| Multiple Linear Regression - Estimated Regression Equation |
| dollar/euro[t] = -0.490341429831448 + 0.0069849570837074`Japanseyen/euro`[t] + 0.928187504675763`pond/euro`[t] + 0.00347990209464552`roebel/euro`[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) | -0.490341429831448 | 0.123628 | -3.9663 | 0.00021 | 0.000105 |
| `Japanseyen/euro` | 0.0069849570837074 | 0.000505 | 13.8237 | 0 | 0 |
| `pond/euro` | 0.928187504675763 | 0.147549 | 6.2907 | 0 | 0 |
| `roebel/euro` | 0.00347990209464552 | 0.003528 | 0.9863 | 0.328233 | 0.164116 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.906051036391935 |
| R-squared | 0.8209284805469 |
| Adjusted R-squared | 0.811335363433341 |
| F-TEST (value) | 85.574737682145 |
| F-TEST (DF numerator) | 3 |
| F-TEST (DF denominator) | 56 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 0.0461281743809974 |
| Sum Squared Residuals | 0.119157274416528 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 1.4816 | 1.44662396038971 | 0.0349760396102876 |
| 2 | 1.4562 | 1.42274445810746 | 0.0334555418925436 |
| 3 | 1.4268 | 1.41277589502566 | 0.0140241049743409 |
| 4 | 1.4088 | 1.39284793713196 | 0.0159520628680381 |
| 5 | 1.4016 | 1.40209797670013 | -0.000497976700126948 |
| 6 | 1.365 | 1.4031629967699 | -0.0381629967699009 |
| 7 | 1.319 | 1.40641185827983 | -0.0874118582798278 |
| 8 | 1.305 | 1.41200544251669 | -0.107005442516685 |
| 9 | 1.2785 | 1.31860478010443 | -0.0401047801044301 |
| 10 | 1.3239 | 1.34551795856165 | -0.0216179585616515 |
| 11 | 1.3449 | 1.33680063811953 | 0.00809936188046522 |
| 12 | 1.2732 | 1.26283253170295 | 0.0103674682970481 |
| 13 | 1.3322 | 1.29501925048518 | 0.037180749514822 |
| 14 | 1.4369 | 1.44817201154749 | -0.0112720115474950 |
| 15 | 1.4975 | 1.51461201651881 | -0.0171120165188105 |
| 16 | 1.577 | 1.55055275965494 | 0.0264472403450574 |
| 17 | 1.5553 | 1.53362051240164 | 0.0216794875983627 |
| 18 | 1.5557 | 1.50701799788494 | 0.0486820021150581 |
| 19 | 1.575 | 1.50486492311930 | 0.0701350768806974 |
| 20 | 1.5527 | 1.45087315132694 | 0.101826848673064 |
| 21 | 1.4748 | 1.43583406356451 | 0.0389659364354909 |
| 22 | 1.4718 | 1.43700054555028 | 0.0347994544497162 |
| 23 | 1.457 | 1.44549243628146 | 0.0115075637185426 |
| 24 | 1.4684 | 1.4304750783428 | 0.0379249216572 |
| 25 | 1.4227 | 1.4311670087032 | -0.00846700870319987 |
| 26 | 1.3896 | 1.38779109807616 | 0.00180890192383823 |
| 27 | 1.3622 | 1.37113354778812 | -0.00893354778811688 |
| 28 | 1.3716 | 1.42233785305469 | -0.0507378530546891 |
| 29 | 1.3419 | 1.40714506765064 | -0.0652450676506372 |
| 30 | 1.3511 | 1.40362133867007 | -0.0525213386700705 |
| 31 | 1.3516 | 1.38402374837953 | -0.0324237483795294 |
| 32 | 1.3242 | 1.34565898600650 | -0.0214589860064955 |
| 33 | 1.3074 | 1.35024657115262 | -0.0428465711526214 |
| 34 | 1.2999 | 1.33890209406761 | -0.0390020940676065 |
| 35 | 1.3213 | 1.33647243785466 | -0.0151724378546556 |
| 36 | 1.2881 | 1.30994810935688 | -0.0218481093568753 |
| 37 | 1.2611 | 1.29711675662686 | -0.0360167566268556 |
| 38 | 1.2727 | 1.29548371019472 | -0.0227837101947153 |
| 39 | 1.2811 | 1.29450483259568 | -0.0134048325956764 |
| 40 | 1.2684 | 1.29157912539424 | -0.0231791253942422 |
| 41 | 1.265 | 1.27946385622636 | -0.0144638562263600 |
| 42 | 1.277 | 1.26083341444467 | 0.0161665855553298 |
| 43 | 1.2271 | 1.27499161111732 | -0.0478916111173178 |
| 44 | 1.202 | 1.25067150147115 | -0.0486715014711534 |
| 45 | 1.1938 | 1.24405899743853 | -0.0502589974385282 |
| 46 | 1.2103 | 1.24240295556499 | -0.0321029555649924 |
| 47 | 1.1856 | 1.24089923408211 | -0.0552992340821139 |
| 48 | 1.1786 | 1.23326705824168 | -0.0546670582416781 |
| 49 | 1.2015 | 1.22582283091650 | -0.0243228309165039 |
| 50 | 1.2256 | 1.20998527948738 | 0.0156147205126247 |
| 51 | 1.2292 | 1.21737006988776 | 0.0118299301122367 |
| 52 | 1.2037 | 1.20930127915572 | -0.00560127915571699 |
| 53 | 1.2165 | 1.17485617819313 | 0.0416438218068685 |
| 54 | 1.2694 | 1.21352574891656 | 0.0558742510834422 |
| 55 | 1.2938 | 1.23854189366279 | 0.0552581063372052 |
| 56 | 1.3201 | 1.24893521773219 | 0.0711647822678146 |
| 57 | 1.3014 | 1.23024393529982 | 0.0711560647001775 |
| 58 | 1.3119 | 1.23313446509509 | 0.0787655349049095 |
| 59 | 1.3408 | 1.25684052729893 | 0.08395947270107 |
| 60 | 1.2991 | 1.23786048010697 | 0.061239519893027 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 7 | 0.372537788880416 | 0.745075577760832 | 0.627462211119584 |
| 8 | 0.294496345832938 | 0.588992691665875 | 0.705503654167062 |
| 9 | 0.906101323543443 | 0.187797352913113 | 0.0938986764565567 |
| 10 | 0.998336892110027 | 0.00332621577994571 | 0.00166310788997285 |
| 11 | 0.999867228725017 | 0.000265542549965279 | 0.000132771274982639 |
| 12 | 0.999836929572446 | 0.000326140855108308 | 0.000163070427554154 |
| 13 | 0.999703793130679 | 0.00059241373864285 | 0.000296206869321425 |
| 14 | 0.999976553583157 | 4.68928336859157e-05 | 2.34464168429578e-05 |
| 15 | 0.99999099429621 | 1.80114075820852e-05 | 9.00570379104259e-06 |
| 16 | 0.999986350252534 | 2.72994949328160e-05 | 1.36497474664080e-05 |
| 17 | 0.999985820062801 | 2.83598743971819e-05 | 1.41799371985909e-05 |
| 18 | 0.999985713866819 | 2.85722663624448e-05 | 1.42861331812224e-05 |
| 19 | 0.999989001048615 | 2.19979027702950e-05 | 1.09989513851475e-05 |
| 20 | 0.999997227847556 | 5.54430488890952e-06 | 2.77215244445476e-06 |
| 21 | 0.999993545959475 | 1.29080810499248e-05 | 6.45404052496242e-06 |
| 22 | 0.999986337105197 | 2.73257896066549e-05 | 1.36628948033274e-05 |
| 23 | 0.999983385013616 | 3.32299727687359e-05 | 1.66149863843680e-05 |
| 24 | 0.999990588440074 | 1.88231198509696e-05 | 9.41155992548479e-06 |
| 25 | 0.999993737410045 | 1.25251799103851e-05 | 6.26258995519253e-06 |
| 26 | 0.999995828967032 | 8.34206593652637e-06 | 4.17103296826318e-06 |
| 27 | 0.999995482133329 | 9.03573334233633e-06 | 4.51786667116816e-06 |
| 28 | 0.999997153038782 | 5.69392243629754e-06 | 2.84696121814877e-06 |
| 29 | 0.999998914282173 | 2.17143565346138e-06 | 1.08571782673069e-06 |
| 30 | 0.999998910235376 | 2.17952924869400e-06 | 1.08976462434700e-06 |
| 31 | 0.99999744776029 | 5.10447942170033e-06 | 2.55223971085016e-06 |
| 32 | 0.999993518683295 | 1.29626334091588e-05 | 6.48131670457938e-06 |
| 33 | 0.999987982914923 | 2.40341701530138e-05 | 1.20170850765069e-05 |
| 34 | 0.999986490729335 | 2.70185413306563e-05 | 1.35092706653282e-05 |
| 35 | 0.99997123560954 | 5.75287809219423e-05 | 2.87643904609711e-05 |
| 36 | 0.999928604460823 | 0.000142791078354719 | 7.13955391773595e-05 |
| 37 | 0.9998396934742 | 0.000320613051599773 | 0.000160306525799886 |
| 38 | 0.999619058096077 | 0.00076188380784572 | 0.00038094190392286 |
| 39 | 0.999152027122437 | 0.00169594575512567 | 0.000847972877562836 |
| 40 | 0.998388225304869 | 0.00322354939026257 | 0.00161177469513129 |
| 41 | 0.997991555023313 | 0.0040168899533735 | 0.00200844497668675 |
| 42 | 0.999483499866368 | 0.00103300026726339 | 0.000516500133631695 |
| 43 | 0.999468181399912 | 0.00106363720017695 | 0.000531818600088474 |
| 44 | 0.999718264599379 | 0.000563470801241896 | 0.000281735400620948 |
| 45 | 0.999629497495575 | 0.000741005008849226 | 0.000370502504424613 |
| 46 | 0.999164066333486 | 0.00167186733302823 | 0.000835933666514114 |
| 47 | 0.998487853155667 | 0.00302429368866503 | 0.00151214684433251 |
| 48 | 0.997346667677195 | 0.00530666464561073 | 0.00265333232280537 |
| 49 | 0.994982723245615 | 0.0100345535087692 | 0.00501727675438461 |
| 50 | 0.989477086680946 | 0.0210458266381073 | 0.0105229133190536 |
| 51 | 0.978615487972674 | 0.0427690240546521 | 0.0213845120273261 |
| 52 | 0.991600512464463 | 0.0167989750710732 | 0.00839948753553661 |
| 53 | 0.97109332610466 | 0.0578133477906806 | 0.0289066738953403 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 39 | 0.829787234042553 | NOK |
| 5% type I error level | 43 | 0.914893617021277 | NOK |
| 10% type I error level | 44 | 0.936170212765957 | NOK |
