| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 3.11142857142857 -1.91506493506493X[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) | 3.11142857142857 | 0.123665 | 25.1602 | 0 | 0 |
| X | -1.91506493506493 | 0.288818 | -6.6307 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.656645782998115 |
| R-squared | 0.431183684329208 |
| Adjusted R-squared | 0.421376506472815 |
| F-TEST (value) | 43.9661328307749 |
| F-TEST (DF numerator) | 1 |
| F-TEST (DF denominator) | 58 |
| p-value | 1.21933612096115e-08 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 0.865651583823886 |
| Sum Squared Residuals | 43.4624545454545 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 2.11 | 3.11142857142857 | -1.00142857142857 |
| 2 | 2.09 | 3.11142857142857 | -1.02142857142857 |
| 3 | 2.05 | 3.11142857142857 | -1.06142857142857 |
| 4 | 2.08 | 3.11142857142857 | -1.03142857142857 |
| 5 | 2.06 | 3.11142857142857 | -1.05142857142857 |
| 6 | 2.06 | 3.11142857142857 | -1.05142857142857 |
| 7 | 2.08 | 3.11142857142857 | -1.03142857142857 |
| 8 | 2.07 | 3.11142857142857 | -1.04142857142857 |
| 9 | 2.06 | 3.11142857142857 | -1.05142857142857 |
| 10 | 2.07 | 3.11142857142857 | -1.04142857142857 |
| 11 | 2.06 | 3.11142857142857 | -1.05142857142857 |
| 12 | 2.09 | 3.11142857142857 | -1.02142857142857 |
| 13 | 2.07 | 3.11142857142857 | -1.04142857142857 |
| 14 | 2.09 | 3.11142857142857 | -1.02142857142857 |
| 15 | 2.28 | 3.11142857142857 | -0.831428571428572 |
| 16 | 2.33 | 3.11142857142857 | -0.781428571428571 |
| 17 | 2.35 | 3.11142857142857 | -0.761428571428571 |
| 18 | 2.52 | 3.11142857142857 | -0.591428571428571 |
| 19 | 2.63 | 3.11142857142857 | -0.481428571428572 |
| 20 | 2.58 | 3.11142857142857 | -0.531428571428571 |
| 21 | 2.7 | 3.11142857142857 | -0.411428571428571 |
| 22 | 2.81 | 3.11142857142857 | -0.301428571428571 |
| 23 | 2.97 | 3.11142857142857 | -0.141428571428571 |
| 24 | 3.04 | 3.11142857142857 | -0.0714285714285714 |
| 25 | 3.28 | 3.11142857142857 | 0.168571428571428 |
| 26 | 3.33 | 3.11142857142857 | 0.218571428571429 |
| 27 | 3.5 | 3.11142857142857 | 0.388571428571429 |
| 28 | 3.56 | 3.11142857142857 | 0.448571428571429 |
| 29 | 3.57 | 3.11142857142857 | 0.458571428571428 |
| 30 | 3.69 | 3.11142857142857 | 0.578571428571429 |
| 31 | 3.82 | 3.11142857142857 | 0.708571428571428 |
| 32 | 3.79 | 3.11142857142857 | 0.678571428571429 |
| 33 | 3.96 | 3.11142857142857 | 0.848571428571429 |
| 34 | 4.06 | 3.11142857142857 | 0.948571428571428 |
| 35 | 4.05 | 3.11142857142857 | 0.938571428571428 |
| 36 | 4.03 | 3.11142857142857 | 0.91857142857143 |
| 37 | 3.94 | 3.11142857142857 | 0.828571428571429 |
| 38 | 4.02 | 3.11142857142857 | 0.908571428571428 |
| 39 | 3.88 | 3.11142857142857 | 0.768571428571428 |
| 40 | 4.02 | 3.11142857142857 | 0.908571428571428 |
| 41 | 4.03 | 3.11142857142857 | 0.91857142857143 |
| 42 | 4.09 | 3.11142857142857 | 0.978571428571428 |
| 43 | 3.99 | 3.11142857142857 | 0.87857142857143 |
| 44 | 4.01 | 3.11142857142857 | 0.898571428571428 |
| 45 | 4.01 | 3.11142857142857 | 0.898571428571428 |
| 46 | 4.19 | 3.11142857142857 | 1.07857142857143 |
| 47 | 4.3 | 3.11142857142857 | 1.18857142857143 |
| 48 | 4.27 | 3.11142857142857 | 1.15857142857143 |
| 49 | 3.82 | 3.11142857142857 | 0.708571428571428 |
| 50 | 3.15 | 1.19636363636364 | 1.95363636363636 |
| 51 | 2.49 | 1.19636363636364 | 1.29363636363636 |
| 52 | 1.81 | 1.19636363636364 | 0.613636363636364 |
| 53 | 1.26 | 1.19636363636364 | 0.0636363636363636 |
| 54 | 1.06 | 1.19636363636364 | -0.136363636363636 |
| 55 | 0.84 | 1.19636363636364 | -0.356363636363637 |
| 56 | 0.78 | 1.19636363636364 | -0.416363636363636 |
| 57 | 0.7 | 1.19636363636364 | -0.496363636363637 |
| 58 | 0.36 | 1.19636363636364 | -0.836363636363637 |
| 59 | 0.35 | 1.19636363636364 | -0.846363636363636 |
| 60 | 0.36 | 1.19636363636364 | -0.836363636363637 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 5 | 4.92583207289033e-05 | 9.85166414578066e-05 | 0.999950741679271 |
| 6 | 1.74754472862918e-06 | 3.49508945725836e-06 | 0.999998252455271 |
| 7 | 5.0105776046226e-08 | 1.00211552092452e-07 | 0.999999949894224 |
| 8 | 1.40386465382395e-09 | 2.80772930764790e-09 | 0.999999998596135 |
| 9 | 4.86784975658016e-11 | 9.73569951316031e-11 | 0.999999999951321 |
| 10 | 1.36409523544758e-12 | 2.72819047089517e-12 | 0.999999999998636 |
| 11 | 4.89555080371057e-14 | 9.79110160742114e-14 | 0.999999999999951 |
| 12 | 2.36464312045412e-15 | 4.72928624090825e-15 | 0.999999999999998 |
| 13 | 8.04500219998019e-17 | 1.60900043999604e-16 | 1 |
| 14 | 4.64620433407642e-18 | 9.29240866815284e-18 | 1 |
| 15 | 1.79591377650468e-12 | 3.59182755300937e-12 | 0.999999999998204 |
| 16 | 7.02073602644622e-11 | 1.40414720528924e-10 | 0.999999999929793 |
| 17 | 4.52415508815239e-10 | 9.04831017630479e-10 | 0.999999999547585 |
| 18 | 2.27204815422638e-08 | 4.54409630845276e-08 | 0.999999977279519 |
| 19 | 6.26834000981579e-07 | 1.25366800196316e-06 | 0.999999373166 |
| 20 | 2.87666122074002e-06 | 5.75332244148004e-06 | 0.99999712333878 |
| 21 | 2.06819084352559e-05 | 4.13638168705118e-05 | 0.999979318091565 |
| 22 | 0.000159119039839074 | 0.000318238079678149 | 0.99984088096016 |
| 23 | 0.00133411334809071 | 0.00266822669618141 | 0.99866588665191 |
| 24 | 0.00671486398023413 | 0.0134297279604683 | 0.993285136019766 |
| 25 | 0.0339940255371765 | 0.0679880510743529 | 0.966005974462824 |
| 26 | 0.0934139401488708 | 0.186827880297742 | 0.90658605985113 |
| 27 | 0.204376644876570 | 0.408753289753139 | 0.79562335512343 |
| 28 | 0.330512624073092 | 0.661025248146183 | 0.669487375926908 |
| 29 | 0.438591629083093 | 0.877183258166186 | 0.561408370916907 |
| 30 | 0.54104403872371 | 0.91791192255258 | 0.45895596127629 |
| 31 | 0.632210094355862 | 0.735579811288276 | 0.367789905644138 |
| 32 | 0.685411289436822 | 0.629177421126356 | 0.314588710563178 |
| 33 | 0.737571041957803 | 0.524857916084394 | 0.262428958042197 |
| 34 | 0.778658702898026 | 0.442682594203949 | 0.221341297101974 |
| 35 | 0.798962531130838 | 0.402074937738323 | 0.201037468869161 |
| 36 | 0.804712999579105 | 0.390574000841790 | 0.195287000420895 |
| 37 | 0.795214307541464 | 0.409571384917071 | 0.204785692458536 |
| 38 | 0.784054562142551 | 0.431890875714897 | 0.215945437857449 |
| 39 | 0.75883688283009 | 0.48232623433982 | 0.24116311716991 |
| 40 | 0.734124665089604 | 0.531750669820793 | 0.265875334910396 |
| 41 | 0.702858261809966 | 0.594283476380068 | 0.297141738190034 |
| 42 | 0.668139425560929 | 0.663721148878143 | 0.331860574439071 |
| 43 | 0.620333600903233 | 0.759332798193533 | 0.379666399096767 |
| 44 | 0.566904227371427 | 0.866191545257147 | 0.433095772628573 |
| 45 | 0.507837716443704 | 0.984324567112591 | 0.492162283556296 |
| 46 | 0.453108446907733 | 0.906216893815467 | 0.546891553092266 |
| 47 | 0.403527410647877 | 0.807054821295754 | 0.596472589352123 |
| 48 | 0.352327763264358 | 0.704655526528717 | 0.647672236735642 |
| 49 | 0.273222751017958 | 0.546445502035917 | 0.726777248982042 |
| 50 | 0.649056657089955 | 0.70188668582009 | 0.350943342910045 |
| 51 | 0.911643779671042 | 0.176712440657916 | 0.088356220328958 |
| 52 | 0.977926625721444 | 0.0441467485571113 | 0.0220733742785557 |
| 53 | 0.984141685423091 | 0.0317166291538175 | 0.0158583145769087 |
| 54 | 0.98436710186168 | 0.0312657962766398 | 0.0156328981383199 |
| 55 | 0.969840039468292 | 0.0603199210634169 | 0.0301599605317084 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 19 | 0.372549019607843 | NOK |
| 5% type I error level | 23 | 0.450980392156863 | NOK |
| 10% type I error level | 25 | 0.490196078431373 | NOK |
