| Multiple Linear Regression - Estimated Regression Equation |
| Y_t[t] = + 4.73467 -0.0682697X_1t[t] + 0.0129274X_2t[t] -0.00886996X_3t[t] + 0.0291562X_4t[t] -0.0642349X_5t[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) | 4.73467 | 0.952706 | 4.97 | 1.75671e-06 | 8.78353e-07 |
| X_1t | -0.0682697 | 0.0526053 | -1.298 | 0.196294 | 0.098147 |
| X_2t | 0.0129274 | 0.0194087 | 0.6661 | 0.506361 | 0.253181 |
| X_3t | -0.00886996 | 0.0183788 | -0.4826 | 0.630047 | 0.315024 |
| X_4t | 0.0291562 | 0.0309548 | 0.9419 | 0.347712 | 0.173856 |
| X_5t | -0.0642349 | 0.0227051 | -2.829 | 0.00528576 | 0.00264288 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.334264 |
| R-squared | 0.111732 |
| Adjusted R-squared | 0.0830785 |
| F-TEST (value) | 3.89939 |
| F-TEST (DF numerator) | 5 |
| F-TEST (DF denominator) | 155 |
| p-value | 0.00234046 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 0.762219 |
| Sum Squared Residuals | 90.0516 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 3 | 4.08712 | -1.08712 |
| 2 | 5 | 4.43188 | 0.568117 |
| 3 | 4 | 3.89213 | 0.107872 |
| 4 | 4 | 4.08042 | -0.0804217 |
| 5 | 5 | 3.41743 | 1.58257 |
| 6 | 5 | 4.27428 | 0.725722 |
| 7 | 2 | 3.61754 | -1.61754 |
| 8 | 5 | 4.14687 | 0.853128 |
| 9 | 4 | 4.34326 | -0.343257 |
| 10 | 4 | 4.20514 | -0.20514 |
| 11 | 5 | 4.39463 | 0.605366 |
| 12 | 3 | 4.59722 | -1.59722 |
| 13 | 5 | 3.90216 | 1.09784 |
| 14 | 3 | 4.05938 | -1.05938 |
| 15 | 5 | 4.23766 | 0.762336 |
| 16 | 3 | 3.95492 | -0.954922 |
| 17 | 4 | 3.94723 | 0.0527681 |
| 18 | 5 | 4.26831 | 0.73169 |
| 19 | 4 | 4.12146 | -0.121464 |
| 20 | 3 | 4.01807 | -1.01807 |
| 21 | 4 | 4.58946 | -0.589461 |
| 22 | 4 | 3.94054 | 0.0594644 |
| 23 | 3 | 4.06126 | -1.06126 |
| 24 | 3 | 3.83976 | -0.839757 |
| 25 | 4 | 4.40273 | -0.402727 |
| 26 | 5 | 4.39207 | 0.607929 |
| 27 | 4 | 3.96683 | 0.03317 |
| 28 | 4 | 3.86813 | 0.131865 |
| 29 | 4 | 4.06528 | -0.0652752 |
| 30 | 4 | 4.02581 | -0.0258128 |
| 31 | 4 | 4.4341 | -0.434101 |
| 32 | 3 | 3.87403 | -0.874034 |
| 33 | 4 | 4.38171 | -0.381707 |
| 34 | 5 | 4.23543 | 0.764573 |
| 35 | 4 | 4.13989 | -0.139891 |
| 36 | 4 | 4.46691 | -0.466913 |
| 37 | 3 | 3.47096 | -0.470959 |
| 38 | 4 | 4.23253 | -0.232527 |
| 39 | 4 | 4.34656 | -0.346557 |
| 40 | 4 | 4.28976 | -0.289757 |
| 41 | 5 | 4.44703 | 0.552971 |
| 42 | 4 | 3.97082 | 0.0291806 |
| 43 | 3 | 4.55335 | -1.55335 |
| 44 | 3 | 3.93539 | -0.935392 |
| 45 | 4 | 4.14296 | -0.142959 |
| 46 | 4 | 3.91032 | 0.0896842 |
| 47 | 4 | 4.39787 | -0.397867 |
| 48 | 5 | 4.24911 | 0.75089 |
| 49 | 4 | 4.12205 | -0.122055 |
| 50 | 5 | 4.27317 | 0.726826 |
| 51 | 4 | 4.36236 | -0.362363 |
| 52 | 4 | 4.0498 | -0.0498015 |
| 53 | 4 | 3.67878 | 0.321216 |
| 54 | 4 | 3.80984 | 0.190155 |
| 55 | 4 | 4.16645 | -0.166454 |
| 56 | 5 | 4.25432 | 0.745675 |
| 57 | 4 | 4.15909 | -0.159091 |
| 58 | 4 | 4.39414 | -0.39414 |
| 59 | 4 | 4.19158 | -0.191576 |
| 60 | 4 | 3.86229 | 0.137713 |
| 61 | 3 | 3.48134 | -0.48134 |
| 62 | 4 | 4.05466 | -0.0546603 |
| 63 | 5 | 4.00404 | 0.995962 |
| 64 | 1 | 3.78772 | -2.78772 |
| 65 | 3 | 4.02364 | -1.02364 |
| 66 | 5 | 4.10257 | 0.897426 |
| 67 | 4 | 3.70872 | 0.291282 |
| 68 | 4 | 4.05244 | -0.0524444 |
| 69 | 3 | 4.14498 | -1.14498 |
| 70 | 4 | 4.05565 | -0.0556502 |
| 71 | 4 | 4.13838 | -0.138381 |
| 72 | 3 | 3.95999 | -0.959992 |
| 73 | 5 | 4.15749 | 0.842513 |
| 74 | 4 | 4.24762 | -0.247622 |
| 75 | 5 | 4.19754 | 0.802455 |
| 76 | 4 | 3.69254 | 0.307463 |
| 77 | 4 | 4.13578 | -0.135783 |
| 78 | 4 | 3.70839 | 0.291614 |
| 79 | 4 | 4.08261 | -0.082613 |
| 80 | 3 | 4.29653 | -1.29653 |
| 81 | 5 | 4.1631 | 0.8369 |
| 82 | NA | NA | 0.623175 |
| 83 | 5 | 5.34288 | -0.34288 |
| 84 | 4 | 3.96714 | 0.0328614 |
| 85 | 4 | 2.91328 | 1.08672 |
| 86 | 5 | 5.14093 | -0.140927 |
| 87 | 4 | 4.15572 | -0.155719 |
| 88 | 4 | 4.83162 | -0.831619 |
| 89 | 3 | 2.38642 | 0.613584 |
| 90 | 4 | 4.13536 | -0.135358 |
| 91 | 4 | 4.99038 | -0.99038 |
| 92 | 3 | 2.08441 | 0.915595 |
| 93 | 5 | 4.00331 | 0.996693 |
| 94 | 5 | 4.17053 | 0.829467 |
| 95 | 5 | 5.26982 | -0.269821 |
| 96 | 4 | 3.88331 | 0.116693 |
| 97 | 4 | 4.20415 | -0.204149 |
| 98 | 4 | 4.35913 | -0.359132 |
| 99 | 4 | 4.14614 | -0.146138 |
| 100 | 4 | 4.41855 | -0.418554 |
| 101 | 4 | 3.81504 | 0.184963 |
| 102 | 4 | 3.15793 | 0.842066 |
| 103 | 5 | 5.10451 | -0.104508 |
| 104 | 4 | 3.95186 | 0.0481447 |
| 105 | 4 | 4.66853 | -0.668525 |
| 106 | 3 | 2.33403 | 0.665967 |
| 107 | 5 | 4.85047 | 0.149534 |
| 108 | 4 | 4.80803 | -0.808032 |
| 109 | 3 | 4.05351 | -1.05351 |
| 110 | 2 | 0.949353 | 1.05065 |
| 111 | 5 | 4.79029 | 0.209709 |
| 112 | 4 | 3.11578 | 0.88422 |
| 113 | 5 | 7.89069 | -2.89069 |
| 114 | 1 | 0.324053 | 0.675947 |
| 115 | 5 | 4.20714 | 0.792859 |
| 116 | 5 | 5.83749 | -0.83749 |
| 117 | 3 | 3.05119 | -0.0511916 |
| 118 | 4 | 3.20301 | 0.796986 |
| 119 | 5 | 3.94164 | 1.05836 |
| 120 | 5 | 5.80982 | -0.809822 |
| 121 | 3 | 2.79041 | 0.209595 |
| 122 | 4 | 3.13286 | 0.867142 |
| 123 | 5 | 5.38977 | -0.389775 |
| 124 | 4 | 4.27572 | -0.27572 |
| 125 | 4 | 4.17381 | -0.173813 |
| 126 | 4 | 3.52716 | 0.472838 |
| 127 | 5 | 5.40124 | -0.401239 |
| 128 | 4 | 3.21146 | 0.788545 |
| 129 | 5 | 5.15536 | -0.155365 |
| 130 | 4 | 4.18674 | -0.18674 |
| 131 | 4 | 3.44916 | 0.550838 |
| 132 | 4 | 4.30896 | -0.308957 |
| 133 | 4 | 5.01836 | -1.01836 |
| 134 | 3 | 3.2011 | -0.201105 |
| 135 | 4 | 2.98044 | 1.01956 |
| 136 | 5 | 5.40347 | -0.403469 |
| 137 | 3 | 2.89477 | 0.105233 |
| 138 | 4 | 4.62712 | -0.627119 |
| 139 | 3 | 3.2067 | -0.206695 |
| 140 | 4 | 5.09184 | -1.09184 |
| 141 | 3 | 4.09561 | -1.09561 |
| 142 | 3 | 2.04678 | 0.953221 |
| 143 | 5 | 4.10807 | 0.891933 |
| 144 | 5 | 4.25659 | 0.74341 |
| 145 | 5 | 4.3271 | 0.672902 |
| 146 | 5 | 4.33146 | 0.668537 |
| 147 | 5 | 5.02506 | -0.0250577 |
| 148 | 4 | 4.17532 | -0.175324 |
| 149 | 4 | 3.46735 | 0.532651 |
| 150 | 4 | 3.16605 | 0.833951 |
| 151 | 5 | 3.75859 | 1.24141 |
| 152 | 5 | 5.04284 | -0.0428351 |
| 153 | 4 | 4.01064 | -0.0106419 |
| 154 | 4 | 3.38134 | 0.61866 |
| 155 | 4 | 2.83603 | 1.16397 |
| 156 | 5 | 5.99038 | -0.99038 |
| 157 | 3 | 2.91944 | 0.0805579 |
| 158 | 4 | 3.21146 | 0.788545 |
| 159 | 5 | 4.2134 | 0.786605 |
| 160 | 5 | 3.62193 | 1.37807 |
| 161 | 5 | 3.79654 | 1.20346 |
| 162 | 5 | NA | NA |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 9 | 0.199291 | 0.398581 | 0.800709 |
| 10 | 0.109431 | 0.218862 | 0.890569 |
| 11 | 0.0836245 | 0.167249 | 0.916376 |
| 12 | 0.914958 | 0.170084 | 0.0850421 |
| 13 | 0.975236 | 0.049529 | 0.0247645 |
| 14 | 0.970073 | 0.0598539 | 0.0299269 |
| 15 | 0.953531 | 0.0929384 | 0.0464692 |
| 16 | 0.979865 | 0.0402692 | 0.0201346 |
| 17 | 0.970597 | 0.0588052 | 0.0294026 |
| 18 | 0.969435 | 0.0611297 | 0.0305648 |
| 19 | 0.959756 | 0.0804887 | 0.0402443 |
| 20 | 0.977866 | 0.0442672 | 0.0221336 |
| 21 | 0.97044 | 0.0591201 | 0.0295601 |
| 22 | 0.956518 | 0.0869632 | 0.0434816 |
| 23 | 0.964183 | 0.0716337 | 0.0358169 |
| 24 | 0.962547 | 0.0749062 | 0.0374531 |
| 25 | 0.948018 | 0.103964 | 0.0519818 |
| 26 | 0.950987 | 0.0980264 | 0.0490132 |
| 27 | 0.932758 | 0.134483 | 0.0672415 |
| 28 | 0.910967 | 0.178066 | 0.0890328 |
| 29 | 0.883052 | 0.233896 | 0.116948 |
| 30 | 0.849849 | 0.300302 | 0.150151 |
| 31 | 0.823193 | 0.353614 | 0.176807 |
| 32 | 0.826905 | 0.346189 | 0.173095 |
| 33 | 0.791554 | 0.416892 | 0.208446 |
| 34 | 0.800293 | 0.399414 | 0.199707 |
| 35 | 0.757844 | 0.484312 | 0.242156 |
| 36 | 0.721811 | 0.556378 | 0.278189 |
| 37 | 0.684094 | 0.631812 | 0.315906 |
| 38 | 0.634101 | 0.731798 | 0.365899 |
| 39 | 0.585202 | 0.829597 | 0.414798 |
| 40 | 0.53437 | 0.931261 | 0.46563 |
| 41 | 0.519516 | 0.960967 | 0.480484 |
| 42 | 0.466813 | 0.933625 | 0.533187 |
| 43 | 0.599036 | 0.801929 | 0.400964 |
| 44 | 0.610424 | 0.779153 | 0.389576 |
| 45 | 0.560777 | 0.878445 | 0.439223 |
| 46 | 0.509548 | 0.980904 | 0.490452 |
| 47 | 0.46737 | 0.934741 | 0.53263 |
| 48 | 0.481347 | 0.962693 | 0.518653 |
| 49 | 0.432269 | 0.864538 | 0.567731 |
| 50 | 0.443365 | 0.88673 | 0.556635 |
| 51 | 0.401267 | 0.802535 | 0.598733 |
| 52 | 0.354877 | 0.709755 | 0.645123 |
| 53 | 0.320729 | 0.641457 | 0.679271 |
| 54 | 0.279403 | 0.558805 | 0.720597 |
| 55 | 0.240105 | 0.480211 | 0.759895 |
| 56 | 0.249787 | 0.499573 | 0.750213 |
| 57 | 0.213578 | 0.427156 | 0.786422 |
| 58 | 0.185927 | 0.371853 | 0.814073 |
| 59 | 0.15643 | 0.312861 | 0.84357 |
| 60 | 0.129976 | 0.259953 | 0.870024 |
| 61 | 0.113642 | 0.227284 | 0.886358 |
| 62 | 0.0919244 | 0.183849 | 0.908076 |
| 63 | 0.108177 | 0.216354 | 0.891823 |
| 64 | 0.564772 | 0.870456 | 0.435228 |
| 65 | 0.589643 | 0.820715 | 0.410357 |
| 66 | 0.607795 | 0.784411 | 0.392205 |
| 67 | 0.569443 | 0.861115 | 0.430557 |
| 68 | 0.526202 | 0.947596 | 0.473798 |
| 69 | 0.587361 | 0.825279 | 0.412639 |
| 70 | 0.542818 | 0.914364 | 0.457182 |
| 71 | 0.497713 | 0.995426 | 0.502287 |
| 72 | 0.523343 | 0.953313 | 0.476657 |
| 73 | 0.537148 | 0.925704 | 0.462852 |
| 74 | 0.495304 | 0.990608 | 0.504696 |
| 75 | 0.508131 | 0.983739 | 0.491869 |
| 76 | 0.469068 | 0.938136 | 0.530932 |
| 77 | 0.430749 | 0.861499 | 0.569251 |
| 78 | 0.395861 | 0.791721 | 0.604139 |
| 79 | 0.357142 | 0.714285 | 0.642858 |
| 80 | 0.436084 | 0.872168 | 0.563916 |
| 81 | 0.452033 | 0.904067 | 0.547967 |
| 82 | 0.437999 | 0.875998 | 0.562001 |
| 83 | 0.405899 | 0.811798 | 0.594101 |
| 84 | 0.367235 | 0.73447 | 0.632765 |
| 85 | 0.417313 | 0.834627 | 0.582687 |
| 86 | 0.375188 | 0.750375 | 0.624812 |
| 87 | 0.334343 | 0.668686 | 0.665657 |
| 88 | 0.344345 | 0.688689 | 0.655655 |
| 89 | 0.335722 | 0.671445 | 0.664278 |
| 90 | 0.303675 | 0.60735 | 0.696325 |
| 91 | 0.336308 | 0.672615 | 0.663692 |
| 92 | 0.351222 | 0.702445 | 0.648778 |
| 93 | 0.377851 | 0.755702 | 0.622149 |
| 94 | 0.387217 | 0.774434 | 0.612783 |
| 95 | 0.353668 | 0.707335 | 0.646332 |
| 96 | 0.311611 | 0.623221 | 0.688389 |
| 97 | 0.275401 | 0.550802 | 0.724599 |
| 98 | 0.25612 | 0.512239 | 0.74388 |
| 99 | 0.222177 | 0.444354 | 0.777823 |
| 100 | 0.20904 | 0.418079 | 0.79096 |
| 101 | 0.17785 | 0.355701 | 0.82215 |
| 102 | 0.177491 | 0.354982 | 0.822509 |
| 103 | 0.148079 | 0.296157 | 0.851921 |
| 104 | 0.122409 | 0.244817 | 0.877591 |
| 105 | 0.115316 | 0.230632 | 0.884684 |
| 106 | 0.104821 | 0.209642 | 0.895179 |
| 107 | 0.0856456 | 0.171291 | 0.914354 |
| 108 | 0.085454 | 0.170908 | 0.914546 |
| 109 | 0.127544 | 0.255088 | 0.872456 |
| 110 | 0.146605 | 0.29321 | 0.853395 |
| 111 | 0.122153 | 0.244307 | 0.877847 |
| 112 | 0.147682 | 0.295364 | 0.852318 |
| 113 | 0.82527 | 0.34946 | 0.17473 |
| 114 | 0.802133 | 0.395734 | 0.197867 |
| 115 | 0.787557 | 0.424886 | 0.212443 |
| 116 | 0.820373 | 0.359254 | 0.179627 |
| 117 | 0.783763 | 0.432475 | 0.216237 |
| 118 | 0.811067 | 0.377865 | 0.188933 |
| 119 | 0.809556 | 0.380888 | 0.190444 |
| 120 | 0.830869 | 0.338262 | 0.169131 |
| 121 | 0.798228 | 0.403543 | 0.201772 |
| 122 | 0.792073 | 0.415854 | 0.207927 |
| 123 | 0.755552 | 0.488896 | 0.244448 |
| 124 | 0.715425 | 0.569149 | 0.284575 |
| 125 | 0.664554 | 0.670892 | 0.335446 |
| 126 | 0.621987 | 0.756027 | 0.378013 |
| 127 | 0.652368 | 0.695264 | 0.347632 |
| 128 | 0.613995 | 0.77201 | 0.386005 |
| 129 | 0.578814 | 0.842372 | 0.421186 |
| 130 | 0.517729 | 0.964542 | 0.482271 |
| 131 | 0.491578 | 0.983156 | 0.508422 |
| 132 | 0.489486 | 0.978973 | 0.510514 |
| 133 | 0.573212 | 0.853577 | 0.426788 |
| 134 | 0.572743 | 0.854514 | 0.427257 |
| 135 | 0.557536 | 0.884928 | 0.442464 |
| 136 | 0.653796 | 0.692408 | 0.346204 |
| 137 | 0.599054 | 0.801892 | 0.400946 |
| 138 | 0.61373 | 0.77254 | 0.38627 |
| 139 | 0.565082 | 0.869836 | 0.434918 |
| 140 | 0.689103 | 0.621793 | 0.310897 |
| 141 | 0.845785 | 0.30843 | 0.154215 |
| 142 | 0.797547 | 0.404906 | 0.202453 |
| 143 | 0.779715 | 0.44057 | 0.220285 |
| 144 | 0.715068 | 0.569864 | 0.284932 |
| 145 | 0.637015 | 0.725969 | 0.362985 |
| 146 | 0.554735 | 0.89053 | 0.445265 |
| 147 | 0.452784 | 0.905569 | 0.547216 |
| 148 | 0.348783 | 0.697567 | 0.651217 |
| 149 | 0.257281 | 0.514561 | 0.742719 |
| 150 | 0.189321 | 0.378643 | 0.810679 |
| 151 | 0.373372 | 0.746745 | 0.626628 |
| 152 | 0.274329 | 0.548658 | 0.725671 |
| 153 | 0.182404 | 0.364809 | 0.817596 |
| 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 | 3 | 0.0206897 | OK |
| 10% type I error level | 13 | 0.0896552 | OK |
