| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 0.786353370023588 + 1.07738832106354X[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) | 0.786353370023588 | 0.06706 | 11.7262 | 0 | 0 |
| X | 1.07738832106354 | 0.031879 | 33.7962 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.975537820871888 |
| R-squared | 0.951674039951472 |
| Adjusted R-squared | 0.95084083374374 |
| F-TEST (value) | 1142.18308879446 |
| F-TEST (DF numerator) | 1 |
| F-TEST (DF denominator) | 58 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 0.243401448295706 |
| Sum Squared Residuals | 3.43616737188193 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 2.05 | 1.86374169108712 | 0.186258308912882 |
| 2 | 2.11 | 1.86374169108713 | 0.246258308912869 |
| 3 | 2.09 | 1.86374169108713 | 0.226258308912872 |
| 4 | 2.05 | 1.86374169108713 | 0.186258308912872 |
| 5 | 2.08 | 1.86374169108713 | 0.216258308912872 |
| 6 | 2.06 | 1.86374169108713 | 0.196258308912872 |
| 7 | 2.06 | 1.86374169108713 | 0.196258308912872 |
| 8 | 2.08 | 1.86374169108713 | 0.216258308912872 |
| 9 | 2.07 | 1.86374169108713 | 0.206258308912872 |
| 10 | 2.06 | 1.86374169108713 | 0.196258308912872 |
| 11 | 2.07 | 1.86374169108713 | 0.206258308912872 |
| 12 | 2.06 | 1.86374169108713 | 0.196258308912872 |
| 13 | 2.09 | 1.86374169108713 | 0.226258308912872 |
| 14 | 2.07 | 1.86374169108713 | 0.206258308912872 |
| 15 | 2.09 | 1.86374169108713 | 0.226258308912872 |
| 16 | 2.28 | 2.13308877135301 | 0.146911228646987 |
| 17 | 2.33 | 2.13308877135301 | 0.196911228646987 |
| 18 | 2.35 | 2.13308877135301 | 0.216911228646987 |
| 19 | 2.52 | 2.4024358516189 | 0.117564148381102 |
| 20 | 2.63 | 2.4024358516189 | 0.227564148381102 |
| 21 | 2.58 | 2.4024358516189 | 0.177564148381102 |
| 22 | 2.7 | 2.67178293188478 | 0.028217068115217 |
| 23 | 2.81 | 2.67178293188478 | 0.138217068115217 |
| 24 | 2.97 | 2.94113001215067 | 0.0288699878493318 |
| 25 | 3.04 | 2.94113001215067 | 0.0988699878493317 |
| 26 | 3.28 | 3.21047709241655 | 0.0695229075834463 |
| 27 | 3.33 | 3.21047709241655 | 0.119522907583447 |
| 28 | 3.5 | 3.47982417268244 | 0.0201758273175613 |
| 29 | 3.56 | 3.47982417268244 | 0.0801758273175614 |
| 30 | 3.57 | 3.47982417268244 | 0.0901758273175612 |
| 31 | 3.69 | 3.74917125294832 | -0.059171252948324 |
| 32 | 3.82 | 3.74917125294832 | 0.0708287470516759 |
| 33 | 3.79 | 3.74917125294832 | 0.0408287470516761 |
| 34 | 3.96 | 4.01851833321421 | -0.0585183332142091 |
| 35 | 4.06 | 4.01851833321421 | 0.0414816667857906 |
| 36 | 4.05 | 4.01851833321421 | 0.0314816667857908 |
| 37 | 4.03 | 4.01851833321421 | 0.0114816667857912 |
| 38 | 3.94 | 4.01851833321421 | -0.0785183332142091 |
| 39 | 4.02 | 4.01851833321421 | 0.00148166678579054 |
| 40 | 3.88 | 4.01851833321421 | -0.138518333214209 |
| 41 | 4.02 | 4.01851833321421 | 0.00148166678579054 |
| 42 | 4.03 | 4.01851833321421 | 0.0114816667857912 |
| 43 | 4.09 | 4.01851833321421 | 0.0714816667857908 |
| 44 | 3.99 | 4.01851833321421 | -0.0285183332142088 |
| 45 | 4.01 | 4.01851833321421 | -0.00851833321420925 |
| 46 | 4.01 | 4.01851833321421 | -0.00851833321420925 |
| 47 | 4.19 | 4.28786541348009 | -0.097865413480094 |
| 48 | 4.3 | 4.28786541348009 | 0.0121345865199055 |
| 49 | 4.27 | 4.28786541348009 | -0.0178654134800948 |
| 50 | 3.82 | 4.28786541348009 | -0.467865413480095 |
| 51 | 3.15 | 3.74917125294832 | -0.599171252948324 |
| 52 | 2.49 | 2.94113001215067 | -0.451130012150668 |
| 53 | 1.81 | 1.86374169108713 | -0.0537416910871276 |
| 54 | 1.26 | 1.86374169108713 | -0.603741691087128 |
| 55 | 1.06 | 1.32504753055536 | -0.265047530555357 |
| 56 | 0.84 | 1.05570045028947 | -0.215700450289472 |
| 57 | 0.78 | 1.05570045028947 | -0.275700450289472 |
| 58 | 0.7 | 1.05570045028947 | -0.355700450289472 |
| 59 | 0.36 | 1.05570045028947 | -0.695700450289472 |
| 60 | 0.35 | 1.05570045028947 | -0.705700450289472 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 5 | 0.00257879709879177 | 0.00515759419758355 | 0.997421202901208 |
| 6 | 0.000306143000412585 | 0.00061228600082517 | 0.999693856999587 |
| 7 | 3.37775326166875e-05 | 6.7555065233375e-05 | 0.999966222467383 |
| 8 | 3.38700148833636e-06 | 6.77400297667271e-06 | 0.999996612998512 |
| 9 | 3.07753646685977e-07 | 6.15507293371955e-07 | 0.999999692246353 |
| 10 | 3.1442146778976e-08 | 6.2884293557952e-08 | 0.999999968557853 |
| 11 | 2.73940405681772e-09 | 5.47880811363544e-09 | 0.999999997260596 |
| 12 | 2.74784026159835e-10 | 5.4956805231967e-10 | 0.999999999725216 |
| 13 | 4.38231086453373e-11 | 8.76462172906745e-11 | 0.999999999956177 |
| 14 | 4.2037846880127e-12 | 8.4075693760254e-12 | 0.999999999995796 |
| 15 | 7.46854972902404e-13 | 1.49370994580481e-12 | 0.999999999999253 |
| 16 | 7.06883184458372e-14 | 1.41376636891674e-13 | 0.99999999999993 |
| 17 | 5.69199413668236e-14 | 1.13839882733647e-13 | 0.999999999999943 |
| 18 | 5.05693192107701e-14 | 1.01138638421540e-13 | 0.99999999999995 |
| 19 | 1.93618565966237e-14 | 3.87237131932475e-14 | 0.99999999999998 |
| 20 | 4.05899264790126e-13 | 8.11798529580252e-13 | 0.999999999999594 |
| 21 | 1.14851253983602e-13 | 2.29702507967203e-13 | 0.999999999999885 |
| 22 | 4.35623463342582e-12 | 8.71246926685163e-12 | 0.999999999995644 |
| 23 | 2.04365242513389e-12 | 4.08730485026778e-12 | 0.999999999997956 |
| 24 | 9.64920070496751e-13 | 1.92984014099350e-12 | 0.999999999999035 |
| 25 | 4.24737141935536e-13 | 8.49474283871073e-13 | 0.999999999999575 |
| 26 | 1.42398009899030e-13 | 2.84796019798060e-13 | 0.999999999999858 |
| 27 | 2.53418222693250e-13 | 5.06836445386499e-13 | 0.999999999999747 |
| 28 | 5.76768283943989e-14 | 1.15353656788798e-13 | 0.999999999999942 |
| 29 | 3.46123327527579e-14 | 6.92246655055159e-14 | 0.999999999999965 |
| 30 | 2.42041927093232e-14 | 4.84083854186463e-14 | 0.999999999999976 |
| 31 | 3.0511868177214e-14 | 6.1023736354428e-14 | 0.99999999999997 |
| 32 | 2.67744670931039e-14 | 5.35489341862079e-14 | 0.999999999999973 |
| 33 | 8.2430938513789e-15 | 1.64861877027578e-14 | 0.999999999999992 |
| 34 | 3.19690703424305e-15 | 6.3938140684861e-15 | 0.999999999999997 |
| 35 | 1.79871736950881e-15 | 3.59743473901762e-15 | 0.999999999999998 |
| 36 | 6.42231013288584e-16 | 1.28446202657717e-15 | 1 |
| 37 | 1.52224283669293e-16 | 3.04448567338587e-16 | 1 |
| 38 | 1.43868913142298e-16 | 2.87737826284596e-16 | 1 |
| 39 | 3.31699621762463e-17 | 6.63399243524926e-17 | 1 |
| 40 | 3.97204215430517e-16 | 7.94408430861033e-16 | 1 |
| 41 | 1.07524708704602e-16 | 2.15049417409204e-16 | 1 |
| 42 | 3.56736167822965e-17 | 7.1347233564593e-17 | 1 |
| 43 | 9.83009729734105e-17 | 1.96601945946821e-16 | 1 |
| 44 | 3.10746875391818e-17 | 6.21493750783637e-17 | 1 |
| 45 | 1.26021136772998e-17 | 2.52042273545995e-17 | 1 |
| 46 | 7.186052624078e-18 | 1.4372105248156e-17 | 1 |
| 47 | 4.61249347728168e-18 | 9.22498695456336e-18 | 1 |
| 48 | 2.60713505625503e-17 | 5.21427011251007e-17 | 1 |
| 49 | 1.87997043908413e-15 | 3.75994087816826e-15 | 0.999999999999998 |
| 50 | 4.90184432450248e-08 | 9.80368864900497e-08 | 0.999999950981557 |
| 51 | 0.000399679238536783 | 0.000799358477073566 | 0.999600320761463 |
| 52 | 0.00436420959525487 | 0.00872841919050974 | 0.995635790404745 |
| 53 | 0.0237213910577516 | 0.0474427821155032 | 0.976278608942248 |
| 54 | 0.134938094444008 | 0.269876188888015 | 0.865061905555992 |
| 55 | 0.0981065478757 | 0.1962130957514 | 0.9018934521243 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 48 | 0.941176470588235 | NOK |
| 5% type I error level | 49 | 0.96078431372549 | NOK |
| 10% type I error level | 49 | 0.96078431372549 | NOK |
