| Multiple Linear Regression - Estimated Regression Equation |
| Y_t [t] = + 4.86568 + 0.245042X_1t[t] -0.0726865X_2t[t] + 0.0141811X_3t[t] -0.0166972X_4t[t] + 0.0157767X_5t[t] -0.0714425X_6t[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) | 4.86568 | 0.947736 | 5.134 | 8.44843e-07 | 4.22421e-07 |
| X_1t | 0.245042 | 0.131135 | 1.869 | 0.0635742 | 0.0317871 |
| X_2t | -0.0726865 | 0.052241 | -1.391 | 0.16612 | 0.08306 |
| X_3t | 0.0141811 | 0.0192662 | 0.7361 | 0.462815 | 0.231408 |
| X_4t | -0.0166972 | 0.0187078 | -0.8925 | 0.373504 | 0.186752 |
| X_5t | 0.0157767 | 0.0315326 | 0.5003 | 0.617558 | 0.308779 |
| X_6t | -0.0714425 | 0.0228526 | -3.126 | 0.00211706 | 0.00105853 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.362527 |
| R-squared | 0.131426 |
| Adjusted R-squared | 0.0975856 |
| F-TEST (value) | 3.88369 |
| F-TEST (DF numerator) | 6 |
| F-TEST (DF denominator) | 154 |
| p-value | 0.0012229 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 0.756165 |
| Sum Squared Residuals | 88.055 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 3 | 4.15745 | -1.15745 |
| 2 | 5 | 4.50919 | 0.490809 |
| 3 | 4 | 4.00671 | -0.00670532 |
| 4 | 4 | 3.9679 | 0.0320993 |
| 5 | 5 | 3.39076 | 1.60924 |
| 6 | 5 | 4.35843 | 0.641571 |
| 7 | 2 | 3.67691 | -1.67691 |
| 8 | 5 | 4.2357 | 0.764297 |
| 9 | 4 | 4.44067 | -0.440668 |
| 10 | 4 | 4.26312 | -0.263117 |
| 11 | 5 | 4.24964 | 0.750356 |
| 12 | 3 | 4.66336 | -1.66336 |
| 13 | 5 | 3.78789 | 1.21211 |
| 14 | 3 | 4.09044 | -1.09044 |
| 15 | 5 | 4.26669 | 0.733312 |
| 16 | 3 | 3.79806 | -0.798063 |
| 17 | 4 | 3.7988 | 0.201202 |
| 18 | 5 | 4.30636 | 0.693637 |
| 19 | 4 | 3.95424 | 0.0457581 |
| 20 | 3 | 4.09011 | -1.09011 |
| 21 | 4 | 4.43395 | -0.433954 |
| 22 | 4 | 4.08768 | -0.0876752 |
| 23 | 3 | 4.12909 | -1.12909 |
| 24 | 3 | 3.90959 | -0.909587 |
| 25 | 4 | 4.24837 | -0.248372 |
| 26 | 5 | 4.61113 | 0.388866 |
| 27 | 4 | 3.77653 | 0.223472 |
| 28 | 4 | 3.91905 | 0.080945 |
| 29 | 4 | 4.14575 | -0.14575 |
| 30 | 4 | 3.92322 | 0.0767753 |
| 31 | 4 | 4.57386 | -0.573863 |
| 32 | 3 | 3.72932 | -0.729323 |
| 33 | 4 | 4.48051 | -0.480505 |
| 34 | 5 | 4.30747 | 0.692531 |
| 35 | 4 | 4.02065 | -0.0206463 |
| 36 | 4 | 4.33096 | -0.330959 |
| 37 | 3 | 3.35406 | -0.354063 |
| 38 | 4 | 4.08614 | -0.086136 |
| 39 | 4 | 4.43974 | -0.439743 |
| 40 | 4 | 4.18329 | -0.183287 |
| 41 | 5 | 4.33134 | 0.668658 |
| 42 | 4 | 4.03033 | -0.0303341 |
| 43 | 3 | 4.43274 | -1.43274 |
| 44 | 3 | 3.80905 | -0.809053 |
| 45 | 4 | 4.32177 | -0.321765 |
| 46 | 4 | 4.03204 | -0.0320421 |
| 47 | 4 | 4.47368 | -0.473684 |
| 48 | 5 | 4.34338 | 0.65662 |
| 49 | 4 | 4.1376 | -0.137604 |
| 50 | 5 | 4.17108 | 0.828916 |
| 51 | 4 | 4.42232 | -0.422316 |
| 52 | 4 | 3.92084 | 0.0791584 |
| 53 | 4 | 3.53765 | 0.46235 |
| 54 | 4 | 3.88374 | 0.116258 |
| 55 | 4 | 4.07022 | -0.0702215 |
| 56 | 5 | 4.36206 | 0.637944 |
| 57 | 4 | 4.22867 | -0.228671 |
| 58 | 4 | 4.50223 | -0.502227 |
| 59 | 4 | 4.07309 | -0.073094 |
| 60 | 4 | 3.96596 | 0.0340446 |
| 61 | 3 | 3.40256 | -0.402559 |
| 62 | 4 | 3.92087 | 0.0791255 |
| 63 | 5 | 4.13363 | 0.866372 |
| 64 | 1 | 3.85016 | -2.85016 |
| 65 | 3 | 4.11939 | -1.11939 |
| 66 | 5 | 3.99773 | 1.00227 |
| 67 | 4 | 3.80478 | 0.195222 |
| 68 | 4 | 3.98122 | 0.0187837 |
| 69 | 3 | 4.1854 | -1.1854 |
| 70 | 4 | 3.86228 | 0.137719 |
| 71 | 4 | 3.97719 | 0.0228127 |
| 72 | 3 | 3.97824 | -0.978236 |
| 73 | 5 | 4.20388 | 0.796124 |
| 74 | 4 | 4.05112 | -0.051119 |
| 75 | 5 | 4.12516 | 0.87484 |
| 76 | 4 | 3.8037 | 0.196302 |
| 77 | 4 | 4.16599 | -0.165994 |
| 78 | 4 | 3.80207 | 0.197929 |
| 79 | 4 | 3.93464 | 0.0653606 |
| 80 | 3 | 4.2379 | -1.2379 |
| 81 | 5 | 3.99226 | 1.00774 |
| 82 | NA | NA | 0.535465 |
| 83 | 5 | 5.18878 | -0.18878 |
| 84 | 4 | 4.0397 | -0.0396967 |
| 85 | 4 | 3.01675 | 0.98325 |
| 86 | 5 | 4.94287 | 0.0571276 |
| 87 | 4 | 4.25616 | -0.256161 |
| 88 | 4 | 4.93004 | -0.93004 |
| 89 | 3 | 2.52068 | 0.479317 |
| 90 | 4 | 4.17029 | -0.170292 |
| 91 | 4 | 5.10199 | -1.10199 |
| 92 | 3 | 2.11198 | 0.888023 |
| 93 | 5 | 4.12784 | 0.872165 |
| 94 | 5 | 4.32065 | 0.679353 |
| 95 | 5 | 5.33816 | -0.338162 |
| 96 | 4 | 3.97886 | 0.0211357 |
| 97 | 4 | 4.33337 | -0.33337 |
| 98 | 4 | 4.18662 | -0.186616 |
| 99 | 4 | 3.97683 | 0.0231679 |
| 100 | 4 | 4.48389 | -0.483887 |
| 101 | 4 | 3.66114 | 0.338864 |
| 102 | 4 | 3.20748 | 0.792521 |
| 103 | 5 | 5.04855 | -0.0485471 |
| 104 | 4 | 3.97537 | 0.0246322 |
| 105 | 4 | 4.5648 | -0.5648 |
| 106 | 3 | 2.41336 | 0.586635 |
| 107 | 5 | 4.62571 | 0.374285 |
| 108 | 4 | 4.68684 | -0.686844 |
| 109 | 3 | 4.05323 | -1.05323 |
| 110 | 2 | 1.01382 | 0.986177 |
| 111 | 5 | 4.91015 | 0.0898483 |
| 112 | 4 | 3.18077 | 0.819235 |
| 113 | 5 | 7.72662 | -2.72662 |
| 114 | 1 | 0.375992 | 0.624008 |
| 115 | 5 | 4.05762 | 0.942384 |
| 116 | 5 | 5.86772 | -0.867719 |
| 117 | 3 | 3.09872 | -0.0987161 |
| 118 | 4 | 3.30842 | 0.691582 |
| 119 | 5 | 4.00666 | 0.993343 |
| 120 | 5 | 5.8875 | -0.887502 |
| 121 | 3 | 2.91105 | 0.0889523 |
| 122 | 4 | 3.18543 | 0.814574 |
| 123 | 5 | 5.47496 | -0.474956 |
| 124 | 4 | 4.39347 | -0.393471 |
| 125 | 4 | 4.30016 | -0.300162 |
| 126 | 4 | 3.39001 | 0.609987 |
| 127 | 5 | 5.44619 | -0.446195 |
| 128 | 4 | 3.22772 | 0.772281 |
| 129 | 5 | 5.24555 | -0.245554 |
| 130 | 4 | 4.0693 | -0.069301 |
| 131 | 4 | 3.32318 | 0.676815 |
| 132 | 4 | 4.39131 | -0.391312 |
| 133 | 4 | 4.86696 | -0.866957 |
| 134 | 3 | 3.01683 | -0.016831 |
| 135 | 4 | 3.06876 | 0.931239 |
| 136 | 5 | 5.30738 | -0.307382 |
| 137 | 3 | 2.72034 | 0.279655 |
| 138 | 4 | 4.71845 | -0.718447 |
| 139 | 3 | 3.29906 | -0.299055 |
| 140 | 4 | 4.95028 | -0.950283 |
| 141 | 3 | 4.18258 | -1.18258 |
| 142 | 3 | 1.85724 | 1.14276 |
| 143 | 5 | 4.19692 | 0.80308 |
| 144 | 5 | 4.1822 | 0.817797 |
| 145 | 5 | 4.43583 | 0.564171 |
| 146 | 5 | 4.4631 | 0.5369 |
| 147 | 5 | 4.9015 | 0.0985048 |
| 148 | 4 | 4.08692 | -0.0869187 |
| 149 | 4 | 3.34852 | 0.651479 |
| 150 | 4 | 3.20245 | 0.797553 |
| 151 | 5 | 3.81534 | 1.18466 |
| 152 | 5 | 4.84096 | 0.159041 |
| 153 | 4 | 4.0968 | -0.096797 |
| 154 | 4 | 3.48748 | 0.512518 |
| 155 | 4 | 2.93451 | 1.06549 |
| 156 | 5 | 6.10199 | -1.10199 |
| 157 | 3 | 2.97632 | 0.0236835 |
| 158 | 4 | 3.22772 | 0.772281 |
| 159 | 5 | 4.35691 | 0.643086 |
| 160 | 5 | 3.69239 | 1.30761 |
| 161 | 5 | 3.86271 | 1.13729 |
| 162 | 5 | NA | NA |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 10 | 0.232006 | 0.464012 | 0.767994 |
| 11 | 0.150397 | 0.300793 | 0.849603 |
| 12 | 0.951703 | 0.0965946 | 0.0482973 |
| 13 | 0.978262 | 0.0434757 | 0.0217379 |
| 14 | 0.97585 | 0.0483009 | 0.0241504 |
| 15 | 0.960142 | 0.079715 | 0.0398575 |
| 16 | 0.989832 | 0.0203354 | 0.0101677 |
| 17 | 0.984553 | 0.0308934 | 0.0154467 |
| 18 | 0.983391 | 0.033217 | 0.0166085 |
| 19 | 0.977481 | 0.0450375 | 0.0225187 |
| 20 | 0.986905 | 0.0261908 | 0.0130954 |
| 21 | 0.983309 | 0.0333819 | 0.016691 |
| 22 | 0.974622 | 0.0507551 | 0.0253776 |
| 23 | 0.97868 | 0.0426404 | 0.0213202 |
| 24 | 0.976835 | 0.046331 | 0.0231655 |
| 25 | 0.966437 | 0.0671263 | 0.0335631 |
| 26 | 0.970565 | 0.0588703 | 0.0294352 |
| 27 | 0.958545 | 0.0829095 | 0.0414547 |
| 28 | 0.943163 | 0.113673 | 0.0568367 |
| 29 | 0.922999 | 0.154002 | 0.0770012 |
| 30 | 0.897937 | 0.204125 | 0.102063 |
| 31 | 0.878519 | 0.242963 | 0.121481 |
| 32 | 0.878741 | 0.242517 | 0.121259 |
| 33 | 0.852193 | 0.295615 | 0.147807 |
| 34 | 0.857108 | 0.285784 | 0.142892 |
| 35 | 0.821539 | 0.356922 | 0.178461 |
| 36 | 0.787615 | 0.42477 | 0.212385 |
| 37 | 0.751356 | 0.497289 | 0.248644 |
| 38 | 0.704317 | 0.591365 | 0.295683 |
| 39 | 0.661331 | 0.677337 | 0.338669 |
| 40 | 0.610567 | 0.778867 | 0.389433 |
| 41 | 0.601714 | 0.796572 | 0.398286 |
| 42 | 0.549431 | 0.901139 | 0.450569 |
| 43 | 0.661773 | 0.676453 | 0.338227 |
| 44 | 0.662152 | 0.675695 | 0.337848 |
| 45 | 0.61755 | 0.7649 | 0.38245 |
| 46 | 0.566175 | 0.86765 | 0.433825 |
| 47 | 0.527794 | 0.944412 | 0.472206 |
| 48 | 0.531509 | 0.936981 | 0.468491 |
| 49 | 0.482266 | 0.964533 | 0.517734 |
| 50 | 0.505544 | 0.988913 | 0.494456 |
| 51 | 0.465113 | 0.930225 | 0.534887 |
| 52 | 0.417059 | 0.834119 | 0.582941 |
| 53 | 0.387076 | 0.774152 | 0.612924 |
| 54 | 0.340808 | 0.681616 | 0.659192 |
| 55 | 0.296091 | 0.592182 | 0.703909 |
| 56 | 0.29868 | 0.597361 | 0.70132 |
| 57 | 0.26 | 0.52 | 0.74 |
| 58 | 0.233616 | 0.467232 | 0.766384 |
| 59 | 0.197794 | 0.395588 | 0.802206 |
| 60 | 0.165747 | 0.331494 | 0.834253 |
| 61 | 0.144331 | 0.288663 | 0.855669 |
| 62 | 0.118312 | 0.236625 | 0.881688 |
| 63 | 0.128463 | 0.256927 | 0.871537 |
| 64 | 0.636581 | 0.726838 | 0.363419 |
| 65 | 0.673054 | 0.653892 | 0.326946 |
| 66 | 0.702962 | 0.594076 | 0.297038 |
| 67 | 0.66538 | 0.669239 | 0.33462 |
| 68 | 0.623769 | 0.752463 | 0.376231 |
| 69 | 0.690023 | 0.619953 | 0.309977 |
| 70 | 0.648281 | 0.703437 | 0.351719 |
| 71 | 0.603776 | 0.792448 | 0.396224 |
| 72 | 0.634224 | 0.731551 | 0.365776 |
| 73 | 0.643321 | 0.713359 | 0.356679 |
| 74 | 0.599718 | 0.800564 | 0.400282 |
| 75 | 0.623517 | 0.752967 | 0.376483 |
| 76 | 0.583121 | 0.833758 | 0.416879 |
| 77 | 0.54755 | 0.9049 | 0.45245 |
| 78 | 0.510225 | 0.97955 | 0.489775 |
| 79 | 0.465763 | 0.931525 | 0.534237 |
| 80 | 0.535143 | 0.929715 | 0.464857 |
| 81 | 0.575692 | 0.848616 | 0.424308 |
| 82 | 0.556315 | 0.887369 | 0.443685 |
| 83 | 0.514455 | 0.971091 | 0.485545 |
| 84 | 0.475775 | 0.95155 | 0.524225 |
| 85 | 0.514644 | 0.970713 | 0.485356 |
| 86 | 0.468093 | 0.936186 | 0.531907 |
| 87 | 0.42828 | 0.856559 | 0.57172 |
| 88 | 0.457777 | 0.915555 | 0.542223 |
| 89 | 0.43369 | 0.86738 | 0.56631 |
| 90 | 0.401208 | 0.802415 | 0.598792 |
| 91 | 0.462886 | 0.925773 | 0.537114 |
| 92 | 0.476862 | 0.953723 | 0.523138 |
| 93 | 0.488845 | 0.977691 | 0.511155 |
| 94 | 0.480148 | 0.960296 | 0.519852 |
| 95 | 0.450605 | 0.90121 | 0.549395 |
| 96 | 0.403953 | 0.807907 | 0.596047 |
| 97 | 0.373539 | 0.747077 | 0.626461 |
| 98 | 0.335373 | 0.670746 | 0.664627 |
| 99 | 0.292776 | 0.585552 | 0.707224 |
| 100 | 0.284427 | 0.568854 | 0.715573 |
| 101 | 0.254168 | 0.508336 | 0.745832 |
| 102 | 0.249615 | 0.49923 | 0.750385 |
| 103 | 0.213108 | 0.426216 | 0.786892 |
| 104 | 0.180659 | 0.361319 | 0.819341 |
| 105 | 0.163903 | 0.327806 | 0.836097 |
| 106 | 0.146887 | 0.293774 | 0.853113 |
| 107 | 0.124885 | 0.24977 | 0.875115 |
| 108 | 0.115218 | 0.230437 | 0.884782 |
| 109 | 0.164362 | 0.328724 | 0.835638 |
| 110 | 0.177902 | 0.355804 | 0.822098 |
| 111 | 0.147297 | 0.294594 | 0.852703 |
| 112 | 0.16847 | 0.336939 | 0.83153 |
| 113 | 0.79709 | 0.405821 | 0.20291 |
| 114 | 0.769771 | 0.460458 | 0.230229 |
| 115 | 0.76541 | 0.46918 | 0.23459 |
| 116 | 0.80454 | 0.390921 | 0.19546 |
| 117 | 0.766883 | 0.466233 | 0.233117 |
| 118 | 0.785076 | 0.429847 | 0.214924 |
| 119 | 0.779193 | 0.441614 | 0.220807 |
| 120 | 0.812394 | 0.375211 | 0.187606 |
| 121 | 0.778936 | 0.442128 | 0.221064 |
| 122 | 0.768696 | 0.462608 | 0.231304 |
| 123 | 0.733585 | 0.53283 | 0.266415 |
| 124 | 0.699221 | 0.601558 | 0.300779 |
| 125 | 0.647841 | 0.704319 | 0.352159 |
| 126 | 0.623289 | 0.753421 | 0.376711 |
| 127 | 0.644533 | 0.710933 | 0.355467 |
| 128 | 0.603765 | 0.79247 | 0.396235 |
| 129 | 0.578522 | 0.842957 | 0.421478 |
| 130 | 0.518297 | 0.963406 | 0.481703 |
| 131 | 0.506331 | 0.987339 | 0.493669 |
| 132 | 0.513938 | 0.972124 | 0.486062 |
| 133 | 0.563485 | 0.87303 | 0.436515 |
| 134 | 0.528546 | 0.942908 | 0.471454 |
| 135 | 0.500594 | 0.998811 | 0.499406 |
| 136 | 0.585615 | 0.828769 | 0.414385 |
| 137 | 0.524196 | 0.951609 | 0.475804 |
| 138 | 0.548948 | 0.902104 | 0.451052 |
| 139 | 0.503556 | 0.992887 | 0.496444 |
| 140 | 0.609352 | 0.781296 | 0.390648 |
| 141 | 0.80922 | 0.38156 | 0.19078 |
| 142 | 0.767811 | 0.464377 | 0.232189 |
| 143 | 0.733486 | 0.533029 | 0.266514 |
| 144 | 0.674775 | 0.650451 | 0.325225 |
| 145 | 0.585535 | 0.828931 | 0.414465 |
| 146 | 0.49136 | 0.98272 | 0.50864 |
| 147 | 0.388024 | 0.776049 | 0.611976 |
| 148 | 0.295682 | 0.591364 | 0.704318 |
| 149 | 0.226235 | 0.452469 | 0.773765 |
| 150 | 0.154553 | 0.309105 | 0.845447 |
| 151 | 0.273238 | 0.546477 | 0.726762 |
| 152 | 0.141947 | 0.283895 | 0.858053 |
| 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 | 10 | 0.0699301 | NOK |
| 10% type I error level | 16 | 0.111888 | NOK |
