 | -14697.9264069264 | 8571.470239 | -1.7147 | 0.09173 | 0.045865 |
| M5 | -11813.4949494950 | 8569.170716 | -1.3786 | 0.173311 | 0.086656 |
| M6 | -12045.0634920635 | 8568.404072 | -1.4058 | 0.165132 | 0.082566 |
| M7 | -14989.7987012987 | 8569.170716 | -1.7493 | 0.085534 | 0.042767 |
| M8 | -16747.7005772006 | 8571.470239 | -1.9539 | 0.055542 | 0.027771 |
| M9 | -21823.7691197691 | 8575.301406 | -2.545 | 0.013612 | 0.006806 |
| M10 | -23024.5043290043 | 8580.662167 | -2.6833 | 0.009484 | 0.004742 |
| M11 | -1199.73953823954 | 8587.549656 | -0.1397 | 0.889376 | 0.444688 |
| t | -466.098124098123 | 114.622992 | -4.0664 | 0.000146 | 7.3e-05 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.604313480269635 |
| R-squared | 0.365194782435599 |
| Adjusted R-squared | 0.222910854360819 |
| F-TEST (value) | 2.56666221812252 |
| F-TEST (DF numerator) | 13 |
| F-TEST (DF denominator) | 58 |
| p-value | 0.00718756475655868 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 14782.3669355914 |
| Sum Squared Residuals | 12674065588.671 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 269645 | 285306.085137085 | -15661.0851370854 |
| 2 | 267037 | 280311.585137085 | -13274.5851370851 |
| 3 | 258113 | 274190.918470418 | -16077.9184704185 |
| 4 | 262813 | 276912.085137085 | -14099.0851370852 |
| 5 | 267413 | 279330.418470418 | -11917.4184704185 |
| 6 | 267366 | 278632.751803752 | -11266.7518037518 |
| 7 | 264777 | 275221.918470418 | -10444.9184704184 |
| 8 | 258863 | 272997.918470418 | -14134.9184704184 |
| 9 | 254844 | 267455.751803752 | -12611.7518037518 |
| 10 | 254868 | 265788.918470418 | -10920.9184704185 |
| 11 | 277267 | 287147.585137085 | -9880.58513708513 |
| 12 | 285351 | 287881.226551227 | -2530.22655122652 |
| 13 | 286602 | 279712.907647908 | 6889.0923520924 |
| 14 | 283042 | 274718.407647908 | 8323.59235209234 |
| 15 | 276687 | 268597.740981241 | 8089.25901875903 |
| 16 | 277915 | 271318.907647908 | 6596.09235209236 |
| 17 | 277128 | 273737.240981241 | 3390.75901875902 |
| 18 | 277103 | 273039.574314574 | 4063.4256854257 |
| 19 | 275037 | 269628.740981241 | 5408.25901875902 |
| 20 | 270150 | 267404.740981241 | 2745.25901875902 |
| 21 | 267140 | 261862.574314574 | 5277.4256854257 |
| 22 | 264993 | 260195.740981241 | 4797.25901875903 |
| 23 | 287259 | 281554.407647908 | 5704.59235209236 |
| 24 | 291186 | 282288.049062049 | 8897.95093795095 |
| 25 | 292300 | 274119.73015873 | 18180.2698412699 |
| 26 | 288186 | 269125.23015873 | 19060.7698412698 |
| 27 | 281477 | 263004.563492063 | 18472.4365079365 |
| 28 | 282656 | 265725.73015873 | 16930.2698412698 |
| 29 | 280190 | 268144.063492063 | 12045.9365079365 |
| 30 | 280408 | 267446.396825397 | 12961.6031746032 |
| 31 | 276836 | 264035.563492063 | 12800.4365079365 |
| 32 | 275216 | 261811.563492063 | 13404.4365079365 |
| 33 | 274352 | 256269.396825397 | 18082.6031746032 |
| 34 | 271311 | 254602.563492063 | 16708.4365079365 |
| 35 | 289802 | 275961.23015873 | 13840.7698412698 |
| 36 | 290726 | 276694.871572872 | 14031.1284271284 |
| 37 | 292300 | 268526.552669553 | 23773.4473304474 |
| 38 | 278506 | 263532.052669553 | 14973.9473304473 |
| 39 | 269826 | 257411.386002886 | 12414.613997114 |
| 40 | 265861 | 260132.552669553 | 5728.44733044733 |
| 41 | 269034 | 262550.886002886 | 6483.11399711399 |
| 42 | 264176 | 261853.219336219 | 2322.78066378066 |
| 43 | 255198 | 258442.386002886 | -3244.38600288601 |
| 44 | 253353 | 256218.386002886 | -2865.38600288601 |
| 45 | 246057 | 250676.219336219 | -4619.21933621934 |
| 46 | 235372 | 249009.386002886 | -13637.386002886 |
| 47 | 258556 | 270368.052669553 | -11812.0526695527 |
| 48 | 260993 | 271101.694083694 | -10108.6940836941 |
| 49 | 254663 | 262933.375180375 | -8270.37518037515 |
| 50 | 250643 | 257938.875180375 | -7295.87518037519 |
| 51 | 243422 | 251818.208513709 | -8396.20851370851 |
| 52 | 247105 | 254539.375180375 | -7434.37518037519 |
| 53 | 248541 | 256957.708513709 | -8416.70851370853 |
| 54 | 245039 | 256260.041847042 | -11221.0418470419 |
| 55 | 237080 | 252849.208513709 | -15769.2085137085 |
| 56 | 237085 | 250625.208513709 | -13540.2085137085 |
| 57 | 225554 | 245083.041847042 | -19529.0418470419 |
| 58 | 226839 | 243416.208513709 | -16577.2085137085 |
| 59 | 247934 | 264774.875180375 | -16840.8751803752 |
| 60 | 248333 | 280048.668109668 | -31715.6681096681 |
| 61 | 246969 | 271880.349206349 | -24911.3492063492 |
| 62 | 245098 | 266885.849206349 | -21787.8492063492 |
| 63 | 246263 | 260765.182539683 | -14502.1825396825 |
| 64 | 255765 | 263486.349206349 | -7721.3492063492 |
| 65 | 264319 | 265904.682539683 | -1585.68253968255 |
| 66 | 268347 | 265207.015873016 | 3139.98412698413 |
| 67 | 273046 | 261796.182539683 | 11249.8174603175 |
| 68 | 273963 | 259572.182539683 | 14390.8174603175 |
| 69 | 267430 | 254030.015873016 | 13399.9841269841 |
| 70 | 271993 | 252363.182539683 | 19629.8174603175 |
| 71 | 292710 | 273721.849206349 | 18988.1507936508 |
| 72 | 295881 | 274455.490620491 | 21425.5093795094 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 17 | 0.0105643893795071 | 0.0211287787590142 | 0.989435610620493 |
| 18 | 0.00412955282320748 | 0.00825910564641496 | 0.995870447176793 |
| 19 | 0.00119497016606071 | 0.00238994033212143 | 0.99880502983394 |
| 20 | 0.000282591866769184 | 0.000565183733538368 | 0.99971740813323 |
| 21 | 5.62148872296459e-05 | 0.000112429774459292 | 0.99994378511277 |
| 22 | 1.54180663869641e-05 | 3.08361327739283e-05 | 0.999984581933613 |
| 23 | 4.26377260924846e-06 | 8.52754521849692e-06 | 0.99999573622739 |
| 24 | 3.66984776907621e-06 | 7.33969553815242e-06 | 0.999996330152231 |
| 25 | 1.19437668518472e-06 | 2.38875337036944e-06 | 0.999998805623315 |
| 26 | 4.26474606810519e-07 | 8.52949213621037e-07 | 0.999999573525393 |
| 27 | 1.02210862865224e-07 | 2.04421725730448e-07 | 0.999999897789137 |
| 28 | 3.3776797790584e-08 | 6.7553595581168e-08 | 0.999999966223202 |
| 29 | 4.83771713586087e-08 | 9.67543427172173e-08 | 0.999999951622829 |
| 30 | 3.45875257246162e-08 | 6.91750514492324e-08 | 0.999999965412474 |
| 31 | 2.74860752128265e-08 | 5.4972150425653e-08 | 0.999999972513925 |
| 32 | 7.12427047817952e-09 | 1.42485409563590e-08 | 0.99999999287573 |
| 33 | 1.48713334622535e-09 | 2.97426669245070e-09 | 0.999999998512867 |
| 34 | 3.29161973301676e-10 | 6.58323946603352e-10 | 0.999999999670838 |
| 35 | 1.49480577153677e-10 | 2.98961154307353e-10 | 0.99999999985052 |
| 36 | 4.72108591561327e-10 | 9.44217183122653e-10 | 0.999999999527891 |
| 37 | 1.54227989749339e-09 | 3.08455979498677e-09 | 0.99999999845772 |
| 38 | 1.17587064016743e-07 | 2.35174128033486e-07 | 0.999999882412936 |
| 39 | 2.05708651646353e-06 | 4.11417303292706e-06 | 0.999997942913484 |
| 40 | 3.90471129930782e-05 | 7.80942259861563e-05 | 0.999960952887007 |
| 41 | 0.000135615896295662 | 0.000271231792591325 | 0.999864384103704 |
| 42 | 0.000568539583699382 | 0.00113707916739876 | 0.9994314604163 |
| 43 | 0.00247890590940587 | 0.00495781181881174 | 0.997521094090594 |
| 44 | 0.00459679146846378 | 0.00919358293692755 | 0.995403208531536 |
| 45 | 0.0121230228895578 | 0.0242460457791156 | 0.987876977110442 |
| 46 | 0.0301070042964394 | 0.0602140085928788 | 0.96989299570356 |
| 47 | 0.0620165314299403 | 0.124033062859881 | 0.93798346857006 |
| 48 | 0.163713863304977 | 0.327427726609953 | 0.836286136695023 |
| 49 | 0.332446477796711 | 0.664892955593423 | 0.667553522203289 |
| 50 | 0.57105095093648 | 0.857898098127039 | 0.428949049063519 |
| 51 | 0.750322420008347 | 0.499355159983306 | 0.249677579991653 |
| 52 | 0.883187977830419 | 0.233624044339162 | 0.116812022169581 |
| 53 | 0.959397531184096 | 0.0812049376318073 | 0.0406024688159036 |
| 54 | 0.993933999374835 | 0.0121320012503307 | 0.00606600062516535 |
| 55 | 0.98803987157295 | 0.0239202568541021 | 0.0119601284270511 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 27 | 0.692307692307692 | NOK |
| 5% type I error level | 31 | 0.794871794871795 | NOK |
| 10% type I error level | 33 | 0.846153846153846 | NOK |
