| Multiple Linear Regression - Estimated Regression Equation |
| eu/us[t] = + 3.14689431591185 -1.52758658767174`us/ch`[t] -0.00114121297467551t + 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) | 3.14689431591185 | 0.051064 | 61.6262 | 0 | 0 |
| `us/ch` | -1.52758658767174 | 0.046768 | -32.6629 | 0 | 0 |
| t | -0.00114121297467551 | 8.7e-05 | -13.084 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.960534672716085 |
| R-squared | 0.922626857489797 |
| Adjusted R-squared | 0.92110973704842 |
| F-TEST (value) | 608.1434488172 |
| F-TEST (DF numerator) | 2 |
| F-TEST (DF denominator) | 102 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 0.0270799927376016 |
| Sum Squared Residuals | 0.0747992526801926 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 1.3954 | 1.51352683400991 | -0.118126834009909 |
| 2 | 1.479 | 1.46273905693591 | 0.0162609430640904 |
| 3 | 1.4619 | 1.46373646518397 | -0.00183646518397477 |
| 4 | 1.467 | 1.46534490806711 | 0.00165509193289207 |
| 5 | 1.4799 | 1.47718818108764 | 0.00271181891235740 |
| 6 | 1.4508 | 1.45695213576707 | -0.00615213576707027 |
| 7 | 1.4678 | 1.46910092610514 | -0.00130092610513892 |
| 8 | 1.4824 | 1.48155523376074 | 0.000844766239258157 |
| 9 | 1.5189 | 1.54655852003225 | -0.0276585200322531 |
| 10 | 1.5348 | 1.57046972709539 | -0.0356697270953941 |
| 11 | 1.5666 | 1.60767093747128 | -0.0410709374712793 |
| 12 | 1.5446 | 1.59186489325496 | -0.0472648932549552 |
| 13 | 1.5803 | 1.61256816848399 | -0.0322681684839853 |
| 14 | 1.5718 | 1.59111005389328 | -0.0193100538932756 |
| 15 | 1.5832 | 1.60432815484271 | -0.0211281548427146 |
| 16 | 1.5801 | 1.57294072743214 | 0.00715927256786147 |
| 17 | 1.5605 | 1.54537226649074 | 0.0151277335092582 |
| 18 | 1.5416 | 1.5138320804214 | 0.0277679195786015 |
| 19 | 1.5479 | 1.53514639028550 | 0.0127536097145021 |
| 20 | 1.558 | 1.52407586449096 | 0.0339241355090443 |
| 21 | 1.579 | 1.56188810950191 | 0.0171118904980901 |
| 22 | 1.5554 | 1.52897309550366 | 0.0264269044963377 |
| 23 | 1.5761 | 1.5617443047753 | 0.0143556952247007 |
| 24 | 1.536 | 1.51706687405198 | 0.0189331259480208 |
| 25 | 1.5621 | 1.53822842525731 | 0.0238715747426889 |
| 26 | 1.5773 | 1.56015376975648 | 0.0171462302435212 |
| 27 | 1.571 | 1.55213841713728 | 0.0188615828627195 |
| 28 | 1.5925 | 1.56214858625261 | 0.0303514137473912 |
| 29 | 1.5844 | 1.55291116436327 | 0.0314888356367271 |
| 30 | 1.5696 | 1.52855063525599 | 0.041049364744013 |
| 31 | 1.554 | 1.50632872737144 | 0.0476712726285585 |
| 32 | 1.5012 | 1.45859612347278 | 0.0426038765272222 |
| 33 | 1.4676 | 1.43347180107166 | 0.0341281989283441 |
| 34 | 1.477 | 1.42942817358040 | 0.047571826419596 |
| 35 | 1.466 | 1.42385695950148 | 0.0421430404985193 |
| 36 | 1.4241 | 1.40010746502926 | 0.0239925349707368 |
| 37 | 1.4214 | 1.37559417726321 | 0.0458058227367899 |
| 38 | 1.4469 | 1.42012780325992 | 0.0267721967400806 |
| 39 | 1.4618 | 1.43976176787758 | 0.0220382321224202 |
| 40 | 1.3834 | 1.38072502323015 | 0.00267497676985486 |
| 41 | 1.3412 | 1.36705760023656 | -0.0258576002365614 |
| 42 | 1.3437 | 1.36713845653202 | -0.0234384565320235 |
| 43 | 1.263 | 1.31665619677555 | -0.0536561967755506 |
| 44 | 1.2759 | 1.33231843626526 | -0.056418436265264 |
| 45 | 1.2743 | 1.29573721445660 | -0.0214372144566043 |
| 46 | 1.2797 | 1.28329186073316 | -0.00359186073315770 |
| 47 | 1.2573 | 1.22669925462600 | 0.0306007453740021 |
| 48 | 1.2705 | 1.2391535622816 | 0.0313464377183991 |
| 49 | 1.268 | 1.22273648343021 | 0.0452635165697921 |
| 50 | 1.3371 | 1.29232252946473 | 0.0447774705352658 |
| 51 | 1.3885 | 1.39658479103941 | -0.00808479103940915 |
| 52 | 1.406 | 1.45731083486544 | -0.0513108348654394 |
| 53 | 1.3855 | 1.43050616721788 | -0.0450061672178783 |
| 54 | 1.3431 | 1.38139873539031 | -0.0382987353903103 |
| 55 | 1.3257 | 1.37567476265262 | -0.0499747626526192 |
| 56 | 1.2978 | 1.31556870739381 | -0.0177687073938144 |
| 57 | 1.2793 | 1.30602576818694 | -0.0267257681869442 |
| 58 | 1.2945 | 1.30457903789473 | -0.0100790378947345 |
| 59 | 1.289 | 1.31092299919965 | -0.0219229991996508 |
| 60 | 1.2848 | 1.31665592586950 | -0.0318559258694980 |
| 61 | 1.2694 | 1.29244815542098 | -0.0230481554209789 |
| 62 | 1.2636 | 1.30459694575905 | -0.0409969457590478 |
| 63 | 1.29 | 1.25900296308312 | 0.0309970369168756 |
| 64 | 1.3559 | 1.34829487609862 | 0.00760512390138371 |
| 65 | 1.3305 | 1.32760055480174 | 0.00289944519825767 |
| 66 | 1.3482 | 1.34280451831515 | 0.00539548168484533 |
| 67 | 1.3146 | 1.30133501942595 | 0.0132649805740548 |
| 68 | 1.3027 | 1.28629276850346 | 0.0164072314965433 |
| 69 | 1.3247 | 1.32807673864236 | -0.00337673864235721 |
| 70 | 1.3267 | 1.33212932006577 | -0.00542932006576573 |
| 71 | 1.3621 | 1.37559363545110 | -0.0134936354511049 |
| 72 | 1.3479 | 1.34894172646231 | -0.00104172646231135 |
| 73 | 1.4011 | 1.40691811443053 | -0.00581811443053234 |
| 74 | 1.4135 | 1.43159311478751 | -0.0180931147875092 |
| 75 | 1.3964 | 1.40188603262337 | -0.00548603262337207 |
| 76 | 1.401 | 1.41159068442117 | -0.0105906844211662 |
| 77 | 1.3955 | 1.40938016083512 | -0.0138801608351203 |
| 78 | 1.4077 | 1.40548929200264 | 0.00221070799736438 |
| 79 | 1.3975 | 1.39640462877207 | 0.00109537122793278 |
| 80 | 1.3949 | 1.39923514092534 | -0.00433514092533808 |
| 81 | 1.4138 | 1.41275875919231 | 0.00104124080768851 |
| 82 | 1.421 | 1.41711685793325 | 0.00388314206674577 |
| 83 | 1.4253 | 1.41948909411022 | 0.00581090588977628 |
| 84 | 1.4169 | 1.39696166890814 | 0.0199383310918563 |
| 85 | 1.4174 | 1.40834666595238 | 0.00905333404762343 |
| 86 | 1.4346 | 1.43439649423826 | 0.000203505761741944 |
| 87 | 1.4296 | 1.42836700418303 | 0.00123299581696705 |
| 88 | 1.4311 | 1.42829510181973 | 0.00280489818027217 |
| 89 | 1.4594 | 1.46121906975013 | -0.00181906975013220 |
| 90 | 1.4722 | 1.47260406679436 | -0.000404066794365051 |
| 91 | 1.4669 | 1.47039354320832 | -0.00349354320831896 |
| 92 | 1.4571 | 1.46054508668391 | -0.00344508668391482 |
| 93 | 1.4709 | 1.46368111615472 | 0.00721888384527997 |
| 94 | 1.4893 | 1.48362059808991 | 0.00567940191008534 |
| 95 | 1.4997 | 1.49653318172182 | 0.00316681827818095 |
| 96 | 1.4713 | 1.47033954870933 | 0.00096045129067302 |
| 97 | 1.4846 | 1.48264109770616 | 0.00195890229383685 |
| 98 | 1.4914 | 1.48959609364615 | 0.00180390635385247 |
| 99 | 1.4859 | 1.47959487846298 | 0.00630512153702406 |
| 100 | 1.4957 | 1.49540987661146 | 0.00029012338854309 |
| 101 | 1.4843 | 1.47838176312500 | 0.00591823687500459 |
| 102 | 1.4619 | 1.45096606084237 | 0.0109339391576343 |
| 103 | 1.434 | 1.43714587919001 | -0.00314587919001482 |
| 104 | 1.4426 | 1.44623949635274 | -0.00363949635273973 |
| 105 | 1.4318 | 1.44632035264820 | -0.0145203526482020 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 6 | 0.564749258971833 | 0.870501482056334 | 0.435250741028167 |
| 7 | 0.401639903883082 | 0.803279807766165 | 0.598360096116918 |
| 8 | 0.37255779620874 | 0.74511559241748 | 0.62744220379126 |
| 9 | 0.676350301333858 | 0.647299397332283 | 0.323649698666142 |
| 10 | 0.642708826642338 | 0.714582346715323 | 0.357291173357662 |
| 11 | 0.642524590161945 | 0.714950819676111 | 0.357475409838055 |
| 12 | 0.614792758398428 | 0.770414483203145 | 0.385207241601572 |
| 13 | 0.582579137855629 | 0.834841724288743 | 0.417420862144371 |
| 14 | 0.519647679671268 | 0.960704640657465 | 0.480352320328732 |
| 15 | 0.470820540406278 | 0.941641080812555 | 0.529179459593722 |
| 16 | 0.395918859985251 | 0.791837719970501 | 0.604081140014749 |
| 17 | 0.380647618553827 | 0.761295237107654 | 0.619352381446173 |
| 18 | 0.390282338880439 | 0.780564677760879 | 0.60971766111956 |
| 19 | 0.387874984874965 | 0.77574996974993 | 0.612125015125035 |
| 20 | 0.326496293936426 | 0.652992587872851 | 0.673503706063574 |
| 21 | 0.268158667494986 | 0.536317334989972 | 0.731841332505014 |
| 22 | 0.243098925443696 | 0.486197850887392 | 0.756901074556304 |
| 23 | 0.209925993063705 | 0.41985198612741 | 0.790074006936295 |
| 24 | 0.249550716848658 | 0.499101433697317 | 0.750449283151342 |
| 25 | 0.216694479086696 | 0.433388958173393 | 0.783305520913304 |
| 26 | 0.183679339187673 | 0.367358678375346 | 0.816320660812327 |
| 27 | 0.160649944898048 | 0.321299889796097 | 0.839350055101952 |
| 28 | 0.122986177219916 | 0.245972354439831 | 0.877013822780084 |
| 29 | 0.0958384522965923 | 0.191676904593185 | 0.904161547703408 |
| 30 | 0.0802202885905023 | 0.160440577181005 | 0.919779711409498 |
| 31 | 0.0780651148735719 | 0.156130229747144 | 0.921934885126428 |
| 32 | 0.128909884767053 | 0.257819769534106 | 0.871090115232947 |
| 33 | 0.232106378523230 | 0.464212757046461 | 0.76789362147677 |
| 34 | 0.303501747689026 | 0.607003495378051 | 0.696498252310974 |
| 35 | 0.410954763616824 | 0.821909527233648 | 0.589045236383176 |
| 36 | 0.581369493380769 | 0.837261013238463 | 0.418630506619231 |
| 37 | 0.732904501209634 | 0.534190997580733 | 0.267095498790366 |
| 38 | 0.865082678951326 | 0.269834642097348 | 0.134917321048674 |
| 39 | 0.967176008240186 | 0.0656479835196271 | 0.0328239917598135 |
| 40 | 0.994120478042045 | 0.0117590439159095 | 0.00587952195795477 |
| 41 | 0.999313038340332 | 0.00137392331933531 | 0.000686961659667655 |
| 42 | 0.999827323783195 | 0.000345352433609302 | 0.000172676216804651 |
| 43 | 0.999991631718944 | 1.67365621114710e-05 | 8.36828105573552e-06 |
| 44 | 0.999999393639233 | 1.21272153381855e-06 | 6.06360766909273e-07 |
| 45 | 0.99999919891755 | 1.60216490196375e-06 | 8.01082450981874e-07 |
| 46 | 0.999998428819074 | 3.14236185245212e-06 | 1.57118092622606e-06 |
| 47 | 0.999998709573888 | 2.58085222400450e-06 | 1.29042611200225e-06 |
| 48 | 0.999999165945261 | 1.66810947793880e-06 | 8.34054738969401e-07 |
| 49 | 0.999999891454966 | 2.17090067775693e-07 | 1.08545033887846e-07 |
| 50 | 0.999999999680346 | 6.39307924060609e-10 | 3.19653962030305e-10 |
| 51 | 0.999999999928045 | 1.43910698201954e-10 | 7.19553491009772e-11 |
| 52 | 0.999999999980349 | 3.93022442263613e-11 | 1.96511221131806e-11 |
| 53 | 0.999999999986453 | 2.70944793630686e-11 | 1.35472396815343e-11 |
| 54 | 0.999999999986687 | 2.66264255233636e-11 | 1.33132127616818e-11 |
| 55 | 0.999999999998165 | 3.6699022156932e-12 | 1.8349511078466e-12 |
| 56 | 0.999999999995775 | 8.45003601120456e-12 | 4.22501800560228e-12 |
| 57 | 0.999999999996095 | 7.81046599029504e-12 | 3.90523299514752e-12 |
| 58 | 0.999999999988983 | 2.20341930849873e-11 | 1.10170965424936e-11 |
| 59 | 0.99999999998572 | 2.85600187890865e-11 | 1.42800093945433e-11 |
| 60 | 0.999999999996681 | 6.63745278938776e-12 | 3.31872639469388e-12 |
| 61 | 0.999999999998712 | 2.57666857797557e-12 | 1.28833428898779e-12 |
| 62 | 1 | 4.02576789407143e-16 | 2.01288394703572e-16 |
| 63 | 1 | 5.55663949613671e-17 | 2.77831974806835e-17 |
| 64 | 1 | 1.38003103621412e-16 | 6.9001551810706e-17 |
| 65 | 1 | 6.03209932550747e-16 | 3.01604966275374e-16 |
| 66 | 1 | 2.01824773121104e-15 | 1.00912386560552e-15 |
| 67 | 0.999999999999998 | 3.40901842958178e-15 | 1.70450921479089e-15 |
| 68 | 1 | 1.58772159011483e-15 | 7.93860795057417e-16 |
| 69 | 0.999999999999996 | 7.37740973175052e-15 | 3.68870486587526e-15 |
| 70 | 0.999999999999984 | 3.2311781528179e-14 | 1.61558907640895e-14 |
| 71 | 0.99999999999997 | 5.92805433815337e-14 | 2.96402716907669e-14 |
| 72 | 0.999999999999867 | 2.66395263036691e-13 | 1.33197631518346e-13 |
| 73 | 0.99999999999945 | 1.09925779342188e-12 | 5.49628896710942e-13 |
| 74 | 0.999999999999747 | 5.06846428839487e-13 | 2.53423214419743e-13 |
| 75 | 0.99999999999912 | 1.75827086867666e-12 | 8.79135434338331e-13 |
| 76 | 0.999999999998928 | 2.14477784392273e-12 | 1.07238892196136e-12 |
| 77 | 0.99999999999979 | 4.19042496351513e-13 | 2.09521248175756e-13 |
| 78 | 0.999999999998988 | 2.02413004628655e-12 | 1.01206502314327e-12 |
| 79 | 0.999999999995584 | 8.8320450035694e-12 | 4.4160225017847e-12 |
| 80 | 0.999999999993118 | 1.37635472822496e-11 | 6.88177364112479e-12 |
| 81 | 0.99999999997605 | 4.7898486903637e-11 | 2.39492434518185e-11 |
| 82 | 0.9999999998935 | 2.13000383466694e-10 | 1.06500191733347e-10 |
| 83 | 0.999999999491664 | 1.01667109309592e-09 | 5.0833554654796e-10 |
| 84 | 0.999999999880096 | 2.39807920647698e-10 | 1.19903960323849e-10 |
| 85 | 0.999999999799275 | 4.01450324457317e-10 | 2.00725162228659e-10 |
| 86 | 0.999999998855519 | 2.28896272362232e-09 | 1.14448136181116e-09 |
| 87 | 0.999999994017 | 1.19659981687334e-08 | 5.98299908436672e-09 |
| 88 | 0.99999997921597 | 4.15680591897576e-08 | 2.07840295948788e-08 |
| 89 | 0.999999894942475 | 2.10115049466120e-07 | 1.05057524733060e-07 |
| 90 | 0.999999503388402 | 9.93223195108437e-07 | 4.96611597554219e-07 |
| 91 | 0.999998550365631 | 2.89926873766898e-06 | 1.44963436883449e-06 |
| 92 | 0.99999707774388 | 5.84451223979454e-06 | 2.92225611989727e-06 |
| 93 | 0.999985203973668 | 2.95920526643151e-05 | 1.47960263321575e-05 |
| 94 | 0.999928330577961 | 0.000143338844077359 | 7.16694220386793e-05 |
| 95 | 0.999700913861095 | 0.00059817227780943 | 0.000299086138904715 |
| 96 | 0.999104216057235 | 0.00179156788553018 | 0.000895783942765092 |
| 97 | 0.997897685808405 | 0.00420462838318919 | 0.00210231419159459 |
| 98 | 0.995710883671363 | 0.00857823265727366 | 0.00428911632863683 |
| 99 | 0.9873147163652 | 0.0253705672695987 | 0.0126852836347993 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 58 | 0.617021276595745 | NOK |
| 5% type I error level | 60 | 0.638297872340426 | NOK |
| 10% type I error level | 61 | 0.648936170212766 | NOK |
