| Multiple Linear Regression - Estimated Regression Equation |
| eu/us[t] = + 3.06886493595529 -1.51139049137114`us/ch`[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) | 3.06886493595529 | 0.082594 | 37.156 | 0 | 0 |
| `us/ch` | -1.51139049137114 | 0.07614 | -19.8502 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.890375586990514 |
| R-squared | 0.792768685908702 |
| Adjusted R-squared | 0.790756731402962 |
| F-TEST (value) | 394.029131198881 |
| F-TEST (DF numerator) | 1 |
| F-TEST (DF denominator) | 103 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 0.0441024371267238 |
| Sum Squared Residuals | 0.200337570933212 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 1.3954 | 1.45394419592521 | -0.0585441959252147 |
| 2 | 1.479 | 1.40482400495566 | 0.074175995044338 |
| 3 | 1.4619 | 1.40693995164358 | 0.0549600483564183 |
| 4 | 1.467 | 1.40966045452805 | 0.0573395454719506 |
| 5 | 1.4799 | 1.42250727370470 | 0.0573927262952955 |
| 6 | 1.4508 | 1.40361489256257 | 0.0471851074374349 |
| 7 | 1.4678 | 1.41676398983749 | 0.0510360101625059 |
| 8 | 1.4824 | 1.43021536521070 | 0.0521846347893028 |
| 9 | 1.5189 | 1.49565857348707 | 0.0232414265129321 |
| 10 | 1.5348 | 1.52044537754555 | 0.0143546224544455 |
| 11 | 1.5666 | 1.55838127887897 | 0.0082187211210298 |
| 12 | 1.5446 | 1.54387193016181 | 0.00072806983819268 |
| 13 | 1.5803 | 1.56548481418841 | 0.0148151858115856 |
| 14 | 1.5718 | 1.54538332065318 | 0.0264166793468218 |
| 15 | 1.5832 | 1.55959039127207 | 0.023609608727933 |
| 16 | 1.5801 | 1.52966485954292 | 0.0504351404570816 |
| 17 | 1.5605 | 1.50351780404220 | 0.0569821959578025 |
| 18 | 1.5416 | 1.47344113326391 | 0.0681588667360883 |
| 19 | 1.5479 | 1.49565857348707 | 0.0522414265129323 |
| 20 | 1.558 | 1.48583453529316 | 0.072165464706845 |
| 21 | 1.579 | 1.52437499282312 | 0.0546250071768806 |
| 22 | 1.5554 | 1.4929380706026 | 0.0624619293974002 |
| 23 | 1.5761 | 1.52649093951104 | 0.049609060488961 |
| 24 | 1.536 | 1.48341631050696 | 0.0525836894930385 |
| 25 | 1.5621 | 1.50548261168098 | 0.0566173883190199 |
| 26 | 1.5773 | 1.52830460810068 | 0.0489953918993157 |
| 27 | 1.571 | 1.52150335088951 | 0.0494966491104858 |
| 28 | 1.5925 | 1.53253650147652 | 0.0599634985234764 |
| 29 | 1.5844 | 1.52452613187226 | 0.0598738681277436 |
| 30 | 1.5696 | 1.50155299640342 | 0.0680470035965848 |
| 31 | 1.554 | 1.48069580762249 | 0.0733041923775066 |
| 32 | 1.5012 | 1.43459839763567 | 0.0666016023643265 |
| 33 | 1.4676 | 1.41086956692115 | 0.0567304330788534 |
| 34 | 1.477 | 1.40799792498754 | 0.0690020750124587 |
| 35 | 1.466 | 1.40361489256257 | 0.0623851074374347 |
| 36 | 1.4241 | 1.38124631329027 | 0.0428536867097278 |
| 37 | 1.4214 | 1.35812203877229 | 0.0632779612277062 |
| 38 | 1.4469 | 1.40331261446429 | 0.0435873855357094 |
| 39 | 1.4618 | 1.42386752514694 | 0.0379324748530617 |
| 40 | 1.3834 | 1.36658582552397 | 0.0168141744760280 |
| 41 | 1.3412 | 1.35419242349473 | -0.0129924234947286 |
| 42 | 1.3437 | 1.35540153588783 | -0.0117015358878258 |
| 43 | 1.263 | 1.30658362301654 | -0.0435836230165379 |
| 44 | 1.2759 | 1.32320891842162 | -0.0473089184216202 |
| 45 | 1.2743 | 1.28814465902181 | -0.0138446590218099 |
| 46 | 1.2797 | 1.27696036938566 | 0.00273963061433678 |
| 47 | 1.2573 | 1.22209689454889 | 0.0352031054511093 |
| 48 | 1.2705 | 1.23554826992209 | 0.0349517300779062 |
| 49 | 1.268 | 1.22043436500838 | 0.0475656349916176 |
| 50 | 1.3371 | 1.29041174475887 | 0.0466882552411336 |
| 51 | 1.3885 | 1.39469768866348 | -0.00619768866347539 |
| 52 | 1.406 | 1.45590900356401 | -0.0499090035640068 |
| 53 | 1.3855 | 1.43051764330897 | -0.0450176433089713 |
| 54 | 1.3431 | 1.38305998187992 | -0.0399599818799176 |
| 55 | 1.3257 | 1.37852581040580 | -0.0528258104058039 |
| 56 | 1.2978 | 1.32018613743888 | -0.0223861374388779 |
| 57 | 1.2793 | 1.31187348973634 | -0.0325734897363364 |
| 58 | 1.2945 | 1.31157121163806 | -0.0170712116380624 |
| 59 | 1.289 | 1.31897702504578 | -0.0299770250457812 |
| 60 | 1.2848 | 1.32577828225695 | -0.0409782822569513 |
| 61 | 1.2694 | 1.30295628583725 | -0.0335562858372467 |
| 62 | 1.2636 | 1.31610538311218 | -0.0525053831121759 |
| 63 | 1.29 | 1.27212391981328 | 0.0178760801867245 |
| 64 | 1.3559 | 1.36159823690245 | -0.00569823690244727 |
| 65 | 1.3305 | 1.34225243861290 | -0.0117524386128965 |
| 66 | 1.3482 | 1.35842431687057 | -0.0102243168705679 |
| 67 | 1.3146 | 1.31852360789837 | -0.00392360789836986 |
| 68 | 1.3027 | 1.30476995442689 | -0.00206995442689231 |
| 69 | 1.3247 | 1.34724002723442 | -0.0225400272344214 |
| 70 | 1.3267 | 1.35237875490508 | -0.0256787549050834 |
| 71 | 1.3621 | 1.39651135725312 | -0.0344113572531205 |
| 72 | 1.3479 | 1.37127113604722 | -0.0233711360472225 |
| 73 | 1.4011 | 1.42976194806329 | -0.0286619480632858 |
| 74 | 1.4135 | 1.45530444736746 | -0.041804447367458 |
| 75 | 1.3964 | 1.42704144517882 | -0.0306414451788176 |
| 76 | 1.401 | 1.43777231766755 | -0.036772317667553 |
| 77 | 1.3955 | 1.43671434432359 | -0.041214344323593 |
| 78 | 1.4077 | 1.43399384143912 | -0.0262938414391249 |
| 79 | 1.3975 | 1.42613461088400 | -0.0286346108839952 |
| 80 | 1.3949 | 1.43006422616156 | -0.03516422616156 |
| 81 | 1.4138 | 1.44457357487872 | -0.0307735748787231 |
| 82 | 1.421 | 1.45001458064766 | -0.0290145806476592 |
| 83 | 1.4253 | 1.45349077877781 | -0.0281907787778128 |
| 84 | 1.4169 | 1.43233131189862 | -0.0154313118986168 |
| 85 | 1.4174 | 1.44472471392786 | -0.0273247139278602 |
| 86 | 1.4346 | 1.47162746467427 | -0.0370274646742665 |
| 87 | 1.4296 | 1.46679101510188 | -0.0371910151018788 |
| 88 | 1.4311 | 1.46784898844584 | -0.0367489884458387 |
| 89 | 1.4594 | 1.50155299640342 | -0.0421529964034152 |
| 90 | 1.4722 | 1.51394639843266 | -0.0417463984326587 |
| 91 | 1.4669 | 1.51288842508870 | -0.0459884250886985 |
| 92 | 1.4571 | 1.50427349928788 | -0.0471734992878833 |
| 93 | 1.4709 | 1.50850539266372 | -0.0376053926637223 |
| 94 | 1.4893 | 1.52936258144464 | -0.0400625814446442 |
| 95 | 1.4997 | 1.54326737396526 | -0.0435673739652585 |
| 96 | 1.4713 | 1.51848056990677 | -0.0471805699067718 |
| 97 | 1.4846 | 1.53178080623084 | -0.0471808062308382 |
| 98 | 1.4914 | 1.53979117583511 | -0.048391175835105 |
| 99 | 1.4859 | 1.53102511098515 | -0.0451251109851523 |
| 100 | 1.4957 | 1.54780154543937 | -0.0521015454393721 |
| 101 | 1.4843 | 1.53208308432911 | -0.0477830843291124 |
| 102 | 1.4619 | 1.50608716787753 | -0.0441871678775285 |
| 103 | 1.434 | 1.49354262679915 | -0.0595426267991481 |
| 104 | 1.4426 | 1.50366894309133 | -0.0610689430913345 |
| 105 | 1.4318 | 1.50487805548443 | -0.0730780554844318 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 5 | 0.0983310122554686 | 0.196662024510937 | 0.901668987744531 |
| 6 | 0.0822416416228463 | 0.164483283245693 | 0.917758358377154 |
| 7 | 0.0394134972671759 | 0.0788269945343517 | 0.960586502732824 |
| 8 | 0.0663025057069408 | 0.132605011413882 | 0.933697494293059 |
| 9 | 0.277372984922148 | 0.554745969844295 | 0.722627015077852 |
| 10 | 0.234287537694288 | 0.468575075388575 | 0.765712462305712 |
| 11 | 0.180259048392263 | 0.360518096784525 | 0.819740951607737 |
| 12 | 0.118347838885477 | 0.236695677770955 | 0.881652161114522 |
| 13 | 0.086063377242487 | 0.172126754484974 | 0.913936622757513 |
| 14 | 0.0626544915964111 | 0.125308983192822 | 0.937345508403589 |
| 15 | 0.0436799704504399 | 0.0873599409008797 | 0.95632002954956 |
| 16 | 0.0431587462529280 | 0.0863174925058561 | 0.956841253747072 |
| 17 | 0.0415107804720085 | 0.083021560944017 | 0.958489219527991 |
| 18 | 0.044491547648054 | 0.088983095296108 | 0.955508452351946 |
| 19 | 0.0366510308825039 | 0.0733020617650079 | 0.963348969117496 |
| 20 | 0.0458877531816991 | 0.0917755063633981 | 0.95411224681830 |
| 21 | 0.0437955719846287 | 0.0875911439692575 | 0.956204428015371 |
| 22 | 0.0442413166619724 | 0.0884826333239447 | 0.955758683338028 |
| 23 | 0.0393945955475148 | 0.0787891910950295 | 0.960605404452485 |
| 24 | 0.033840335452031 | 0.067680670904062 | 0.966159664547969 |
| 25 | 0.0338003279295784 | 0.0676006558591569 | 0.966199672070422 |
| 26 | 0.032309034505866 | 0.064618069011732 | 0.967690965494134 |
| 27 | 0.0318697583587357 | 0.0637395167174715 | 0.968130241641264 |
| 28 | 0.0434589075525112 | 0.0869178151050225 | 0.95654109244749 |
| 29 | 0.0611687147655088 | 0.122337429531018 | 0.93883128523449 |
| 30 | 0.104165952326951 | 0.208331904653901 | 0.89583404767305 |
| 31 | 0.195726456781621 | 0.391452913563241 | 0.804273543218379 |
| 32 | 0.278546080212467 | 0.557092160424935 | 0.721453919787533 |
| 33 | 0.342383253979891 | 0.684766507959782 | 0.657616746020109 |
| 34 | 0.497110701736885 | 0.99422140347377 | 0.502889298263115 |
| 35 | 0.657110319937642 | 0.685779360124716 | 0.342889680062358 |
| 36 | 0.746684663620162 | 0.506630672759676 | 0.253315336379838 |
| 37 | 0.881148452702595 | 0.237703094594809 | 0.118851547297405 |
| 38 | 0.95473120802408 | 0.0905375839518388 | 0.0452687919759194 |
| 39 | 0.990515352369575 | 0.0189692952608496 | 0.0094846476304248 |
| 40 | 0.996810431446568 | 0.0063791371068647 | 0.00318956855343235 |
| 41 | 0.999302860542528 | 0.00139427891494461 | 0.000697139457472303 |
| 42 | 0.99973481392507 | 0.000530372149857276 | 0.000265186074928638 |
| 43 | 0.99998813390465 | 2.37321907017121e-05 | 1.18660953508560e-05 |
| 44 | 0.999999350502616 | 1.29899476830146e-06 | 6.49497384150728e-07 |
| 45 | 0.999999199326676 | 1.60134664708633e-06 | 8.00673323543164e-07 |
| 46 | 0.999998438009867 | 3.12398026666057e-06 | 1.56199013333028e-06 |
| 47 | 0.999998770132118 | 2.45973576310743e-06 | 1.22986788155371e-06 |
| 48 | 0.999999235113376 | 1.52977324734788e-06 | 7.64886623673941e-07 |
| 49 | 0.999999911803938 | 1.76392123260769e-07 | 8.81960616303845e-08 |
| 50 | 0.999999999737283 | 5.25433433684218e-10 | 2.62716716842109e-10 |
| 51 | 0.999999999903366 | 1.93267201430468e-10 | 9.66336007152342e-11 |
| 52 | 0.999999999989197 | 2.16067688100372e-11 | 1.08033844050186e-11 |
| 53 | 0.999999999997045 | 5.91047143820719e-12 | 2.95523571910359e-12 |
| 54 | 0.999999999998557 | 2.88658274863735e-12 | 1.44329137431868e-12 |
| 55 | 0.999999999999887 | 2.25236871341928e-13 | 1.12618435670964e-13 |
| 56 | 0.999999999999778 | 4.43212246736198e-13 | 2.21606123368099e-13 |
| 57 | 0.999999999999822 | 3.56433092443109e-13 | 1.78216546221555e-13 |
| 58 | 0.999999999999542 | 9.15270914480455e-13 | 4.57635457240227e-13 |
| 59 | 0.999999999999467 | 1.06631345153693e-12 | 5.33156725768467e-13 |
| 60 | 0.99999999999988 | 2.40689570161308e-13 | 1.20344785080654e-13 |
| 61 | 0.999999999999962 | 7.65541770082074e-14 | 3.82770885041037e-14 |
| 62 | 1 | 1.27939285670383e-17 | 6.39696428351916e-18 |
| 63 | 1 | 9.85034280193608e-18 | 4.92517140096804e-18 |
| 64 | 1 | 1.6176404780976e-17 | 8.088202390488e-18 |
| 65 | 1 | 6.55158131620528e-17 | 3.27579065810264e-17 |
| 66 | 1 | 1.81101051449675e-16 | 9.05505257248376e-17 |
| 67 | 1 | 5.29840368619815e-16 | 2.64920184309908e-16 |
| 68 | 1 | 1.31812658880133e-15 | 6.59063294400663e-16 |
| 69 | 0.999999999999998 | 4.67218010782898e-15 | 2.33609005391449e-15 |
| 70 | 0.999999999999994 | 1.27997080192796e-14 | 6.3998540096398e-15 |
| 71 | 0.99999999999999 | 2.19861664497143e-14 | 1.09930832248572e-14 |
| 72 | 0.999999999999962 | 7.56661062782402e-14 | 3.78330531391201e-14 |
| 73 | 0.999999999999886 | 2.28385171437755e-13 | 1.14192585718878e-13 |
| 74 | 0.99999999999979 | 4.18636116655575e-13 | 2.09318058327788e-13 |
| 75 | 0.999999999999326 | 1.34714552853916e-12 | 6.73572764269581e-13 |
| 76 | 0.99999999999831 | 3.3801490942439e-12 | 1.69007454712195e-12 |
| 77 | 0.999999999997522 | 4.95613083956597e-12 | 2.47806541978298e-12 |
| 78 | 0.999999999991466 | 1.70688305530175e-11 | 8.53441527650875e-12 |
| 79 | 0.99999999996924 | 6.15219274500657e-11 | 3.07609637250328e-11 |
| 80 | 0.999999999920824 | 1.58352008640905e-10 | 7.91760043204523e-11 |
| 81 | 0.999999999721504 | 5.56991647949637e-10 | 2.78495823974818e-10 |
| 82 | 0.999999999054979 | 1.89004270219084e-09 | 9.45021351095422e-10 |
| 83 | 0.999999997049589 | 5.90082188604896e-09 | 2.95041094302448e-09 |
| 84 | 0.999999997154775 | 5.69044890302593e-09 | 2.84522445151297e-09 |
| 85 | 0.999999994867223 | 1.02655535860365e-08 | 5.13277679301823e-09 |
| 86 | 0.99999998618277 | 2.76344618185567e-08 | 1.38172309092783e-08 |
| 87 | 0.999999968044158 | 6.39116831120946e-08 | 3.19558415560473e-08 |
| 88 | 0.999999965594873 | 6.88102549004331e-08 | 3.44051274502165e-08 |
| 89 | 0.99999992214524 | 1.55709520505766e-07 | 7.78547602528831e-08 |
| 90 | 0.99999979841551 | 4.03168982296953e-07 | 2.01584491148477e-07 |
| 91 | 0.99999928918323 | 1.42163353973835e-06 | 7.10816769869175e-07 |
| 92 | 0.99999766418139 | 4.67163722084478e-06 | 2.33581861042239e-06 |
| 93 | 0.999998191921065 | 3.61615787026824e-06 | 1.80807893513412e-06 |
| 94 | 0.999995288040872 | 9.42391825643227e-06 | 4.71195912821614e-06 |
| 95 | 0.999977068217156 | 4.58635656884915e-05 | 2.29317828442457e-05 |
| 96 | 0.999912906884839 | 0.000174186230322551 | 8.70931151612753e-05 |
| 97 | 0.999597995488137 | 0.00080400902372625 | 0.000402004511863125 |
| 98 | 0.99811029418265 | 0.00377941163469956 | 0.00188970581734978 |
| 99 | 0.99301593969603 | 0.0139681206079381 | 0.00698406030396907 |
| 100 | 0.973156370856907 | 0.0536872582861867 | 0.0268436291430933 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 59 | 0.614583333333333 | NOK |
| 5% type I error level | 61 | 0.635416666666667 | NOK |
| 10% type I error level | 78 | 0.8125 | NOK |
