| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 1.2035843418843 + 0.823909896346055X[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) | 1.2035843418843 | 0.026673 | 45.1243 | 0 | 0 |
| X | 0.823909896346055 | 0.040904 | 20.1424 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.934366697063404 |
| R-squared | 0.873041124581175 |
| Adjusted R-squared | 0.870889279235094 |
| F-TEST (value) | 405.717411881327 |
| F-TEST (DF numerator) | 1 |
| F-TEST (DF denominator) | 59 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 0.0376961676966682 |
| Sum Squared Residuals | 0.0838390624819047 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 1.58 | 1.65673478487464 | -0.0767347848746352 |
| 2 | 1.59 | 1.65673478487463 | -0.0667347848746309 |
| 3 | 1.6 | 1.65673478487463 | -0.0567347848746306 |
| 4 | 1.6 | 1.65673478487463 | -0.0567347848746306 |
| 5 | 1.6 | 1.65673478487463 | -0.0567347848746306 |
| 6 | 1.6 | 1.66497388383809 | -0.0649738838380912 |
| 7 | 1.61 | 1.66497388383809 | -0.0549738838380912 |
| 8 | 1.61 | 1.66497388383809 | -0.0549738838380912 |
| 9 | 1.62 | 1.66497388383809 | -0.0449738838380911 |
| 10 | 1.63 | 1.66497388383809 | -0.0349738838380914 |
| 11 | 1.63 | 1.65673478487463 | -0.0267347848746308 |
| 12 | 1.63 | 1.66497388383809 | -0.0349738838380914 |
| 13 | 1.63 | 1.65673478487463 | -0.0267347848746308 |
| 14 | 1.63 | 1.65673478487463 | -0.0267347848746308 |
| 15 | 1.64 | 1.66497388383809 | -0.0249738838380913 |
| 16 | 1.64 | 1.65673478487463 | -0.0167347848746308 |
| 17 | 1.64 | 1.65673478487463 | -0.0167347848746308 |
| 18 | 1.65 | 1.65673478487463 | -0.00673478487463078 |
| 19 | 1.65 | 1.65673478487463 | -0.00673478487463078 |
| 20 | 1.65 | 1.64025658694771 | 0.00974341305229031 |
| 21 | 1.65 | 1.64025658694771 | 0.00974341305229031 |
| 22 | 1.65 | 1.64025658694771 | 0.00974341305229031 |
| 23 | 1.66 | 1.64025658694771 | 0.0197434130522903 |
| 24 | 1.67 | 1.64849568591117 | 0.0215043140888298 |
| 25 | 1.68 | 1.64849568591117 | 0.0315043140888298 |
| 26 | 1.68 | 1.64849568591117 | 0.0315043140888298 |
| 27 | 1.68 | 1.65673478487463 | 0.0232652151253692 |
| 28 | 1.68 | 1.65673478487463 | 0.0232652151253692 |
| 29 | 1.69 | 1.64849568591117 | 0.0415043140888298 |
| 30 | 1.7 | 1.65673478487463 | 0.0432652151253693 |
| 31 | 1.7 | 1.66497388383809 | 0.0350261161619087 |
| 32 | 1.71 | 1.68145208176501 | 0.0285479182349877 |
| 33 | 1.73 | 1.68969118072847 | 0.0403088192715272 |
| 34 | 1.73 | 1.69793027969193 | 0.0320697203080666 |
| 35 | 1.73 | 1.69793027969193 | 0.0320697203080666 |
| 36 | 1.74 | 1.69793027969193 | 0.0420697203080666 |
| 37 | 1.74 | 1.68969118072847 | 0.0503088192715272 |
| 38 | 1.74 | 1.69793027969193 | 0.0420697203080666 |
| 39 | 1.75 | 1.69793027969193 | 0.0520697203080666 |
| 40 | 1.78 | 1.71440847761885 | 0.0655915223811455 |
| 41 | 1.82 | 1.73912577450924 | 0.080874225490764 |
| 42 | 1.83 | 1.76384307139962 | 0.0661569286003823 |
| 43 | 1.84 | 1.80503856621692 | 0.0349614337830796 |
| 44 | 1.85 | 1.84623406103422 | 0.00376593896577684 |
| 45 | 1.86 | 1.84623406103422 | 0.0137659389657768 |
| 46 | 1.86 | 1.87919045688807 | -0.0191904568880653 |
| 47 | 1.87 | 1.87919045688807 | -0.0091904568880653 |
| 48 | 1.87 | 1.87095135792460 | -0.000951357924604825 |
| 49 | 1.87 | 1.88742955585153 | -0.0174295558515258 |
| 50 | 1.87 | 1.90390775377845 | -0.033907753778447 |
| 51 | 1.87 | 1.91214685274191 | -0.0421468527419075 |
| 52 | 1.87 | 1.90390775377845 | -0.033907753778447 |
| 53 | 1.87 | 1.90390775377845 | -0.033907753778447 |
| 54 | 1.88 | 1.87919045688807 | 0.000809543111934496 |
| 55 | 1.88 | 1.86271225896114 | 0.0172877410388555 |
| 56 | 1.87 | 1.87095135792460 | -0.000951357924604825 |
| 57 | 1.87 | 1.86271225896114 | 0.00728774103885575 |
| 58 | 1.87 | 1.86271225896114 | 0.00728774103885575 |
| 59 | 1.87 | 1.86271225896114 | 0.00728774103885575 |
| 60 | 1.87 | 1.86271225896114 | 0.00728774103885575 |
| 61 | 1.87 | 1.85447315999768 | 0.0155268400023163 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 5 | 0.0373098577562783 | 0.0746197155125565 | 0.962690142243722 |
| 6 | 0.0109667062701586 | 0.0219334125403172 | 0.989033293729841 |
| 7 | 0.00436461841112589 | 0.00872923682225177 | 0.995635381588874 |
| 8 | 0.00154471177885839 | 0.00308942355771678 | 0.998455288221142 |
| 9 | 0.00125935963169759 | 0.00251871926339518 | 0.998740640368302 |
| 10 | 0.00243007065199096 | 0.00486014130398192 | 0.99756992934801 |
| 11 | 0.0215886639376187 | 0.0431773278752373 | 0.978411336062381 |
| 12 | 0.0209184810960350 | 0.0418369621920699 | 0.979081518903965 |
| 13 | 0.0452408045643361 | 0.0904816091286723 | 0.954759195435664 |
| 14 | 0.0705979784736973 | 0.141195956947395 | 0.929402021526303 |
| 15 | 0.0976378243746222 | 0.195275648749244 | 0.902362175625378 |
| 16 | 0.178394979161777 | 0.356789958323553 | 0.821605020838223 |
| 17 | 0.27144872340234 | 0.54289744680468 | 0.72855127659766 |
| 18 | 0.418865231142182 | 0.837730462284364 | 0.581134768857818 |
| 19 | 0.557884616371058 | 0.884230767257884 | 0.442115383628942 |
| 20 | 0.58089152655073 | 0.83821694689854 | 0.41910847344927 |
| 21 | 0.584340539719559 | 0.831318920560881 | 0.415659460280441 |
| 22 | 0.60019965360673 | 0.79960069278654 | 0.39980034639327 |
| 23 | 0.606994969007861 | 0.786010061984279 | 0.393005030992139 |
| 24 | 0.700140329725125 | 0.599719340549751 | 0.299859670274875 |
| 25 | 0.789775179576204 | 0.420449640847593 | 0.210224820423796 |
| 26 | 0.844123731895051 | 0.311752536209898 | 0.155876268104949 |
| 27 | 0.93234746472215 | 0.135305070555701 | 0.0676525352778506 |
| 28 | 0.97330616716585 | 0.053387665668301 | 0.0266938328341505 |
| 29 | 0.981025543155336 | 0.0379489136893272 | 0.0189744568446636 |
| 30 | 0.993155647106122 | 0.0136887057877565 | 0.00684435289387826 |
| 31 | 0.998611526377696 | 0.00277694724460823 | 0.00138847362230411 |
| 32 | 0.99986372114551 | 0.000272557708979529 | 0.000136278854489765 |
| 33 | 0.999955067976108 | 8.9864047784517e-05 | 4.49320238922585e-05 |
| 34 | 0.99997445517949 | 5.10896410206127e-05 | 2.55448205103063e-05 |
| 35 | 0.999986581392286 | 2.68372154272965e-05 | 1.34186077136483e-05 |
| 36 | 0.999989639625238 | 2.07207495246542e-05 | 1.03603747623271e-05 |
| 37 | 0.999992914049517 | 1.41719009667598e-05 | 7.08595048337989e-06 |
| 38 | 0.999998989893654 | 2.02021269216572e-06 | 1.01010634608286e-06 |
| 39 | 0.999999981653216 | 3.66935686114807e-08 | 1.83467843057403e-08 |
| 40 | 0.999999999640754 | 7.18490896025335e-10 | 3.59245448012667e-10 |
| 41 | 0.999999998787959 | 2.42408250501001e-09 | 1.21204125250500e-09 |
| 42 | 0.999999996977052 | 6.04589568283019e-09 | 3.02294784141510e-09 |
| 43 | 0.999999999225947 | 1.5481066279839e-09 | 7.7405331399195e-10 |
| 44 | 0.999999999967446 | 6.51081611684099e-11 | 3.25540805842050e-11 |
| 45 | 0.999999999976119 | 4.77624147245039e-11 | 2.38812073622519e-11 |
| 46 | 0.999999999995584 | 8.831264032374e-12 | 4.415632016187e-12 |
| 47 | 0.999999999958654 | 8.26929746931182e-11 | 4.13464873465591e-11 |
| 48 | 0.99999999960035 | 7.99298770669757e-10 | 3.99649385334879e-10 |
| 49 | 0.999999996291506 | 7.41698701143813e-09 | 3.70849350571907e-09 |
| 50 | 0.999999967393059 | 6.52138825249516e-08 | 3.26069412624758e-08 |
| 51 | 0.99999972301037 | 5.53979261390577e-07 | 2.76989630695289e-07 |
| 52 | 0.999997763063497 | 4.47387300538111e-06 | 2.23693650269056e-06 |
| 53 | 0.999993115092083 | 1.37698158349266e-05 | 6.88490791746328e-06 |
| 54 | 0.99996247498694 | 7.50500261204738e-05 | 3.75250130602369e-05 |
| 55 | 1 | 8.27832263769462e-56 | 4.13916131884731e-56 |
| 56 | 1 | 0 | 0 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 30 | 0.576923076923077 | NOK |
| 5% type I error level | 35 | 0.673076923076923 | NOK |
| 10% type I error level | 38 | 0.730769230769231 | NOK |
