| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 106.454483611626 + 25.9658008658010D[t] -5.10329828901264M1[t] -16.3488971346114M2[t] -23.3230674087817M3[t] -20.5543805400949M4[t] -19.3428365285508M5[t] -9.34557823129251M6[t] -2.89117707689137M7[t] + 7.59179550608124M8[t] + 19.6033395176252M9[t] + 19.476911976912M10[t] + 14.6741702741703M11[t] + 2.13131313131313t + 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) | 106.454483611626 | 29.478979 | 3.6112 | 0.000569 | 0.000285 |
| D | 25.9658008658010 | 26.03679 | 0.9973 | 0.322067 | 0.161033 |
| M1 | -5.10329828901264 | 34.778106 | -0.1467 | 0.88376 | 0.44188 |
| M2 | -16.3488971346114 | 34.745458 | -0.4705 | 0.639437 | 0.319718 |
| M3 | -23.3230674087817 | 34.720044 | -0.6717 | 0.503956 | 0.251978 |
| M4 | -20.5543805400949 | 34.701879 | -0.5923 | 0.555549 | 0.277775 |
| M5 | -19.3428365285508 | 34.690976 | -0.5576 | 0.578913 | 0.289457 |
| M6 | -9.34557823129251 | 34.687341 | -0.2694 | 0.788397 | 0.394198 |
| M7 | -2.89117707689137 | 34.690976 | -0.0833 | 0.933818 | 0.466909 |
| M8 | 7.59179550608124 | 34.701879 | 0.2188 | 0.827464 | 0.413732 |
| M9 | 19.6033395176252 | 34.720044 | 0.5646 | 0.574143 | 0.287071 |
| M10 | 19.476911976912 | 34.633288 | 0.5624 | 0.575657 | 0.287828 |
| M11 | 14.6741702741703 | 34.622364 | 0.4238 | 0.672986 | 0.336493 |
| t | 2.13131313131313 | 0.502195 | 4.244 | 6.6e-05 | 3.3e-05 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.740505739561174 |
| R-squared | 0.548348750323041 |
| Adjusted R-squared | 0.46447066109732 |
| F-TEST (value) | 6.53744923596676 |
| F-TEST (DF numerator) | 13 |
| F-TEST (DF denominator) | 70 |
| p-value | 6.06570922379035e-08 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 64.7656970041792 |
| Sum Squared Residuals | 293621.6855906 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 96.8 | 103.482498453927 | -6.68249845392727 |
| 2 | 87 | 94.3682127396416 | -7.36821273964157 |
| 3 | 96.3 | 89.5253555967842 | 6.77464440321584 |
| 4 | 107.1 | 94.4253555967842 | 12.6746444032158 |
| 5 | 115.2 | 97.7682127396413 | 17.4317872603587 |
| 6 | 106.1 | 109.896784168213 | -3.79678416821269 |
| 7 | 89.5 | 118.482498453927 | -28.982498453927 |
| 8 | 91.3 | 131.096784168213 | -39.7967841682127 |
| 9 | 97.6 | 145.239641311070 | -47.6396413110699 |
| 10 | 100.7 | 147.244526901670 | -46.5445269016698 |
| 11 | 104.6 | 144.573098330241 | -39.9730983302412 |
| 12 | 94.7 | 132.030241187384 | -37.3302411873841 |
| 13 | 101.8 | 129.058256029685 | -27.2582560296845 |
| 14 | 102.5 | 119.943970315399 | -17.4439703153987 |
| 15 | 105.3 | 115.101113172542 | -9.80111317254176 |
| 16 | 110.3 | 120.001113172542 | -9.70111317254172 |
| 17 | 109.8 | 123.343970315399 | -13.5439703153989 |
| 18 | 117.3 | 135.472541743970 | -18.1725417439703 |
| 19 | 118.8 | 144.058256029685 | -25.2582560296846 |
| 20 | 131.3 | 156.672541743970 | -25.3725417439703 |
| 21 | 125.9 | 170.815398886827 | -44.9153988868274 |
| 22 | 133.1 | 172.820284477427 | -39.7202844774273 |
| 23 | 147 | 170.148855905999 | -23.1488559059988 |
| 24 | 145.8 | 157.605998763142 | -11.8059987631416 |
| 25 | 164.4 | 154.634013605442 | 9.76598639455788 |
| 26 | 149.8 | 145.519727891156 | 4.28027210884358 |
| 27 | 137.7 | 140.676870748299 | -2.97687074829934 |
| 28 | 151.7 | 145.576870748299 | 6.12312925170068 |
| 29 | 156.8 | 148.919727891156 | 7.88027210884356 |
| 30 | 180 | 161.048299319728 | 18.9517006802721 |
| 31 | 180.4 | 169.634013605442 | 10.7659863945578 |
| 32 | 170.4 | 182.248299319728 | -11.8482993197279 |
| 33 | 191.6 | 196.391156462585 | -4.79115646258505 |
| 34 | 199.5 | 198.396042053185 | 1.10395794681510 |
| 35 | 218.2 | 195.724613481756 | 22.4753865182436 |
| 36 | 217.5 | 183.181756338899 | 34.3182436611008 |
| 37 | 205 | 180.209771181200 | 24.7902288188003 |
| 38 | 194 | 171.095485466914 | 22.904514533086 |
| 39 | 199.3 | 166.252628324057 | 33.0473716759431 |
| 40 | 219.3 | 171.152628324057 | 48.1473716759431 |
| 41 | 211.1 | 174.495485466914 | 36.6045145330859 |
| 42 | 215.2 | 186.624056895485 | 28.5759431045145 |
| 43 | 240.2 | 195.209771181200 | 44.9902288188003 |
| 44 | 242.2 | 207.824056895485 | 34.3759431045145 |
| 45 | 240.7 | 221.966914038343 | 18.7330859616574 |
| 46 | 255.4 | 223.971799628943 | 31.4282003710575 |
| 47 | 253 | 221.300371057514 | 31.6996289424861 |
| 48 | 218.2 | 208.757513914657 | 9.4424860853432 |
| 49 | 203.7 | 205.785528756957 | -2.08552875695728 |
| 50 | 205.6 | 196.671243042672 | 8.9287569573284 |
| 51 | 215.6 | 191.828385899814 | 23.7716141001855 |
| 52 | 188.5 | 196.728385899814 | -8.22838589981445 |
| 53 | 202.9 | 200.071243042672 | 2.82875695732839 |
| 54 | 214 | 212.199814471243 | 1.80018552875693 |
| 55 | 230.3 | 220.785528756957 | 9.5144712430427 |
| 56 | 230 | 233.399814471243 | -3.39981447124305 |
| 57 | 241 | 247.5426716141 | -6.5426716141002 |
| 58 | 259.6 | 275.513358070501 | -15.9133580705009 |
| 59 | 247.8 | 272.841929499072 | -25.0419294990724 |
| 60 | 270.3 | 260.299072356215 | 10.0009276437848 |
| 61 | 289.7 | 257.327087198516 | 32.3729128014843 |
| 62 | 322.7 | 248.21280148423 | 74.48719851577 |
| 63 | 315 | 243.369944341373 | 71.630055658627 |
| 64 | 320.2 | 248.269944341373 | 71.930055658627 |
| 65 | 329.5 | 251.61280148423 | 77.88719851577 |
| 66 | 360.6 | 263.741372912802 | 96.8586270871985 |
| 67 | 382.2 | 272.327087198516 | 109.872912801484 |
| 68 | 435.4 | 284.941372912802 | 150.458627087198 |
| 69 | 464 | 299.084230055659 | 164.915769944341 |
| 70 | 468.8 | 301.089115646259 | 167.710884353742 |
| 71 | 403 | 298.41768707483 | 104.58231292517 |
| 72 | 351.6 | 285.874829931973 | 65.7251700680272 |
| 73 | 252 | 282.902844774273 | -30.9028447742733 |
| 74 | 188 | 273.788559059988 | -85.7885590599876 |
| 75 | 146.5 | 268.945701917131 | -122.445701917131 |
| 76 | 152.9 | 273.845701917130 | -120.945701917130 |
| 77 | 148.1 | 277.188559059988 | -129.088559059988 |
| 78 | 165.1 | 289.317130488559 | -124.217130488559 |
| 79 | 177 | 297.902844774273 | -120.902844774273 |
| 80 | 206.1 | 310.517130488559 | -104.417130488559 |
| 81 | 244.9 | 324.659987631416 | -79.7599876314162 |
| 82 | 228.6 | 326.664873222016 | -98.0648732220161 |
| 83 | 253.4 | 323.993444650588 | -70.5934446505875 |
| 84 | 241.1 | 311.45058750773 | -70.3505875077304 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 17 | 0.000947862732703297 | 0.00189572546540659 | 0.999052137267297 |
| 18 | 8.46882013730509e-05 | 0.000169376402746102 | 0.999915311798627 |
| 19 | 6.96739554422517e-05 | 0.000139347910884503 | 0.999930326044558 |
| 20 | 6.99210838898216e-05 | 0.000139842167779643 | 0.99993007891611 |
| 21 | 1.68541541393958e-05 | 3.37083082787915e-05 | 0.99998314584586 |
| 22 | 4.7921151991973e-06 | 9.5842303983946e-06 | 0.9999952078848 |
| 23 | 2.44695753206073e-06 | 4.89391506412146e-06 | 0.999997553042468 |
| 24 | 1.91929947807331e-06 | 3.83859895614661e-06 | 0.999998080700522 |
| 25 | 1.50416846641238e-06 | 3.00833693282476e-06 | 0.999998495831534 |
| 26 | 4.28191431788229e-07 | 8.56382863576458e-07 | 0.999999571808568 |
| 27 | 9.1631075452779e-08 | 1.83262150905558e-07 | 0.999999908368925 |
| 28 | 1.80312908351082e-08 | 3.60625816702164e-08 | 0.99999998196871 |
| 29 | 3.49201164116366e-09 | 6.98402328232732e-09 | 0.999999996507988 |
| 30 | 2.16804399870083e-09 | 4.33608799740166e-09 | 0.999999997831956 |
| 31 | 2.22729850471351e-09 | 4.45459700942701e-09 | 0.999999997772701 |
| 32 | 8.52536473282281e-10 | 1.70507294656456e-09 | 0.999999999147464 |
| 33 | 1.29793898985294e-09 | 2.59587797970589e-09 | 0.999999998702061 |
| 34 | 1.50769576315348e-09 | 3.01539152630696e-09 | 0.999999998492304 |
| 35 | 2.46959829668889e-09 | 4.93919659337778e-09 | 0.999999997530402 |
| 36 | 3.83668623705395e-09 | 7.6733724741079e-09 | 0.999999996163314 |
| 37 | 1.06461803487717e-09 | 2.12923606975434e-09 | 0.999999998935382 |
| 38 | 2.83787147662344e-10 | 5.67574295324688e-10 | 0.999999999716213 |
| 39 | 7.30123923235793e-11 | 1.46024784647159e-10 | 0.999999999926988 |
| 40 | 2.26441432390822e-11 | 4.52882864781644e-11 | 0.999999999977356 |
| 41 | 5.1269152717163e-12 | 1.02538305434326e-11 | 0.999999999994873 |
| 42 | 1.19392652257862e-12 | 2.38785304515724e-12 | 0.999999999998806 |
| 43 | 7.9113913577429e-13 | 1.58227827154858e-12 | 0.999999999999209 |
| 44 | 5.61899572452188e-13 | 1.12379914490438e-12 | 0.999999999999438 |
| 45 | 3.45480042583199e-13 | 6.90960085166397e-13 | 0.999999999999654 |
| 46 | 1.6453220644415e-13 | 3.290644128883e-13 | 0.999999999999835 |
| 47 | 3.88541460232303e-14 | 7.77082920464606e-14 | 0.999999999999961 |
| 48 | 1.65296448662065e-14 | 3.3059289732413e-14 | 0.999999999999983 |
| 49 | 3.77423859211557e-14 | 7.54847718423113e-14 | 0.999999999999962 |
| 50 | 2.28643492727117e-14 | 4.57286985454235e-14 | 0.999999999999977 |
| 51 | 8.66444596632846e-15 | 1.73288919326569e-14 | 0.999999999999991 |
| 52 | 4.72421041808255e-14 | 9.4484208361651e-14 | 0.999999999999953 |
| 53 | 4.80509904655557e-14 | 9.61019809311114e-14 | 0.999999999999952 |
| 54 | 2.88485443235013e-14 | 5.76970886470026e-14 | 0.999999999999971 |
| 55 | 9.41439987767628e-15 | 1.88287997553526e-14 | 0.99999999999999 |
| 56 | 2.66829600235489e-15 | 5.33659200470978e-15 | 0.999999999999997 |
| 57 | 5.93425824482947e-16 | 1.18685164896589e-15 | 1 |
| 58 | 1.91289627262613e-14 | 3.82579254525226e-14 | 0.99999999999998 |
| 59 | 6.08236509242856e-11 | 1.21647301848571e-10 | 0.999999999939176 |
| 60 | 0.000203260480254132 | 0.000406520960508264 | 0.999796739519746 |
| 61 | 0.0327243131308355 | 0.065448626261671 | 0.967275686869165 |
| 62 | 0.0732416985654277 | 0.146483397130855 | 0.926758301434572 |
| 63 | 0.0594217208359866 | 0.118843441671973 | 0.940578279164013 |
| 64 | 0.045430177124541 | 0.090860354249082 | 0.95456982287546 |
| 65 | 0.0287282593946798 | 0.0574565187893596 | 0.97127174060532 |
| 66 | 0.0197803899432742 | 0.0395607798865485 | 0.980219610056726 |
| 67 | 0.0143993182891717 | 0.0287986365783434 | 0.985600681710828 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 44 | 0.862745098039216 | NOK |
| 5% type I error level | 46 | 0.901960784313726 | NOK |
| 10% type I error level | 49 | 0.96078431372549 | NOK |
