| Multiple Linear Regression - Estimated Regression Equation |
| Y_t [t] = + 4.76674 -0.0702613X_1t[t] + 0.0183558X_2t[t] -0.0125763X_3t[t] + 0.0243342X_4t[t] -0.0637158X_5t[t] -0.22045M1[t] -0.0262015M2[t] + 0.325625M3[t] -0.192451M4[t] + 0.0839012M5[t] + 0.146362M6[t] -0.144542M7[t] -0.203434M8[t] -0.173177M9[t] -0.080801M10[t] + 0.207269M11[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) | 4.76674 | 1.01976 | 4.674 | 6.71368e-06 | 3.35684e-06 |
| X_1t | -0.0702613 | 0.0548355 | -1.281 | 0.202144 | 0.101072 |
| X_2t | 0.0183558 | 0.0204684 | 0.8968 | 0.371328 | 0.185664 |
| X_3t | -0.0125763 | 0.0193426 | -0.6502 | 0.516608 | 0.258304 |
| X_4t | 0.0243342 | 0.0326969 | 0.7442 | 0.457946 | 0.228973 |
| X_5t | -0.0637158 | 0.024007 | -2.654 | 0.00884752 | 0.00442376 |
| M1 | -0.22045 | 0.30009 | -0.7346 | 0.463768 | 0.231884 |
| M2 | -0.0262015 | 0.30434 | -0.08609 | 0.931512 | 0.465756 |
| M3 | 0.325625 | 0.30126 | 1.081 | 0.281559 | 0.14078 |
| M4 | -0.192451 | 0.303095 | -0.635 | 0.526468 | 0.263234 |
| M5 | 0.0839012 | 0.299701 | 0.28 | 0.779918 | 0.389959 |
| M6 | 0.146362 | 0.301981 | 0.4847 | 0.628645 | 0.314322 |
| M7 | -0.144542 | 0.303981 | -0.4755 | 0.635155 | 0.317577 |
| M8 | -0.203434 | 0.312604 | -0.6508 | 0.51623 | 0.258115 |
| M9 | -0.173177 | 0.306811 | -0.5644 | 0.573331 | 0.286666 |
| M10 | -0.080801 | 0.31047 | -0.2603 | 0.79504 | 0.39752 |
| M11 | 0.207269 | 0.307795 | 0.6734 | 0.501774 | 0.250887 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.398609 |
| R-squared | 0.158889 |
| Adjusted R-squared | 0.0654323 |
| F-TEST (value) | 1.70013 |
| F-TEST (DF numerator) | 16 |
| F-TEST (DF denominator) | 144 |
| p-value | 0.0526608 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 0.769519 |
| Sum Squared Residuals | 85.2709 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 3 | 3.90524 | -0.905236 |
| 2 | 5 | 4.43981 | 0.560194 |
| 3 | 4 | 4.22721 | -0.227215 |
| 4 | 4 | 3.90441 | 0.0955869 |
| 5 | 5 | 3.49864 | 1.50136 |
| 6 | 5 | 4.4427 | 0.557302 |
| 7 | 2 | 3.53583 | -1.53583 |
| 8 | 5 | 3.95289 | 1.04711 |
| 9 | 4 | 4.19075 | -0.190748 |
| 10 | 4 | 4.14286 | -0.142865 |
| 11 | 5 | 4.63662 | 0.363383 |
| 12 | 3 | 4.60127 | -1.60127 |
| 13 | 5 | 3.73994 | 1.26006 |
| 14 | 3 | 4.05427 | -1.05427 |
| 15 | 5 | 4.54181 | 0.458191 |
| 16 | 3 | 3.77374 | -0.773744 |
| 17 | 4 | 4.06583 | -0.0658347 |
| 18 | 5 | 4.42396 | 0.576039 |
| 19 | 4 | 4.0016 | -0.00160342 |
| 20 | 3 | 3.81746 | -0.81746 |
| 21 | 4 | 4.40663 | -0.406627 |
| 22 | 4 | 3.88945 | 0.11055 |
| 23 | 3 | 4.29624 | -1.29624 |
| 24 | 3 | 3.86359 | -0.863587 |
| 25 | 4 | 4.22122 | -0.221223 |
| 26 | 5 | 4.4552 | 0.544797 |
| 27 | 4 | 4.29886 | -0.298861 |
| 28 | 4 | 3.67808 | 0.321921 |
| 29 | 4 | 4.16305 | -0.163048 |
| 30 | 4 | 4.21024 | -0.210244 |
| 31 | 4 | 4.30369 | -0.303688 |
| 32 | 3 | 3.66577 | -0.665769 |
| 33 | 4 | 4.23782 | -0.237816 |
| 34 | 5 | 4.15754 | 0.842456 |
| 35 | 4 | 4.38188 | -0.381881 |
| 36 | 4 | 4.46742 | -0.467419 |
| 37 | 3 | 3.28213 | -0.282126 |
| 38 | 4 | 4.23544 | -0.235444 |
| 39 | 4 | 4.66003 | -0.660032 |
| 40 | 4 | 4.1296 | -0.129602 |
| 41 | 5 | 4.56763 | 0.432374 |
| 42 | 4 | 4.12768 | -0.127676 |
| 43 | 3 | 4.44559 | -1.44559 |
| 44 | 3 | 3.76916 | -0.76916 |
| 45 | 4 | 4.03825 | -0.0382523 |
| 46 | 4 | 3.87247 | 0.127527 |
| 47 | 4 | 4.62132 | -0.621315 |
| 48 | 5 | 4.25772 | 0.742283 |
| 49 | 4 | 3.9061 | 0.0939039 |
| 50 | 5 | 4.29978 | 0.700221 |
| 51 | 4 | 4.67299 | -0.672993 |
| 52 | 4 | 3.88173 | 0.118265 |
| 53 | 4 | 3.79249 | 0.207508 |
| 54 | 4 | 3.96746 | 0.032542 |
| 55 | 4 | 4.04697 | -0.0469701 |
| 56 | 5 | 4.08914 | 0.910857 |
| 57 | 4 | 4.02132 | -0.021317 |
| 58 | 4 | 4.30119 | -0.301186 |
| 59 | 4 | 4.43371 | -0.433709 |
| 60 | 4 | 3.8963 | 0.103698 |
| 61 | 3 | 3.31388 | -0.313876 |
| 62 | 4 | 4.07039 | -0.0703884 |
| 63 | 5 | 4.35781 | 0.642192 |
| 64 | 1 | 3.58971 | -2.58971 |
| 65 | 3 | 4.12975 | -1.12975 |
| 66 | 5 | 4.28139 | 0.718608 |
| 67 | 4 | 3.60577 | 0.394225 |
| 68 | 4 | 3.88027 | 0.11973 |
| 69 | 3 | 3.99179 | -0.991786 |
| 70 | 4 | 3.98475 | 0.0152479 |
| 71 | 4 | 4.37985 | -0.379847 |
| 72 | 3 | 3.94017 | -0.940172 |
| 73 | 5 | 3.93557 | 1.06443 |
| 74 | 4 | 4.22872 | -0.228716 |
| 75 | 5 | 4.5708 | 0.429197 |
| 76 | 4 | 3.57272 | 0.427283 |
| 77 | 4 | 4.22829 | -0.228289 |
| 78 | 4 | 3.88868 | 0.111321 |
| 79 | 4 | 3.93169 | 0.068306 |
| 80 | 3 | 4.15398 | -1.15398 |
| 81 | 5 | 3.98913 | 1.01087 |
| 82 | NA | NA | 0.4086 |
| 83 | 5 | 5.3746 | -0.374597 |
| 84 | 4 | 3.74441 | 0.255589 |
| 85 | 4 | 2.9067 | 1.0933 |
| 86 | 5 | 5.48481 | -0.484809 |
| 87 | 4 | 3.97722 | 0.0227831 |
| 88 | 4 | 4.91956 | -0.919555 |
| 89 | 3 | 2.59137 | 0.408629 |
| 90 | 4 | 3.97255 | 0.0274515 |
| 91 | 4 | 4.83097 | -0.830972 |
| 92 | 3 | 1.90579 | 1.09421 |
| 93 | 5 | 3.95482 | 1.04518 |
| 94 | 5 | 4.38665 | 0.613346 |
| 95 | 5 | 5.29677 | -0.296773 |
| 96 | 4 | 3.70653 | 0.293467 |
| 97 | 4 | 4.21136 | -0.211361 |
| 98 | 4 | 4.70543 | -0.705434 |
| 99 | 4 | 3.94495 | 0.0550485 |
| 100 | 4 | 4.52063 | -0.520629 |
| 101 | 4 | 4.00308 | -0.00308421 |
| 102 | 4 | 3.02087 | 0.979128 |
| 103 | 5 | 4.94379 | 0.0562132 |
| 104 | 4 | 3.77334 | 0.226658 |
| 105 | 4 | 4.67483 | -0.674829 |
| 106 | 3 | 2.56852 | 0.431477 |
| 107 | 5 | 4.88258 | 0.117419 |
| 108 | 4 | 4.63296 | -0.632963 |
| 109 | 3 | 4.08344 | -1.08344 |
| 110 | 2 | 1.26687 | 0.733133 |
| 111 | 5 | 4.61867 | 0.38133 |
| 112 | 4 | 3.18656 | 0.813439 |
| 113 | 5 | 8.04884 | -3.04884 |
| 114 | 1 | 0.195886 | 0.804114 |
| 115 | 5 | 4.03012 | 0.969875 |
| 116 | 5 | 5.65308 | -0.653079 |
| 117 | 3 | 2.96805 | 0.031951 |
| 118 | 4 | 3.41498 | 0.585016 |
| 119 | 5 | 3.97489 | 1.02511 |
| 120 | 5 | 5.60141 | -0.601411 |
| 121 | 3 | 2.78631 | 0.213689 |
| 122 | 4 | 3.47172 | 0.528282 |
| 123 | 5 | 5.20927 | -0.209271 |
| 124 | 4 | 4.37935 | -0.379348 |
| 125 | 4 | 4.33128 | -0.331276 |
| 126 | 4 | 3.41802 | 0.581982 |
| 127 | 5 | 5.23544 | -0.235439 |
| 128 | 4 | 3.0162 | 0.983798 |
| 129 | 5 | 5.09877 | -0.098773 |
| 130 | 4 | 4.41054 | -0.410538 |
| 131 | 4 | 3.47164 | 0.528356 |
| 132 | 4 | 4.12148 | -0.121483 |
| 133 | 4 | 4.98708 | -0.987084 |
| 134 | 3 | 3.54275 | -0.542745 |
| 135 | 4 | 2.80246 | 1.19754 |
| 136 | 5 | 5.53883 | -0.538829 |
| 137 | 3 | 3.05386 | -0.0538552 |
| 138 | 4 | 4.48909 | -0.489094 |
| 139 | 3 | 3.02073 | -0.0207334 |
| 140 | 4 | 4.92287 | -0.922868 |
| 141 | 3 | 4.01149 | -1.01149 |
| 142 | 3 | 2.24311 | 0.756895 |
| 143 | 5 | 4.10202 | 0.897976 |
| 144 | 5 | 4.07518 | 0.924821 |
| 145 | 5 | 4.35181 | 0.648191 |
| 146 | 5 | 4.6839 | 0.316099 |
| 147 | 5 | 4.87041 | 0.129586 |
| 148 | 4 | 4.28799 | -0.287989 |
| 149 | 4 | 3.66969 | 0.33031 |
| 150 | 4 | 3.03243 | 0.967569 |
| 151 | 5 | 3.61027 | 1.38973 |
| 152 | 5 | 4.85305 | 0.14695 |
| 153 | 4 | 3.94377 | 0.0562328 |
| 154 | 4 | 3.63518 | 0.364817 |
| 155 | 4 | 2.87103 | 1.12897 |
| 156 | 5 | 5.81396 | -0.813956 |
| 157 | 3 | 2.88969 | 0.110312 |
| 158 | 4 | 3.515 | 0.484996 |
| 159 | 5 | 4.04702 | 0.952984 |
| 160 | 5 | 3.72141 | 1.27859 |
| 161 | 5 | 3.95977 | 1.04023 |
| 162 | 5 | NA | NA |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 20 | 0.582958 | 0.834084 | 0.417042 |
| 21 | 0.965905 | 0.0681905 | 0.0340952 |
| 22 | 0.946359 | 0.107282 | 0.0536412 |
| 23 | 0.948537 | 0.102926 | 0.0514632 |
| 24 | 0.969624 | 0.0607526 | 0.0303763 |
| 25 | 0.950765 | 0.0984691 | 0.0492346 |
| 26 | 0.925547 | 0.148907 | 0.0744533 |
| 27 | 0.89609 | 0.20782 | 0.10391 |
| 28 | 0.87923 | 0.24154 | 0.12077 |
| 29 | 0.885216 | 0.229567 | 0.114784 |
| 30 | 0.881392 | 0.237217 | 0.118608 |
| 31 | 0.840803 | 0.318394 | 0.159197 |
| 32 | 0.81795 | 0.3641 | 0.18205 |
| 33 | 0.76736 | 0.46528 | 0.23264 |
| 34 | 0.746128 | 0.507744 | 0.253872 |
| 35 | 0.692558 | 0.614885 | 0.307442 |
| 36 | 0.658631 | 0.682739 | 0.341369 |
| 37 | 0.594144 | 0.811711 | 0.405856 |
| 38 | 0.530868 | 0.938264 | 0.469132 |
| 39 | 0.496403 | 0.992806 | 0.503597 |
| 40 | 0.432121 | 0.864242 | 0.567879 |
| 41 | 0.378596 | 0.757193 | 0.621404 |
| 42 | 0.327117 | 0.654234 | 0.672883 |
| 43 | 0.390341 | 0.780681 | 0.609659 |
| 44 | 0.363082 | 0.726163 | 0.636918 |
| 45 | 0.312355 | 0.624709 | 0.687645 |
| 46 | 0.265106 | 0.530211 | 0.734894 |
| 47 | 0.233199 | 0.466398 | 0.766801 |
| 48 | 0.353192 | 0.706385 | 0.646808 |
| 49 | 0.30358 | 0.60716 | 0.69642 |
| 50 | 0.288344 | 0.576688 | 0.711656 |
| 51 | 0.259809 | 0.519618 | 0.740191 |
| 52 | 0.221058 | 0.442116 | 0.778942 |
| 53 | 0.185295 | 0.37059 | 0.814705 |
| 54 | 0.153449 | 0.306897 | 0.846551 |
| 55 | 0.135263 | 0.270526 | 0.864737 |
| 56 | 0.176196 | 0.352392 | 0.823804 |
| 57 | 0.147301 | 0.294602 | 0.852699 |
| 58 | 0.128218 | 0.256435 | 0.871782 |
| 59 | 0.107135 | 0.214271 | 0.892865 |
| 60 | 0.0944841 | 0.188968 | 0.905516 |
| 61 | 0.0763529 | 0.152706 | 0.923647 |
| 62 | 0.0595749 | 0.11915 | 0.940425 |
| 63 | 0.0567341 | 0.113468 | 0.943266 |
| 64 | 0.342088 | 0.684177 | 0.657912 |
| 65 | 0.424185 | 0.848371 | 0.575815 |
| 66 | 0.414342 | 0.828685 | 0.585658 |
| 67 | 0.409268 | 0.818535 | 0.590732 |
| 68 | 0.36244 | 0.724879 | 0.63756 |
| 69 | 0.391674 | 0.783348 | 0.608326 |
| 70 | 0.343572 | 0.687145 | 0.656428 |
| 71 | 0.313419 | 0.626839 | 0.686581 |
| 72 | 0.331454 | 0.662909 | 0.668546 |
| 73 | 0.392821 | 0.785641 | 0.607179 |
| 74 | 0.346302 | 0.692605 | 0.653698 |
| 75 | 0.311612 | 0.623223 | 0.688388 |
| 76 | 0.282812 | 0.565624 | 0.717188 |
| 77 | 0.248888 | 0.497776 | 0.751112 |
| 78 | 0.211046 | 0.422092 | 0.788954 |
| 79 | 0.202609 | 0.405218 | 0.797391 |
| 80 | 0.264331 | 0.528662 | 0.735669 |
| 81 | 0.318455 | 0.636909 | 0.681545 |
| 82 | 0.299506 | 0.599011 | 0.700494 |
| 83 | 0.284287 | 0.568574 | 0.715713 |
| 84 | 0.25449 | 0.50898 | 0.74551 |
| 85 | 0.316842 | 0.633683 | 0.683158 |
| 86 | 0.287743 | 0.575485 | 0.712257 |
| 87 | 0.254589 | 0.509178 | 0.745411 |
| 88 | 0.281929 | 0.563858 | 0.718071 |
| 89 | 0.274505 | 0.549009 | 0.725495 |
| 90 | 0.253598 | 0.507195 | 0.746402 |
| 91 | 0.27456 | 0.54912 | 0.72544 |
| 92 | 0.332972 | 0.665943 | 0.667028 |
| 93 | 0.375243 | 0.750485 | 0.624757 |
| 94 | 0.353414 | 0.706828 | 0.646586 |
| 95 | 0.363168 | 0.726337 | 0.636832 |
| 96 | 0.333472 | 0.666945 | 0.666528 |
| 97 | 0.292897 | 0.585794 | 0.707103 |
| 98 | 0.298639 | 0.597278 | 0.701361 |
| 99 | 0.271725 | 0.54345 | 0.728275 |
| 100 | 0.269956 | 0.539912 | 0.730044 |
| 101 | 0.237336 | 0.474672 | 0.762664 |
| 102 | 0.254109 | 0.508217 | 0.745891 |
| 103 | 0.214627 | 0.429254 | 0.785373 |
| 104 | 0.189771 | 0.379542 | 0.810229 |
| 105 | 0.168138 | 0.336276 | 0.831862 |
| 106 | 0.145365 | 0.290729 | 0.854635 |
| 107 | 0.167687 | 0.335373 | 0.832313 |
| 108 | 0.14724 | 0.294479 | 0.85276 |
| 109 | 0.20123 | 0.402459 | 0.79877 |
| 110 | 0.197512 | 0.395023 | 0.802488 |
| 111 | 0.167712 | 0.335423 | 0.832288 |
| 112 | 0.185763 | 0.371527 | 0.814237 |
| 113 | 0.949497 | 0.101005 | 0.0505027 |
| 114 | 0.938664 | 0.122672 | 0.0613359 |
| 115 | 0.936234 | 0.127533 | 0.0637663 |
| 116 | 0.928308 | 0.143385 | 0.0716924 |
| 117 | 0.913462 | 0.173077 | 0.0865383 |
| 118 | 0.897866 | 0.204269 | 0.102134 |
| 119 | 0.898009 | 0.203981 | 0.101991 |
| 120 | 0.872602 | 0.254797 | 0.127398 |
| 121 | 0.835177 | 0.329646 | 0.164823 |
| 122 | 0.802483 | 0.395035 | 0.197517 |
| 123 | 0.807317 | 0.385367 | 0.192683 |
| 124 | 0.784841 | 0.430318 | 0.215159 |
| 125 | 0.730484 | 0.539032 | 0.269516 |
| 126 | 0.672582 | 0.654837 | 0.327418 |
| 127 | 0.764803 | 0.470394 | 0.235197 |
| 128 | 0.73541 | 0.52918 | 0.26459 |
| 129 | 0.666117 | 0.667766 | 0.333883 |
| 130 | 0.621246 | 0.757508 | 0.378754 |
| 131 | 0.552082 | 0.895836 | 0.447918 |
| 132 | 0.516801 | 0.966398 | 0.483199 |
| 133 | 0.471755 | 0.943511 | 0.528245 |
| 134 | 0.462397 | 0.924794 | 0.537603 |
| 135 | 0.394293 | 0.788585 | 0.605707 |
| 136 | 0.451465 | 0.902931 | 0.548535 |
| 137 | 0.444758 | 0.889517 | 0.555242 |
| 138 | 0.361179 | 0.722358 | 0.638821 |
| 139 | 0.321882 | 0.643764 | 0.678118 |
| 140 | 0.243861 | 0.487721 | 0.756139 |
| 141 | 0.745661 | 0.508679 | 0.254339 |
| 142 | 0.731606 | 0.536787 | 0.268394 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 0 | 0 | OK |
| 5% type I error level | 0 | 0 | OK |
| 10% type I error level | 3 | 0.0243902 | OK |
