| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = -0.228903714593018 + 0.0512220684067442X[t] + 0.953263571164633Y1[t] -0.166874438987276Y5[t] -0.775206618339435M1[t] -0.959994739976522M2[t] -0.952057839466697M3[t] -0.573275251722887M4[t] -0.176634951549861M5[t] -0.00332245912141396M6[t] -1.29637927379665M7[t] + 1.29435463178808M8[t] + 0.71759322481859M9[t] -0.0524909907347402M10[t] + 0.184537892904761M11[t] -0.0444618723895546t + 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) | -0.228903714593018 | 1.840167 | -0.1244 | 0.901442 | 0.450721 |
| X | 0.0512220684067442 | 0.019664 | 2.6049 | 0.0117 | 0.00585 |
| Y1 | 0.953263571164633 | 0.068625 | 13.8909 | 0 | 0 |
| Y5 | -0.166874438987276 | 0.062741 | -2.6597 | 0.010136 | 0.005068 |
| M1 | -0.775206618339435 | 2.075813 | -0.3734 | 0.710201 | 0.355101 |
| M2 | -0.959994739976522 | 2.18014 | -0.4403 | 0.661359 | 0.330679 |
| M3 | -0.952057839466697 | 2.237315 | -0.4255 | 0.672049 | 0.336024 |
| M4 | -0.573275251722887 | 2.208944 | -0.2595 | 0.796166 | 0.398083 |
| M5 | -0.176634951549861 | 2.189287 | -0.0807 | 0.935978 | 0.467989 |
| M6 | -0.00332245912141396 | 2.173918 | -0.0015 | 0.998786 | 0.499393 |
| M7 | -1.29637927379665 | 2.216391 | -0.5849 | 0.56092 | 0.28046 |
| M8 | 1.29435463178808 | 2.169092 | 0.5967 | 0.553053 | 0.276526 |
| M9 | 0.71759322481859 | 2.154867 | 0.333 | 0.740348 | 0.370174 |
| M10 | -0.0524909907347402 | 2.149686 | -0.0244 | 0.980604 | 0.490302 |
| M11 | 0.184537892904761 | 2.138932 | 0.0863 | 0.93155 | 0.465775 |
| t | -0.0444618723895546 | 0.025632 | -1.7346 | 0.088213 | 0.044106 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.959537170376185 |
| R-squared | 0.920711581333536 |
| Adjusted R-squared | 0.899846208000257 |
| F-TEST (value) | 44.1262931952921 |
| F-TEST (DF numerator) | 15 |
| F-TEST (DF denominator) | 57 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 3.70244681163037 |
| Sum Squared Residuals | 781.36240639826 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | -1.2 | 0.718045089082084 | -1.91804508908208 |
| 2 | -2.4 | -0.404458682946338 | -1.99554131705366 |
| 3 | 0.8 | -1.67046341642465 | 2.47046341642465 |
| 4 | -0.1 | 1.81558512675933 | -1.91558512675933 |
| 5 | -1.5 | 1.0106120870281 | -2.5106120870281 |
| 6 | -4.4 | -0.299547729465815 | -4.10045227053419 |
| 7 | -4.2 | -3.31001745584596 | -0.889982544154035 |
| 8 | 3.5 | -1.33759022100749 | 4.83759022100749 |
| 9 | 10 | 6.43813360348907 | 3.56186639651093 |
| 10 | 8.6 | 10.7216511641231 | -2.12165116412312 |
| 11 | 9.5 | 10.2172512540259 | -0.717251254025916 |
| 12 | 9.9 | 11.3865009811379 | -1.48650098113786 |
| 13 | 10.4 | 9.99614818331653 | 0.40385181668347 |
| 14 | 16 | 8.28294875169959 | 7.71705124830041 |
| 15 | 12.7 | 14.7351990174047 | -2.03519901740471 |
| 16 | 10.2 | 11.9835734332948 | -1.78357343329478 |
| 17 | 8.9 | 9.05092344254182 | -0.150923442541823 |
| 18 | 12.6 | 7.92368288950183 | 4.67631711049817 |
| 19 | 13.6 | 10.8639486079993 | 2.73605139200068 |
| 20 | 14.8 | 13.2135971899132 | 1.58640281008678 |
| 21 | 9.5 | 14.0612765702878 | -4.56127657028779 |
| 22 | 13.7 | 9.4563005213534 | 4.2436994786466 |
| 23 | 17 | 11.6418988465784 | 5.35810115342156 |
| 24 | 14.7 | 15.3957469679123 | -0.695746967912321 |
| 25 | 17.4 | 13.5611965768614 | 3.83880342313863 |
| 26 | 9 | 16.7287262695237 | -7.7287262695237 |
| 27 | 9.1 | 8.85468981902915 | 0.245310180970845 |
| 28 | 12.2 | 9.33807165004145 | 2.86192834995855 |
| 29 | 15.9 | 12.6091573971707 | 3.29084260282929 |
| 30 | 12.9 | 16.2447876198698 | -3.34478761986975 |
| 31 | 10.9 | 14.4173205996916 | -3.51732059969164 |
| 32 | 10.6 | 12.9453954488230 | -2.34539544882298 |
| 33 | 13.2 | 10.7474291043122 | 2.45257089568784 |
| 34 | 9.6 | 12.6544636263777 | -3.0544636263777 |
| 35 | 6.4 | 12.3438311408765 | -5.94383114087648 |
| 36 | 5.8 | 6.06358017255083 | -0.263580172550834 |
| 37 | -1 | 5.5927910337339 | -6.5927910337339 |
| 38 | -0.2 | -2.27987815695493 | 2.07987815695493 |
| 39 | 2.7 | 0.0150528013387072 | 2.68494719866129 |
| 40 | 3.6 | 2.05482975037993 | 1.54517024962007 |
| 41 | -0.9 | 2.57625020214007 | -3.47625020214007 |
| 42 | 0.3 | -1.22841450273092 | 1.52841450273092 |
| 43 | -1.1 | -1.33526156143898 | 0.235261561438975 |
| 44 | -2.5 | -0.894337984015153 | -1.60566201598485 |
| 45 | -3.4 | -1.59171037690776 | -1.80828962309224 |
| 46 | -3.5 | -1.98054919202594 | -1.51945080797406 |
| 47 | -3.9 | -3.37947619536781 | -0.520523804632187 |
| 48 | -4.6 | -3.50004683251207 | -1.09995316748792 |
| 49 | -0.1 | -4.58434278273186 | 4.48434278273186 |
| 50 | 4.3 | 1.25514206390536 | 3.04485793609464 |
| 51 | 10.2 | 7.16609236803738 | 3.03390763196262 |
| 52 | 8.7 | 12.5101644190482 | -3.81016441904818 |
| 53 | 13.3 | 11.7592700778434 | 1.54072992215656 |
| 54 | 15 | 15.2558433940818 | -0.255843394081838 |
| 55 | 20.7 | 16.5820310201669 | 4.11796897983307 |
| 56 | 20.7 | 23.9512673183448 | -3.25126731834483 |
| 57 | 26.4 | 22.7659248097995 | 3.63407519020054 |
| 58 | 31.2 | 25.9156163209811 | 5.28438367901888 |
| 59 | 31.4 | 28.4281122938833 | 2.97188770611673 |
| 60 | 26.6 | 28.6269329276309 | -2.02693292763088 |
| 61 | 26.6 | 24.0101747350942 | 2.58982526490583 |
| 62 | 19.2 | 22.3175197547726 | -3.11751975477262 |
| 63 | 6.5 | 12.8994294106147 | -6.3994294106147 |
| 64 | 3.1 | -0.00222437952366983 | 3.10222437952367 |
| 65 | -0.2 | -1.50621320672414 | 1.30621320672414 |
| 66 | -4 | -5.49635167125668 | 1.49635167125668 |
| 67 | -12.6 | -9.91802121057296 | -2.68197878942704 |
| 68 | -13 | -13.7783317520584 | 0.77833175205839 |
| 69 | -17.6 | -14.3210537109807 | -3.27894628901929 |
| 70 | -21.7 | -18.8674824408094 | -2.83251755919059 |
| 71 | -23.2 | -22.0516173399963 | -1.1483826600037 |
| 72 | -16.8 | -22.3727142167198 | 5.57271421671981 |
| 73 | -19.8 | -16.9940128353562 | -2.80598716464381 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 19 | 0.230321862284995 | 0.460643724569991 | 0.769678137715005 |
| 20 | 0.115213267882793 | 0.230426535765585 | 0.884786732117207 |
| 21 | 0.323068627621584 | 0.646137255243167 | 0.676931372378416 |
| 22 | 0.415736347755467 | 0.831472695510933 | 0.584263652244533 |
| 23 | 0.343858593129184 | 0.687717186258369 | 0.656141406870816 |
| 24 | 0.337917726432958 | 0.675835452865916 | 0.662082273567042 |
| 25 | 0.29388112119688 | 0.58776224239376 | 0.70611887880312 |
| 26 | 0.557296467999712 | 0.885407064000577 | 0.442703532000288 |
| 27 | 0.482102607107823 | 0.964205214215646 | 0.517897392892177 |
| 28 | 0.405545771584851 | 0.811091543169703 | 0.594454228415149 |
| 29 | 0.398615429586889 | 0.797230859173778 | 0.601384570413111 |
| 30 | 0.428288378051619 | 0.856576756103238 | 0.571711621948381 |
| 31 | 0.366224891562296 | 0.732449783124592 | 0.633775108437704 |
| 32 | 0.2820555567517 | 0.5641111135034 | 0.7179444432483 |
| 33 | 0.258043791684498 | 0.516087583368996 | 0.741956208315502 |
| 34 | 0.314502832959038 | 0.629005665918076 | 0.685497167040962 |
| 35 | 0.505315457300160 | 0.989369085399681 | 0.494684542699840 |
| 36 | 0.418363482566615 | 0.83672696513323 | 0.581636517433385 |
| 37 | 0.57912304150464 | 0.84175391699072 | 0.42087695849536 |
| 38 | 0.502653798214838 | 0.994692403570323 | 0.497346201785162 |
| 39 | 0.48406808802423 | 0.96813617604846 | 0.51593191197577 |
| 40 | 0.443647251185558 | 0.887294502371116 | 0.556352748814442 |
| 41 | 0.391888549836244 | 0.783777099672487 | 0.608111450163756 |
| 42 | 0.363935729051949 | 0.727871458103899 | 0.636064270948051 |
| 43 | 0.284985628495073 | 0.569971256990146 | 0.715014371504927 |
| 44 | 0.234298388389558 | 0.468596776779116 | 0.765701611610442 |
| 45 | 0.176093536635464 | 0.352187073270929 | 0.823906463364536 |
| 46 | 0.143811052969117 | 0.287622105938234 | 0.856188947030883 |
| 47 | 0.110845244893008 | 0.221690489786015 | 0.889154755106992 |
| 48 | 0.131624359715416 | 0.263248719430831 | 0.868375640284584 |
| 49 | 0.137112575139518 | 0.274225150279036 | 0.862887424860482 |
| 50 | 0.121261323960197 | 0.242522647920394 | 0.878738676039803 |
| 51 | 0.153660645188581 | 0.307321290377163 | 0.846339354811419 |
| 52 | 0.14312480395462 | 0.28624960790924 | 0.85687519604538 |
| 53 | 0.0926310057513 | 0.1852620115026 | 0.9073689942487 |
| 54 | 0.168298768238123 | 0.336597536476245 | 0.831701231761877 |
| 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 | 0 | 0 | OK |
| 10% type I error level | 0 | 0 | OK |
