| Multiple Linear Regression - Estimated Regression Equation |
| y[t] = + 9.56057142857143 + 0.960314153439154M1[t] -0.474578042328042M2[t] -0.0797202380952383M3[t] -0.813362433862434M4[t] -1.01412962962963M5[t] -1.27639682539683M6[t] -1.10003902116402M7[t] -1.33568121693122M8[t] -1.58519841269841M9[t] -1.01121560846561M10[t] -0.970857804232805M11[t] -0.00423280423280423t + 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) | 9.56057142857143 | 0.16496 | 57.9568 | 0 | 0 |
| M1 | 0.960314153439154 | 0.203618 | 4.7163 | 1e-05 | 5e-06 |
| M2 | -0.474578042328042 | 0.203501 | -2.3321 | 0.02212 | 0.01106 |
| M3 | -0.0797202380952383 | 0.203395 | -0.3919 | 0.696101 | 0.348051 |
| M4 | -0.813362433862434 | 0.2033 | -4.0008 | 0.000136 | 6.8e-05 |
| M5 | -1.01412962962963 | 0.203216 | -4.9904 | 3e-06 | 2e-06 |
| M6 | -1.27639682539683 | 0.203144 | -6.2832 | 0 | 0 |
| M7 | -1.10003902116402 | 0.203082 | -5.4167 | 1e-06 | 0 |
| M8 | -1.33568121693122 | 0.203032 | -6.5787 | 0 | 0 |
| M9 | -1.58519841269841 | 0.202993 | -7.8091 | 0 | 0 |
| M10 | -1.01121560846561 | 0.202965 | -4.9822 | 3e-06 | 2e-06 |
| M11 | -0.970857804232805 | 0.202948 | -4.7838 | 7e-06 | 4e-06 |
| t | -0.00423280423280423 | 0.001507 | -2.8095 | 0.006187 | 0.003094 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.880761246189551 |
| R-squared | 0.77574037278937 |
| Adjusted R-squared | 0.743317294156508 |
| F-TEST (value) | 23.9255618373983 |
| F-TEST (DF numerator) | 12 |
| F-TEST (DF denominator) | 83 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 0.405884762262812 |
| Sum Squared Residuals | 13.6736225396825 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 12.008 | 10.5166527777778 | 1.49134722222222 |
| 2 | 9.169 | 9.07752777777778 | 0.0914722222222216 |
| 3 | 8.788 | 9.46815277777778 | -0.680152777777778 |
| 4 | 8.417 | 8.73027777777778 | -0.313277777777778 |
| 5 | 8.247 | 8.52527777777778 | -0.278277777777778 |
| 6 | 8.197 | 8.25877777777778 | -0.0617777777777789 |
| 7 | 8.236 | 8.43090277777778 | -0.194902777777777 |
| 8 | 8.253 | 8.19102777777778 | 0.0619722222222226 |
| 9 | 7.733 | 7.93727777777778 | -0.204277777777777 |
| 10 | 8.366 | 8.50702777777778 | -0.141027777777778 |
| 11 | 8.626 | 8.54315277777778 | 0.0828472222222215 |
| 12 | 8.863 | 9.50977777777778 | -0.646777777777779 |
| 13 | 10.102 | 10.4658591269841 | -0.363859126984126 |
| 14 | 8.463 | 9.02673412698413 | -0.563734126984127 |
| 15 | 9.114 | 9.41735912698413 | -0.303359126984126 |
| 16 | 8.563 | 8.67948412698413 | -0.116484126984126 |
| 17 | 8.872 | 8.47448412698413 | 0.397515873015873 |
| 18 | 8.301 | 8.20798412698413 | 0.0930158730158734 |
| 19 | 8.301 | 8.38010912698413 | -0.0791091269841268 |
| 20 | 8.278 | 8.14023412698413 | 0.137765873015873 |
| 21 | 7.736 | 7.88648412698413 | -0.150484126984127 |
| 22 | 7.973 | 8.45623412698413 | -0.483234126984127 |
| 23 | 8.268 | 8.49235912698413 | -0.224359126984126 |
| 24 | 9.476 | 9.45898412698413 | 0.0170158730158738 |
| 25 | 11.1 | 10.4150654761905 | 0.684934523809523 |
| 26 | 8.962 | 8.97594047619048 | -0.0139404761904761 |
| 27 | 9.173 | 9.36656547619048 | -0.193565476190476 |
| 28 | 8.738 | 8.62869047619048 | 0.109309523809523 |
| 29 | 8.459 | 8.42369047619048 | 0.0353095238095237 |
| 30 | 8.078 | 8.15719047619048 | -0.0791904761904766 |
| 31 | 8.411 | 8.32931547619048 | 0.0816845238095234 |
| 32 | 8.291 | 8.08944047619048 | 0.201559523809524 |
| 33 | 7.81 | 7.83569047619048 | -0.0256904761904765 |
| 34 | 8.616 | 8.40544047619048 | 0.210559523809524 |
| 35 | 8.312 | 8.44156547619048 | -0.129565476190477 |
| 36 | 9.692 | 9.40819047619048 | 0.283809523809524 |
| 37 | 9.911 | 10.3642718253968 | -0.453271825396826 |
| 38 | 8.915 | 8.92514682539682 | -0.0101468253968259 |
| 39 | 9.452 | 9.31577182539683 | 0.136228174603175 |
| 40 | 9.112 | 8.57789682539683 | 0.534103174603174 |
| 41 | 8.472 | 8.37289682539683 | 0.0991031746031743 |
| 42 | 8.23 | 8.10639682539682 | 0.123603174603175 |
| 43 | 8.384 | 8.27852182539683 | 0.105478174603175 |
| 44 | 8.625 | 8.03864682539682 | 0.586353174603174 |
| 45 | 8.221 | 7.78489682539683 | 0.436103174603175 |
| 46 | 8.649 | 8.35464682539683 | 0.294353174603174 |
| 47 | 8.625 | 8.39077182539683 | 0.234228174603175 |
| 48 | 10.443 | 9.35739682539683 | 1.08560317460317 |
| 49 | 10.357 | 10.3134781746032 | 0.0435218253968246 |
| 50 | 8.586 | 8.87435317460317 | -0.288353174603174 |
| 51 | 8.892 | 9.26497817460317 | -0.372978174603175 |
| 52 | 8.329 | 8.52710317460317 | -0.198103174603174 |
| 53 | 8.101 | 8.32210317460317 | -0.221103174603174 |
| 54 | 7.922 | 8.05560317460317 | -0.133603174603175 |
| 55 | 8.12 | 8.22772817460318 | -0.107728174603176 |
| 56 | 7.838 | 7.98785317460317 | -0.149853174603175 |
| 57 | 7.735 | 7.73410317460317 | 0.000896825396825762 |
| 58 | 8.406 | 8.30385317460317 | 0.102146825396826 |
| 59 | 8.209 | 8.33997817460317 | -0.130978174603175 |
| 60 | 9.451 | 9.30660317460318 | 0.144396825396826 |
| 61 | 10.041 | 10.2626845238095 | -0.221684523809523 |
| 62 | 9.411 | 8.82355952380952 | 0.587440476190476 |
| 63 | 10.405 | 9.21418452380952 | 1.19081547619048 |
| 64 | 8.467 | 8.47630952380952 | -0.00930952380952354 |
| 65 | 8.464 | 8.27130952380952 | 0.192690476190477 |
| 66 | 8.102 | 8.00480952380952 | 0.0971904761904766 |
| 67 | 7.627 | 8.17693452380952 | -0.549934523809524 |
| 68 | 7.513 | 7.93705952380952 | -0.424059523809524 |
| 69 | 7.51 | 7.68330952380952 | -0.173309523809524 |
| 70 | 8.291 | 8.25305952380952 | 0.0379404761904766 |
| 71 | 8.064 | 8.28918452380952 | -0.225184523809523 |
| 72 | 9.383 | 9.25580952380952 | 0.127190476190475 |
| 73 | 9.706 | 10.2118908730159 | -0.505890873015874 |
| 74 | 8.579 | 8.77276587301587 | -0.193765873015872 |
| 75 | 9.474 | 9.16339087301587 | 0.310609126984127 |
| 76 | 8.318 | 8.42551587301587 | -0.107515873015874 |
| 77 | 8.213 | 8.22051587301587 | -0.00751587301587378 |
| 78 | 8.059 | 7.95401587301587 | 0.104984126984126 |
| 79 | 9.111 | 8.12614087301587 | 0.984859126984128 |
| 80 | 7.708 | 7.88626587301587 | -0.178265873015873 |
| 81 | 7.68 | 7.63251587301587 | 0.0474841269841267 |
| 82 | 8.014 | 8.20226587301587 | -0.188265873015874 |
| 83 | 8.007 | 8.23839087301587 | -0.231390873015873 |
| 84 | 8.718 | 9.20501587301587 | -0.487015873015873 |
| 85 | 9.486 | 10.1610972222222 | -0.675097222222222 |
| 86 | 9.113 | 8.72197222222222 | 0.391027777777778 |
| 87 | 9.025 | 9.11259722222222 | -0.087597222222222 |
| 88 | 8.476 | 8.37472222222222 | 0.101277777777778 |
| 89 | 7.952 | 8.16972222222222 | -0.217722222222222 |
| 90 | 7.759 | 7.90322222222222 | -0.144222222222222 |
| 91 | 7.835 | 8.07534722222222 | -0.240347222222222 |
| 92 | 7.6 | 7.83547222222222 | -0.235472222222223 |
| 93 | 7.651 | 7.58172222222222 | 0.0692777777777776 |
| 94 | 8.319 | 8.15147222222222 | 0.167527777777779 |
| 95 | 8.812 | 8.18759722222222 | 0.624402777777777 |
| 96 | 8.63 | 9.15422222222222 | -0.524222222222222 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 16 | 0.987020014184727 | 0.0259599716305466 | 0.0129799858152733 |
| 17 | 0.993215475638389 | 0.013569048723222 | 0.00678452436161099 |
| 18 | 0.987133351840868 | 0.025733296318263 | 0.0128666481591315 |
| 19 | 0.976790272199248 | 0.0464194556015042 | 0.0232097278007521 |
| 20 | 0.95940300966385 | 0.0811939806723005 | 0.0405969903361503 |
| 21 | 0.935420204405439 | 0.129159591189123 | 0.0645797955945613 |
| 22 | 0.920147365396061 | 0.159705269207879 | 0.0798526346039394 |
| 23 | 0.888482589270836 | 0.223034821458328 | 0.111517410729164 |
| 24 | 0.900965565256398 | 0.198068869487204 | 0.0990344347436022 |
| 25 | 0.9058265065765 | 0.188346986847 | 0.0941734934234999 |
| 26 | 0.875987751693859 | 0.248024496612283 | 0.124012248306141 |
| 27 | 0.860586032019694 | 0.278827935960613 | 0.139413967980306 |
| 28 | 0.822877782747455 | 0.354244434505089 | 0.177122217252544 |
| 29 | 0.76744976597903 | 0.465100468041939 | 0.232550234020969 |
| 30 | 0.71240551845304 | 0.57518896309392 | 0.28759448154696 |
| 31 | 0.650021708427613 | 0.699956583144774 | 0.349978291572387 |
| 32 | 0.578692651821366 | 0.842614696357269 | 0.421307348178634 |
| 33 | 0.512637385115893 | 0.974725229768214 | 0.487362614884107 |
| 34 | 0.484809984751679 | 0.969619969503358 | 0.515190015248321 |
| 35 | 0.432314713691092 | 0.864629427382185 | 0.567685286308907 |
| 36 | 0.417019103367098 | 0.834038206734197 | 0.582980896632902 |
| 37 | 0.656858733725766 | 0.686282532548468 | 0.343141266274234 |
| 38 | 0.60328301618002 | 0.793433967639959 | 0.396716983819979 |
| 39 | 0.589288509767415 | 0.82142298046517 | 0.410711490232585 |
| 40 | 0.597795147391629 | 0.804409705216742 | 0.402204852608371 |
| 41 | 0.530189959504285 | 0.93962008099143 | 0.469810040495715 |
| 42 | 0.460879826955322 | 0.921759653910644 | 0.539120173044678 |
| 43 | 0.394180475756204 | 0.788360951512407 | 0.605819524243796 |
| 44 | 0.410858857266993 | 0.821717714533986 | 0.589141142733007 |
| 45 | 0.389749072926809 | 0.779498145853618 | 0.610250927073191 |
| 46 | 0.340058992320476 | 0.680117984640953 | 0.659941007679524 |
| 47 | 0.284727539765537 | 0.569455079531074 | 0.715272460234463 |
| 48 | 0.627713892307087 | 0.744572215385826 | 0.372286107692913 |
| 49 | 0.664938271041284 | 0.670123457917432 | 0.335061728958716 |
| 50 | 0.675602422558384 | 0.648795154883233 | 0.324397577441616 |
| 51 | 0.761957337323935 | 0.476085325352129 | 0.238042662676065 |
| 52 | 0.741421111660338 | 0.517157776679325 | 0.258578888339662 |
| 53 | 0.72294562840721 | 0.554108743185579 | 0.27705437159279 |
| 54 | 0.684436115801244 | 0.631127768397513 | 0.315563884198756 |
| 55 | 0.642058690125707 | 0.715882619748585 | 0.357941309874293 |
| 56 | 0.609483576280744 | 0.781032847438512 | 0.390516423719256 |
| 57 | 0.543681355337256 | 0.912637289325488 | 0.456318644662744 |
| 58 | 0.473049106543629 | 0.946098213087258 | 0.526950893456371 |
| 59 | 0.431582080451855 | 0.86316416090371 | 0.568417919548145 |
| 60 | 0.384256763377745 | 0.76851352675549 | 0.615743236622255 |
| 61 | 0.375022519268565 | 0.750045038537129 | 0.624977480731435 |
| 62 | 0.397144660165143 | 0.794289320330285 | 0.602855339834857 |
| 63 | 0.766305573884783 | 0.467388852230434 | 0.233694426115217 |
| 64 | 0.705251327541579 | 0.589497344916843 | 0.294748672458421 |
| 65 | 0.665768192845114 | 0.668463614309771 | 0.334231807154885 |
| 66 | 0.600433695029821 | 0.799132609940358 | 0.399566304970179 |
| 67 | 0.754278381359605 | 0.49144323728079 | 0.245721618640395 |
| 68 | 0.731138334731416 | 0.537723330537167 | 0.268861665268584 |
| 69 | 0.68116210810732 | 0.63767578378536 | 0.31883789189268 |
| 70 | 0.597936968161569 | 0.804126063676861 | 0.402063031838431 |
| 71 | 0.601724304488225 | 0.79655139102355 | 0.398275695511775 |
| 72 | 0.604565079524649 | 0.790869840950703 | 0.395434920475351 |
| 73 | 0.553495076281213 | 0.893009847437574 | 0.446504923718787 |
| 74 | 0.561280155085885 | 0.877439689828231 | 0.438719844914115 |
| 75 | 0.492924162609485 | 0.985848325218971 | 0.507075837390515 |
| 76 | 0.401914899464651 | 0.803829798929301 | 0.598085100535349 |
| 77 | 0.298253434051569 | 0.596506868103138 | 0.701746565948431 |
| 78 | 0.208321261470894 | 0.416642522941788 | 0.791678738529106 |
| 79 | 0.778663567912519 | 0.442672864174962 | 0.221336432087481 |
| 80 | 0.688651789357796 | 0.622696421284408 | 0.311348210642204 |
| 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 | 4 | 0.0615384615384615 | NOK |
| 10% type I error level | 5 | 0.0769230769230769 | OK |
