| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 0.918381042450223 + 0.654697232943884X[t] + 1.08057771183516Y1[t] -0.255818518025034Y2[t] -0.201421589282912M1[t] -0.308680635057811M2[t] -0.200007912257289M3[t] -0.304535445515861M4[t] -0.48088115921706M5[t] -0.292490144066929M6[t] -0.403038896054930M7[t] -0.226210468212112M8[t] -0.422739955704922M9[t] -0.322312577454471M10[t] -0.0326139813926506M11[t] -0.0138870270198022t + 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) | 0.918381042450223 | 0.37768 | 2.4316 | 0.019487 | 0.009743 |
| X | 0.654697232943884 | 0.305291 | 2.1445 | 0.037969 | 0.018985 |
| Y1 | 1.08057771183516 | 0.164152 | 6.5828 | 0 | 0 |
| Y2 | -0.255818518025034 | 0.155223 | -1.6481 | 0.106982 | 0.053491 |
| M1 | -0.201421589282912 | 0.336739 | -0.5982 | 0.553028 | 0.276514 |
| M2 | -0.308680635057811 | 0.336817 | -0.9165 | 0.364783 | 0.182391 |
| M3 | -0.200007912257289 | 0.338412 | -0.591 | 0.557752 | 0.278876 |
| M4 | -0.304535445515861 | 0.343353 | -0.8869 | 0.380281 | 0.190141 |
| M5 | -0.48088115921706 | 0.341655 | -1.4075 | 0.166814 | 0.083407 |
| M6 | -0.292490144066929 | 0.345638 | -0.8462 | 0.402335 | 0.201167 |
| M7 | -0.403038896054930 | 0.34213 | -1.178 | 0.245577 | 0.122789 |
| M8 | -0.226210468212112 | 0.34373 | -0.6581 | 0.514149 | 0.257075 |
| M9 | -0.422739955704922 | 0.340734 | -1.2407 | 0.221778 | 0.110889 |
| M10 | -0.322312577454471 | 0.353886 | -0.9108 | 0.367734 | 0.183867 |
| M11 | -0.0326139813926506 | 0.35551 | -0.0917 | 0.927353 | 0.463676 |
| t | -0.0138870270198022 | 0.007196 | -1.9297 | 0.060583 | 0.030291 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.931744212410473 |
| R-squared | 0.868147277360413 |
| Adjusted R-squared | 0.81990847639471 |
| F-TEST (value) | 17.9968668370853 |
| F-TEST (DF numerator) | 15 |
| F-TEST (DF denominator) | 41 |
| p-value | 2.00950367457153e-13 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 0.499925504351956 |
| Sum Squared Residuals | 10.2469459059638 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 2.1 | 2.25026340655775 | -0.150263406557748 |
| 2 | 2 | 2.33950251215658 | -0.339502512156579 |
| 3 | 1.8 | 2.30064858495128 | -0.500648584951281 |
| 4 | 2.7 | 1.99170033410838 | 0.708299665891623 |
| 5 | 2.3 | 2.82515123764403 | -0.525151237644028 |
| 6 | 1.9 | 2.33718747481776 | -0.437187474817762 |
| 7 | 2 | 1.88284801828591 | 0.117151981714092 |
| 8 | 2.3 | 2.25617459750245 | 0.0438254024975471 |
| 9 | 2.8 | 2.34434954473788 | 0.455650455262116 |
| 10 | 2.4 | 2.89443319647860 | -0.494433196478605 |
| 11 | 2.3 | 2.61010442177404 | -0.310104421774041 |
| 12 | 2.7 | 2.62310101217339 | 0.0768989878266132 |
| 13 | 2.7 | 2.86560533240724 | -0.165605332407241 |
| 14 | 2.9 | 2.64213185240253 | 0.257868147597473 |
| 15 | 3 | 2.95303309055028 | 0.0469669094497221 |
| 16 | 2.2 | 2.89151259785041 | -0.691512597850414 |
| 17 | 2.3 | 1.81123583585878 | 0.48876416414122 |
| 18 | 2.8 | 2.29845240959265 | 0.501547590407348 |
| 19 | 2.8 | 2.68872363469993 | 0.111276365300074 |
| 20 | 2.8 | 2.72375577651042 | 0.0762442234895748 |
| 21 | 2.2 | 2.51333926199781 | -0.313339261997812 |
| 22 | 2.6 | 1.95153298612736 | 0.648467013872636 |
| 23 | 2.8 | 2.81306675071847 | -0.0130667507184674 |
| 24 | 2.5 | 2.94558184024833 | -0.445581840248334 |
| 25 | 2.4 | 2.35493620679006 | 0.0450637932099351 |
| 26 | 2.3 | 2.20247791821936 | 0.0975220817806422 |
| 27 | 1.9 | 2.21478769461906 | -0.314787694619064 |
| 28 | 1.7 | 1.68972390140913 | 0.0102760985908709 |
| 29 | 2 | 1.38570302553111 | 0.614296974468891 |
| 30 | 2.1 | 1.93554403081699 | 0.164455969183007 |
| 31 | 1.7 | 1.84242046758520 | -0.142420467585196 |
| 32 | 1.8 | 1.54754893187164 | 0.252451068128356 |
| 33 | 1.8 | 1.54751759575256 | 0.252482404247439 |
| 34 | 1.8 | 1.60847609518071 | 0.191523904819294 |
| 35 | 1.3 | 1.88428766422272 | -0.584287664222725 |
| 36 | 1.3 | 1.36272576267799 | -0.0627257626779923 |
| 37 | 1.3 | 1.27532640538779 | 0.0246735946122057 |
| 38 | 1.2 | 1.15418033259309 | 0.0458196674069067 |
| 39 | 1.4 | 1.14090825719030 | 0.259091742809703 |
| 40 | 2.2 | 1.91888832402534 | 0.281111675974658 |
| 41 | 2.9 | 2.54195404916746 | 0.358045950832536 |
| 42 | 3.1 | 3.26820762116238 | -0.168207621162379 |
| 43 | 3.5 | 3.18081442190409 | 0.319185578095915 |
| 44 | 3.6 | 3.72482320385616 | -0.124823203856159 |
| 45 | 4.4 | 3.52013705331705 | 0.879862946682951 |
| 46 | 4.1 | 4.44555772221332 | -0.345557722213324 |
| 47 | 5.1 | 4.19254116328477 | 0.907458836715234 |
| 48 | 5.8 | 5.36859138490029 | 0.431408615099713 |
| 49 | 5.9 | 5.65386864885715 | 0.246131351142848 |
| 50 | 5.4 | 5.46170738462844 | -0.0617073846284438 |
| 51 | 5.5 | 4.99062237268908 | 0.50937762731092 |
| 52 | 4.8 | 5.10817484260674 | -0.308174842606738 |
| 53 | 3.2 | 4.13595585179862 | -0.93595585179862 |
| 54 | 2.7 | 2.76060846361021 | -0.0606084636102141 |
| 55 | 2.1 | 2.50519345752488 | -0.405193457524884 |
| 56 | 1.9 | 2.14769749025932 | -0.247697490259319 |
| 57 | 0.6 | 1.87465654419469 | -1.27465654419469 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 19 | 0.545195235092514 | 0.909609529814973 | 0.454804764907486 |
| 20 | 0.376182279428507 | 0.752364558857014 | 0.623817720571493 |
| 21 | 0.447594288741657 | 0.895188577483314 | 0.552405711258343 |
| 22 | 0.319108602978687 | 0.638217205957373 | 0.680891397021313 |
| 23 | 0.247362030100271 | 0.494724060200543 | 0.752637969899729 |
| 24 | 0.28189039528837 | 0.56378079057674 | 0.71810960471163 |
| 25 | 0.256230594218741 | 0.512461188437483 | 0.743769405781259 |
| 26 | 0.241597701303076 | 0.483195402606152 | 0.758402298696924 |
| 27 | 0.499736242217337 | 0.999472484434675 | 0.500263757782663 |
| 28 | 0.507493646068328 | 0.985012707863344 | 0.492506353931672 |
| 29 | 0.435017231678514 | 0.870034463357029 | 0.564982768321486 |
| 30 | 0.348481267722258 | 0.696962535444515 | 0.651518732277742 |
| 31 | 0.303593934121942 | 0.607187868243883 | 0.696406065878058 |
| 32 | 0.218856992319492 | 0.437713984638984 | 0.781143007680508 |
| 33 | 0.152177263530724 | 0.304354527061448 | 0.847822736469276 |
| 34 | 0.134780565846445 | 0.269561131692889 | 0.865219434153555 |
| 35 | 0.194034740653128 | 0.388069481306255 | 0.805965259346872 |
| 36 | 0.186383932350750 | 0.372767864701499 | 0.81361606764925 |
| 37 | 0.126815856133369 | 0.253631712266737 | 0.873184143866631 |
| 38 | 0.063261094160008 | 0.126522188320016 | 0.936738905839992 |
| 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 |
