| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = -918.27639098955 + 10.3421732921795X[t] -1.90632391481678M1[t] + 0.108298714811628M2[t] + 5.16145524896801M3[t] + 29.293192545015M4[t] + 10.8408731493808M5[t] + 11.81365323506M6[t] + 7.45047084987543M7[t] + 9.90629621999926M8[t] + 14.0682807093823M9[t] + 23.1802573531665M10[t] -0.405543323044851M11[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) | -918.27639098955 | 82.359041 | -11.1497 | 0 | 0 |
| X | 10.3421732921795 | 0.774498 | 13.3534 | 0 | 0 |
| M1 | -1.90632391481678 | 13.586385 | -0.1403 | 0.889001 | 0.444501 |
| M2 | 0.108298714811628 | 14.249395 | 0.0076 | 0.993967 | 0.496984 |
| M3 | 5.16145524896801 | 14.24766 | 0.3623 | 0.718743 | 0.359371 |
| M4 | 29.293192545015 | 14.431433 | 2.0298 | 0.047938 | 0.023969 |
| M5 | 10.8408731493808 | 14.190929 | 0.7639 | 0.448648 | 0.224324 |
| M6 | 11.81365323506 | 14.184155 | 0.8329 | 0.409039 | 0.20452 |
| M7 | 7.45047084987543 | 14.170264 | 0.5258 | 0.60146 | 0.30073 |
| M8 | 9.90629621999926 | 14.163921 | 0.6994 | 0.487675 | 0.243838 |
| M9 | 14.0682807093823 | 14.160328 | 0.9935 | 0.325449 | 0.162724 |
| M10 | 23.1802573531665 | 14.204123 | 1.6319 | 0.109237 | 0.054618 |
| M11 | -0.405543323044851 | 14.160242 | -0.0286 | 0.977271 | 0.488635 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.893265188168467 |
| R-squared | 0.797922696393646 |
| Adjusted R-squared | 0.747403370492058 |
| F-TEST (value) | 15.7944050549684 |
| F-TEST (DF numerator) | 12 |
| F-TEST (DF denominator) | 48 |
| p-value | 8.69304628281498e-13 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 22.3872153977978 |
| Sum Squared Residuals | 24056.995836835 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 108.5 | 100.693210766676 | 7.80678923332389 |
| 2 | 112.3 | 100.949663936633 | 11.3503360633669 |
| 3 | 116.6 | 102.486481551448 | 14.1135184485515 |
| 4 | 115.5 | 113.380237033506 | 2.11976296649430 |
| 5 | 120.1 | 117.060168483136 | 3.03983151686429 |
| 6 | 132.9 | 124.134830811201 | 8.76516918879918 |
| 7 | 128.1 | 121.529817885687 | 6.57018211431334 |
| 8 | 129.3 | 125.743812715481 | 3.55618728451900 |
| 9 | 132.5 | 133.422136124205 | -0.922136124205162 |
| 10 | 131 | 131.985096009966 | -0.985096009966213 |
| 11 | 124.9 | 126.911785526756 | -2.01178552675617 |
| 12 | 120.8 | 127.317328849801 | -6.51732884980103 |
| 13 | 122 | 123.652835475314 | -1.65283547531385 |
| 14 | 122.1 | 124.840084241568 | -2.74008424156777 |
| 15 | 127.4 | 130.720614639099 | -3.32061463909864 |
| 16 | 135.2 | 141.097261456547 | -5.89726145654676 |
| 17 | 137.3 | 146.225097167082 | -8.9250971670819 |
| 18 | 135 | 146.473925122309 | -11.4739251223086 |
| 19 | 136 | 148.005781513666 | -12.0057815136663 |
| 20 | 138.4 | 154.184789268975 | -15.7847892689747 |
| 21 | 134.7 | 159.174147621732 | -24.4741476217321 |
| 22 | 138.4 | 156.909733644119 | -18.5097336441189 |
| 23 | 133.9 | 151.422736229222 | -17.5227362292217 |
| 24 | 133.6 | 146.760614639099 | -13.1606146390987 |
| 25 | 141.2 | 141.751638736628 | -0.55163873662805 |
| 26 | 151.8 | 146.041539490536 | 5.75846050946409 |
| 27 | 155.4 | 152.439178552676 | 2.9608214473244 |
| 28 | 156.6 | 158.575534320330 | -1.97553432033029 |
| 29 | 161.6 | 164.944430825927 | -3.34443082592689 |
| 30 | 160.7 | 165.813789178684 | -5.11378917868437 |
| 31 | 156 | 166.828536905433 | -10.8285369054331 |
| 32 | 159.5 | 168.043301480495 | -8.54330148049534 |
| 33 | 168.7 | 173.032659833253 | -4.33265983325275 |
| 34 | 169.9 | 170.664824122718 | -0.76482412271762 |
| 35 | 169.9 | 163.729922446915 | 6.17007755308467 |
| 36 | 185.9 | 162.067031111524 | 23.8329688884757 |
| 37 | 190.8 | 165.228372109876 | 25.5716278901245 |
| 38 | 195.8 | 176.550950702465 | 19.2490492975346 |
| 39 | 211.9 | 185.53413308765 | 26.3658669123499 |
| 40 | 227.1 | 195.497092973411 | 31.6029070265889 |
| 41 | 251.3 | 203.7275806716 | 47.5724193283999 |
| 42 | 256.7 | 212.870677658101 | 43.8293223418988 |
| 43 | 251.9 | 210.782773397196 | 41.1172266028039 |
| 44 | 251.2 | 222.960241661969 | 28.2397583380313 |
| 45 | 270.3 | 234.982277853408 | 35.3177221465918 |
| 46 | 267.2 | 233.545237739169 | 33.6547622608308 |
| 47 | 243 | 221.852936348964 | 21.1470636510357 |
| 48 | 229.9 | 221.120840609869 | 8.77915939013054 |
| 49 | 187.2 | 217.352925502460 | -30.1529255024603 |
| 50 | 178.2 | 211.817761628798 | -33.6177616287978 |
| 51 | 175.2 | 215.319592169127 | -40.1195921691272 |
| 52 | 192.4 | 218.249874216206 | -25.8498742162061 |
| 53 | 187 | 225.342722852255 | -38.3427228522554 |
| 54 | 184 | 220.006777229705 | -36.0067772297050 |
| 55 | 194.1 | 218.953090298018 | -24.8530902980179 |
| 56 | 212.7 | 220.16785487308 | -7.46785487308026 |
| 57 | 217.5 | 223.088778567402 | -5.58877856740171 |
| 58 | 200.5 | 213.895108484028 | -13.3951084840281 |
| 59 | 205.9 | 213.682619448142 | -7.78261944814245 |
| 60 | 196.5 | 209.434184789707 | -12.9341847897066 |
| 61 | 206.3 | 207.321017409046 | -1.02101740904615 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 16 | 0.00185641552691344 | 0.00371283105382688 | 0.998143584473087 |
| 17 | 0.000180318462387388 | 0.000360636924774777 | 0.999819681537613 |
| 18 | 0.000150765398518817 | 0.000301530797037634 | 0.99984923460148 |
| 19 | 2.64464834021305e-05 | 5.2892966804261e-05 | 0.999973553516598 |
| 20 | 4.06840388595918e-06 | 8.13680777191835e-06 | 0.999995931596114 |
| 21 | 2.02377698747084e-06 | 4.04755397494169e-06 | 0.999997976223012 |
| 22 | 3.08705348193656e-07 | 6.17410696387312e-07 | 0.999999691294652 |
| 23 | 4.16837259290224e-08 | 8.33674518580449e-08 | 0.999999958316274 |
| 24 | 8.97461230218056e-09 | 1.79492246043611e-08 | 0.999999991025388 |
| 25 | 3.35877216383567e-08 | 6.71754432767134e-08 | 0.999999966412278 |
| 26 | 2.09094509567139e-07 | 4.18189019134278e-07 | 0.99999979090549 |
| 27 | 1.53477869209684e-07 | 3.06955738419368e-07 | 0.99999984652213 |
| 28 | 8.56829075858595e-08 | 1.71365815171719e-07 | 0.999999914317092 |
| 29 | 4.11781909114705e-08 | 8.2356381822941e-08 | 0.99999995882181 |
| 30 | 1.11496889292279e-08 | 2.22993778584558e-08 | 0.999999988850311 |
| 31 | 2.78039505371385e-09 | 5.56079010742769e-09 | 0.999999997219605 |
| 32 | 9.90702611598446e-10 | 1.98140522319689e-09 | 0.999999999009297 |
| 33 | 2.02092387577511e-09 | 4.04184775155021e-09 | 0.999999997979076 |
| 34 | 3.59866706434258e-09 | 7.19733412868516e-09 | 0.999999996401333 |
| 35 | 1.90463266338430e-08 | 3.80926532676861e-08 | 0.999999980953673 |
| 36 | 9.89511362508275e-07 | 1.97902272501655e-06 | 0.999999010488637 |
| 37 | 2.88159849590332e-06 | 5.76319699180665e-06 | 0.999997118401504 |
| 38 | 1.57821656654409e-06 | 3.15643313308818e-06 | 0.999998421783433 |
| 39 | 1.38550378502142e-06 | 2.77100757004283e-06 | 0.999998614496215 |
| 40 | 2.79154236492112e-06 | 5.58308472984223e-06 | 0.999997208457635 |
| 41 | 0.000136976191993031 | 0.000273952383986063 | 0.999863023808007 |
| 42 | 0.00498037159787968 | 0.00996074319575936 | 0.99501962840212 |
| 43 | 0.162388843489480 | 0.324777686978961 | 0.83761115651052 |
| 44 | 0.183578027150105 | 0.367156054300211 | 0.816421972849895 |
| 45 | 0.145465500556288 | 0.290931001112576 | 0.854534499443712 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 27 | 0.9 | NOK |
| 5% type I error level | 27 | 0.9 | NOK |
| 10% type I error level | 27 | 0.9 | NOK |
