| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 41433.5106011802 + 0.998158246327505X[t] -2917.07031357424M1[t] -4883.42917985957M2[t] -5844.67238720495M3[t] -6705.09432199351M4[t] -5706.65455866484M5[t] + 462.027526960597M6[t] + 9147.79114581125M7[t] + 14952.8874585376M8[t] + 9314.87896653174M9[t] + 4907.54056574619M10[t] + 1613.12804336646M11[t] -376.360237931731t + 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) | 41433.5106011802 | 17590.265434 | 2.3555 | 0.021527 | 0.010763 |
| X | 0.998158246327505 | 0.063612 | 15.6914 | 0 | 0 |
| M1 | -2917.07031357424 | 4748.529565 | -0.6143 | 0.541155 | 0.270577 |
| M2 | -4883.42917985957 | 4747.570711 | -1.0286 | 0.307473 | 0.153736 |
| M3 | -5844.67238720495 | 4756.019422 | -1.2289 | 0.22354 | 0.11177 |
| M4 | -6705.09432199351 | 4765.249537 | -1.4071 | 0.164167 | 0.082084 |
| M5 | -5706.65455866484 | 4808.228098 | -1.1869 | 0.239606 | 0.119803 |
| M6 | 462.027526960597 | 4821.111165 | 0.0958 | 0.923947 | 0.461974 |
| M7 | 9147.79114581125 | 4775.871507 | 1.9154 | 0.05984 | 0.02992 |
| M8 | 14952.8874585376 | 4956.181622 | 3.017 | 0.003642 | 0.001821 |
| M9 | 9314.87896653174 | 4950.51654 | 1.8816 | 0.06437 | 0.032185 |
| M10 | 4907.54056574619 | 4926.99516 | 0.9961 | 0.322919 | 0.161459 |
| M11 | 1613.12804336646 | 4925.530201 | 0.3275 | 0.74434 | 0.37217 |
| t | -376.360237931731 | 42.686818 | -8.8168 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.947209342671728 |
| R-squared | 0.897205538844606 |
| Adjusted R-squared | 0.876646646613528 |
| F-TEST (value) | 43.6407530503179 |
| F-TEST (DF numerator) | 13 |
| F-TEST (DF denominator) | 65 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 8525.28419309094 |
| Sum Squared Residuals | 4724230587.2428 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 274412 | 282441.307154824 | -8029.30715482375 |
| 2 | 272433 | 279922.912199253 | -7489.912199253 |
| 3 | 268361 | 275586.841382008 | -7225.84138200802 |
| 4 | 268586 | 273320.958057324 | -4734.95805732407 |
| 5 | 264768 | 269499.237070071 | -4731.23707007095 |
| 6 | 269974 | 276197.88660543 | -6223.88660543005 |
| 7 | 304744 | 312038.490736554 | -7294.49073655419 |
| 8 | 309365 | 323226.599892659 | -13861.5998926585 |
| 9 | 308347 | 316509.527757306 | -8162.52775730634 |
| 10 | 298427 | 309122.632412167 | -10695.6324121669 |
| 11 | 289231 | 296544.295461629 | -7313.29546162884 |
| 12 | 291975 | 299246.15093807 | -7271.15093806991 |
| 13 | 294912 | 300544.248319670 | -5632.24831967046 |
| 14 | 293488 | 298154.615777876 | -4666.61577787602 |
| 15 | 290555 | 294232.780632857 | -3677.78063285699 |
| 16 | 284736 | 287092.890591356 | -2356.89059135583 |
| 17 | 281818 | 283703.372124763 | -1885.37212476252 |
| 18 | 287854 | 289519.649770368 | -1665.64977036810 |
| 19 | 316263 | 320186.799710777 | -3923.79971077679 |
| 20 | 325412 | 333684.647048883 | -8272.64704888297 |
| 21 | 326011 | 328918.974285101 | -2907.97428510106 |
| 22 | 328282 | 320581.832289458 | 7700.16771054213 |
| 23 | 317480 | 310567.763873735 | 6912.23612626488 |
| 24 | 317539 | 309804.013918927 | 7734.9860810729 |
| 25 | 313737 | 305725.032827561 | 8011.96717243862 |
| 26 | 312276 | 303357.359767186 | 8918.64023281386 |
| 27 | 309391 | 299957.561384996 | 9433.4386150036 |
| 28 | 302950 | 293842.779862474 | 9107.2201375264 |
| 29 | 300316 | 291460.403066425 | 8855.59693357526 |
| 30 | 304035 | 295109.679159253 | 8925.3208407467 |
| 31 | 333476 | 325644.074052900 | 7831.92594709957 |
| 32 | 337698 | 334992.577561023 | 2705.42243897683 |
| 33 | 335932 | 330090.157117494 | 5841.8428825056 |
| 34 | 323931 | 321200.035453386 | 2730.96454661423 |
| 35 | 313927 | 310832.619018463 | 3094.38098153691 |
| 36 | 314485 | 310019.959309585 | 4465.04069041498 |
| 37 | 313218 | 304265.070522635 | 8952.92947736457 |
| 38 | 309664 | 302139.949916118 | 7524.05008388223 |
| 39 | 302963 | 297236.925214959 | 5726.07478504119 |
| 40 | 298989 | 294383.126683188 | 4605.87331681205 |
| 41 | 298423 | 294142.797483758 | 4280.20251624208 |
| 42 | 301631 | 296899.720104370 | 4731.2798956303 |
| 43 | 329765 | 323666.067618130 | 6098.9323818695 |
| 44 | 335083 | 330017.101912532 | 5065.89808746825 |
| 45 | 327616 | 325573.834262314 | 2042.16573768637 |
| 46 | 309119 | 307021.540773755 | 2097.45922624525 |
| 47 | 295916 | 294686.754435321 | 1229.24556467944 |
| 48 | 291413 | 288739.568707334 | 2673.43129266618 |
| 49 | 291542 | 288613.294271425 | 2928.70572857498 |
| 50 | 284678 | 281421.522406549 | 3256.47759345106 |
| 51 | 276475 | 271122.454225743 | 5352.5457742565 |
| 52 | 272566 | 268044.070088549 | 4521.92991145105 |
| 53 | 264981 | 261383.587048740 | 3597.41295125958 |
| 54 | 263290 | 256510.588034425 | 6779.41196557525 |
| 55 | 296806 | 287961.292198201 | 8844.70780179947 |
| 56 | 303598 | 295822.539919295 | 7775.46008070471 |
| 57 | 286994 | 283489.829490105 | 3504.17050989542 |
| 58 | 276427 | 274693.534701151 | 1733.46529884927 |
| 59 | 266424 | 263815.061244108 | 2608.93875589164 |
| 60 | 267153 | 265501.789784034 | 1651.21021596563 |
| 61 | 268381 | 263641.714474255 | 4739.2855257453 |
| 62 | 262522 | 257803.445191399 | 4718.55480860128 |
| 63 | 255542 | 248521.500263601 | 7020.49973639899 |
| 64 | 253158 | 247289.708882112 | 5868.29111788766 |
| 65 | 243803 | 236402.025669107 | 7400.97433089318 |
| 66 | 250741 | 243476.980863331 | 7264.01913666862 |
| 67 | 280445 | 272842.532450529 | 7602.46754947099 |
| 68 | 285257 | 278669.533665608 | 6587.46633439169 |
| 69 | 270976 | 271293.67708768 | -317.677087679987 |
| 70 | 261076 | 264642.424370084 | -3566.42437008395 |
| 71 | 255603 | 262134.505966744 | -6531.50596674403 |
| 72 | 260376 | 269629.51734205 | -9253.51734204978 |
| 73 | 263903 | 274874.332429629 | -10971.3324296293 |
| 74 | 264291 | 276552.194741619 | -12261.1947416194 |
| 75 | 263276 | 279904.936895835 | -16628.9368958352 |
| 76 | 262572 | 279583.465834997 | -17011.4658349973 |
| 77 | 256167 | 273684.577537137 | -17517.5775371366 |
| 78 | 264221 | 284031.495462823 | -19810.4954628227 |
| 79 | 293860 | 313019.743232909 | -19159.7432329086 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 17 | 0.000303159900603116 | 0.000606319801206231 | 0.999696840099397 |
| 18 | 0.000413543223750872 | 0.000827086447501745 | 0.99958645677625 |
| 19 | 0.000100428906878789 | 0.000200857813757577 | 0.999899571093121 |
| 20 | 0.000668325464221363 | 0.00133665092844273 | 0.999331674535779 |
| 21 | 0.0019124263939987 | 0.0038248527879974 | 0.998087573606001 |
| 22 | 0.894132999346514 | 0.211734001306973 | 0.105867000653486 |
| 23 | 0.96568565178384 | 0.06862869643232 | 0.03431434821616 |
| 24 | 0.978852331226528 | 0.0422953375469436 | 0.0211476687734718 |
| 25 | 0.980942837929733 | 0.0381143241405343 | 0.0190571620702671 |
| 26 | 0.97799595626149 | 0.0440080874770188 | 0.0220040437385094 |
| 27 | 0.969722554123945 | 0.0605548917521098 | 0.0302774458760549 |
| 28 | 0.970119703976043 | 0.0597605920479131 | 0.0298802960239566 |
| 29 | 0.964740775460913 | 0.0705184490781736 | 0.0352592245390868 |
| 30 | 0.965076668719823 | 0.0698466625603543 | 0.0349233312801772 |
| 31 | 0.982906236989868 | 0.0341875260202629 | 0.0170937630101315 |
| 32 | 0.99990794946334 | 0.000184101073319207 | 9.20505366596034e-05 |
| 33 | 0.999892919714215 | 0.000214160571569930 | 0.000107080285784965 |
| 34 | 0.999990656898267 | 1.8686203466313e-05 | 9.3431017331565e-06 |
| 35 | 0.999997220666625 | 5.55866675083073e-06 | 2.77933337541536e-06 |
| 36 | 0.999997209305513 | 5.58138897490804e-06 | 2.79069448745402e-06 |
| 37 | 0.999995399942145 | 9.2001157093108e-06 | 4.6000578546554e-06 |
| 38 | 0.99999311208741 | 1.37758251820586e-05 | 6.88791259102932e-06 |
| 39 | 0.99999007794924 | 1.98441015197832e-05 | 9.9220507598916e-06 |
| 40 | 0.999991557230387 | 1.68855392259453e-05 | 8.44276961297265e-06 |
| 41 | 0.999993073397532 | 1.38532049357139e-05 | 6.92660246785696e-06 |
| 42 | 0.999989698260467 | 2.06034790649440e-05 | 1.03017395324720e-05 |
| 43 | 0.999973452046162 | 5.30959076763942e-05 | 2.65479538381971e-05 |
| 44 | 0.999950483052518 | 9.90338949647559e-05 | 4.95169474823779e-05 |
| 45 | 0.999993687001995 | 1.26259960098093e-05 | 6.31299800490467e-06 |
| 46 | 0.999999380975051 | 1.23804989712533e-06 | 6.19024948562663e-07 |
| 47 | 0.9999998318634 | 3.362732016508e-07 | 1.681366008254e-07 |
| 48 | 0.999999917811849 | 1.64376302575744e-07 | 8.21881512878721e-08 |
| 49 | 0.999999896509543 | 2.06980913317275e-07 | 1.03490456658638e-07 |
| 50 | 0.999999636146695 | 7.27706609056076e-07 | 3.63853304528038e-07 |
| 51 | 0.999998879428577 | 2.24114284495526e-06 | 1.12057142247763e-06 |
| 52 | 0.999995689378765 | 8.62124246968321e-06 | 4.31062123484161e-06 |
| 53 | 0.999989574436664 | 2.08511266725569e-05 | 1.04255633362785e-05 |
| 54 | 0.99999993287721 | 1.34245578164038e-07 | 6.71227890820189e-08 |
| 55 | 0.99999996676083 | 6.64783390017644e-08 | 3.32391695008822e-08 |
| 56 | 0.99999992922233 | 1.41555340513487e-07 | 7.07776702567435e-08 |
| 57 | 0.999999595896842 | 8.0820631691593e-07 | 4.04103158457965e-07 |
| 58 | 0.999996530745052 | 6.93850989492345e-06 | 3.46925494746172e-06 |
| 59 | 0.999970752024965 | 5.84959500705752e-05 | 2.92479750352876e-05 |
| 60 | 0.999878866915076 | 0.000242266169848753 | 0.000121133084924376 |
| 61 | 0.999803474702866 | 0.000393050594268165 | 0.000196525297134083 |
| 62 | 0.998200024592745 | 0.00359995081451051 | 0.00179997540725526 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 36 | 0.782608695652174 | NOK |
| 5% type I error level | 40 | 0.869565217391304 | NOK |
| 10% type I error level | 45 | 0.978260869565217 | NOK |
