| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 5.97918507128879 -1.18678734507501X[t] + 0.0967005152517632M1[t] + 0.264549164414625M2[t] + 0.206996231711863M3[t] + 0.246094880874725M4[t] + 0.160193530037586M5[t] + 0.218265247879974M6[t] -0.273350388671451M7[t] -0.202108882365732M8[t] -0.125153090345727M9[t] -0.00676872689715154M10[t] -0.039812934877147M11[t] + 0.0259013508371385t + 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) | 5.97918507128879 | 0.100936 | 59.2374 | 0 | 0 |
| X | -1.18678734507501 | 0.09706 | -12.2273 | 0 | 0 |
| M1 | 0.0967005152517632 | 0.11965 | 0.8082 | 0.421533 | 0.210766 |
| M2 | 0.264549164414625 | 0.119611 | 2.2117 | 0.03003 | 0.015015 |
| M3 | 0.206996231711863 | 0.120002 | 1.7249 | 0.088657 | 0.044328 |
| M4 | 0.246094880874725 | 0.11986 | 2.0532 | 0.043541 | 0.021771 |
| M5 | 0.160193530037586 | 0.119746 | 1.3378 | 0.185013 | 0.092506 |
| M6 | 0.218265247879974 | 0.123977 | 1.7605 | 0.082394 | 0.041197 |
| M7 | -0.273350388671451 | 0.123822 | -2.2076 | 0.03033 | 0.015165 |
| M8 | -0.202108882365732 | 0.123695 | -1.6339 | 0.106466 | 0.053233 |
| M9 | -0.125153090345727 | 0.123597 | -1.0126 | 0.314511 | 0.157255 |
| M10 | -0.00676872689715154 | 0.123526 | -0.0548 | 0.956447 | 0.478223 |
| M11 | -0.039812934877147 | 0.123484 | -0.3224 | 0.748036 | 0.374018 |
| t | 0.0259013508371385 | 0.001867 | 13.8755 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.87528582129607 |
| R-squared | 0.766125268961935 |
| Adjusted R-squared | 0.72558698224867 |
| F-TEST (value) | 18.8988073023632 |
| F-TEST (DF numerator) | 13 |
| F-TEST (DF denominator) | 75 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 0.230990987570176 |
| Sum Squared Residuals | 4.00176272539838 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 5.81 | 6.10178693737768 | -0.291786937377685 |
| 2 | 5.76 | 6.2955369373777 | -0.535536937377696 |
| 3 | 5.99 | 6.26388535551207 | -0.273885355512067 |
| 4 | 6.12 | 6.32888535551207 | -0.208885355512069 |
| 5 | 6.03 | 6.26888535551207 | -0.238885355512068 |
| 6 | 6.25 | 6.3528584241916 | -0.102858424191595 |
| 7 | 5.8 | 5.88714413847731 | -0.0871441384773088 |
| 8 | 5.67 | 5.98428699562017 | -0.314286995620166 |
| 9 | 5.89 | 6.0871441384773 | -0.197144138477309 |
| 10 | 5.91 | 6.23142985276302 | -0.321429852763023 |
| 11 | 5.86 | 6.22428699562017 | -0.364286995620166 |
| 12 | 6.07 | 6.29000128133445 | -0.220001281334451 |
| 13 | 6.27 | 6.41260314742335 | -0.142603147423354 |
| 14 | 6.68 | 6.60635314742335 | 0.0736468525766483 |
| 15 | 6.77 | 6.57470156555773 | 0.195298434442270 |
| 16 | 6.71 | 6.63970156555773 | 0.0702984344422701 |
| 17 | 6.62 | 6.57970156555773 | 0.0402984344422701 |
| 18 | 6.5 | 6.66367463423726 | -0.163674634237257 |
| 19 | 5.89 | 6.19796034852297 | -0.307960348522971 |
| 20 | 6.05 | 6.29510320566583 | -0.245103205665828 |
| 21 | 6.43 | 6.39796034852297 | 0.0320396514770291 |
| 22 | 6.47 | 6.54224606280868 | -0.0722460628086852 |
| 23 | 6.62 | 6.53510320566583 | 0.0848967943341721 |
| 24 | 6.77 | 6.60081749138011 | 0.169182508619886 |
| 25 | 6.7 | 6.72341935746902 | -0.0234193574690154 |
| 26 | 6.95 | 6.91716935746901 | 0.0328306425309854 |
| 27 | 6.73 | 6.88551777560339 | -0.155517775603392 |
| 28 | 7.07 | 6.95051777560339 | 0.119482224396608 |
| 29 | 7.28 | 6.89051777560339 | 0.389482224396608 |
| 30 | 7.32 | 6.97449084428292 | 0.345509155717082 |
| 31 | 6.76 | 6.50877655856863 | 0.251223441431367 |
| 32 | 6.93 | 6.60591941571149 | 0.32408058428851 |
| 33 | 6.99 | 6.70877655856863 | 0.281223441431368 |
| 34 | 7.16 | 6.85306227285435 | 0.306937727145653 |
| 35 | 7.28 | 6.84591941571149 | 0.43408058428851 |
| 36 | 7.08 | 6.91163370142578 | 0.168366298574225 |
| 37 | 7.34 | 7.03423556751468 | 0.305764432485322 |
| 38 | 7.87 | 7.22798556751468 | 0.642014432485324 |
| 39 | 6.28 | 6.00954664057404 | 0.270453359425962 |
| 40 | 6.3 | 6.07454664057404 | 0.225453359425962 |
| 41 | 6.36 | 6.01454664057404 | 0.345453359425962 |
| 42 | 6.28 | 6.09851970925356 | 0.181480290746436 |
| 43 | 5.89 | 5.63280542353928 | 0.257194576460721 |
| 44 | 6.04 | 5.72994828068214 | 0.310051719317864 |
| 45 | 5.96 | 5.83280542353928 | 0.127194576460721 |
| 46 | 6.1 | 5.97709113782499 | 0.122908862175006 |
| 47 | 6.26 | 5.96994828068214 | 0.290051719317864 |
| 48 | 6.02 | 6.03566256639642 | -0.0156625663964219 |
| 49 | 6.25 | 6.15826443248532 | 0.0917355675146763 |
| 50 | 6.41 | 6.35201443248532 | 0.0579855675146774 |
| 51 | 6.22 | 6.3203628506197 | -0.100362850619701 |
| 52 | 6.57 | 6.3853628506197 | 0.184637149380300 |
| 53 | 6.18 | 6.3253628506197 | -0.145362850619700 |
| 54 | 6.26 | 6.40933591929923 | -0.149335919299227 |
| 55 | 6.1 | 5.94362163358494 | 0.156378366415059 |
| 56 | 6.02 | 6.0407644907278 | -0.0207644907277982 |
| 57 | 6.06 | 6.14362163358494 | -0.0836216335849412 |
| 58 | 6.35 | 6.28790734787065 | 0.0620926521293446 |
| 59 | 6.21 | 6.2807644907278 | -0.0707644907277982 |
| 60 | 6.48 | 6.34647877644208 | 0.133521223557917 |
| 61 | 6.74 | 6.46908064253099 | 0.270919357469015 |
| 62 | 6.53 | 6.66283064253098 | -0.132830642530985 |
| 63 | 6.8 | 6.63117906066536 | 0.168820939334638 |
| 64 | 6.75 | 6.69617906066536 | 0.0538209393346381 |
| 65 | 6.56 | 6.63617906066536 | -0.0761790606653625 |
| 66 | 6.66 | 6.72015212934489 | -0.0601521293448885 |
| 67 | 6.18 | 6.2544378436306 | -0.0744378436306029 |
| 68 | 6.4 | 6.35158070077346 | 0.0484192992265406 |
| 69 | 6.43 | 6.4544378436306 | -0.024437843630603 |
| 70 | 6.54 | 6.59872355791632 | -0.058723557916317 |
| 71 | 6.44 | 6.59158070077346 | -0.151580700773460 |
| 72 | 6.64 | 6.65729498648775 | -0.0172949864877457 |
| 73 | 6.82 | 6.77989685257665 | 0.0401031474233526 |
| 74 | 6.97 | 6.97364685257665 | -0.00364685257664711 |
| 75 | 7 | 6.94199527071102 | 0.0580047292889757 |
| 76 | 6.91 | 7.00699527071102 | -0.0969952707110238 |
| 77 | 6.74 | 6.94699527071102 | -0.206995270711024 |
| 78 | 6.98 | 7.03096833939055 | -0.0509683393905502 |
| 79 | 6.37 | 6.56525405367626 | -0.195254053676265 |
| 80 | 6.56 | 6.66239691081912 | -0.102396910819122 |
| 81 | 6.63 | 6.76525405367626 | -0.135254053676265 |
| 82 | 6.87 | 6.90953976796198 | -0.0395397679619792 |
| 83 | 6.68 | 6.90239691081912 | -0.222396910819123 |
| 84 | 6.75 | 6.96811119653341 | -0.218111196533408 |
| 85 | 6.84 | 7.09071306262231 | -0.25071306262231 |
| 86 | 7.15 | 7.28446306262231 | -0.134463062622308 |
| 87 | 7.09 | 7.25281148075669 | -0.162811480756686 |
| 88 | 6.97 | 7.31781148075669 | -0.347811480756686 |
| 89 | 7.15 | 7.25781148075669 | -0.107811480756686 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 17 | 0.385637449645481 | 0.771274899290962 | 0.614362550354519 |
| 18 | 0.583079031760847 | 0.833841936478307 | 0.416920968239153 |
| 19 | 0.833399403558263 | 0.333201192883473 | 0.166600596441736 |
| 20 | 0.8462849044067 | 0.307430191186599 | 0.153715095593300 |
| 21 | 0.785267971505576 | 0.429464056988848 | 0.214732028494424 |
| 22 | 0.76058443423127 | 0.47883113153746 | 0.23941556576873 |
| 23 | 0.76335674619542 | 0.473286507609159 | 0.236643253804580 |
| 24 | 0.715337428591277 | 0.569325142817446 | 0.284662571408723 |
| 25 | 0.75106556205209 | 0.497868875895819 | 0.248934437947910 |
| 26 | 0.754989963745908 | 0.490020072508184 | 0.245010036254092 |
| 27 | 0.969377040728405 | 0.0612459185431905 | 0.0306229592715952 |
| 28 | 0.970547350651175 | 0.058905298697649 | 0.0294526493488245 |
| 29 | 0.970583869588648 | 0.0588322608227033 | 0.0294161304113517 |
| 30 | 0.966302598196265 | 0.0673948036074694 | 0.0336974018037347 |
| 31 | 0.960996816020258 | 0.0780063679594832 | 0.0390031839797416 |
| 32 | 0.969070238553024 | 0.0618595228939527 | 0.0309297614469764 |
| 33 | 0.954638558723287 | 0.0907228825534261 | 0.0453614412767131 |
| 34 | 0.94783617414587 | 0.104327651708259 | 0.0521638258541297 |
| 35 | 0.945178317999338 | 0.109643364001325 | 0.0548216820006623 |
| 36 | 0.953418747731906 | 0.0931625045361884 | 0.0465812522680942 |
| 37 | 0.967716175171105 | 0.0645676496577908 | 0.0322838248288954 |
| 38 | 0.974126393324358 | 0.0517472133512831 | 0.0258736066756415 |
| 39 | 0.961152880028214 | 0.0776942399435727 | 0.0388471199717864 |
| 40 | 0.945612630260004 | 0.108774739479993 | 0.0543873697399964 |
| 41 | 0.953425806830863 | 0.0931483863382737 | 0.0465741931691368 |
| 42 | 0.941558088695997 | 0.116883822608006 | 0.0584419113040031 |
| 43 | 0.927203333080677 | 0.145593333838646 | 0.072796666919323 |
| 44 | 0.924921609504019 | 0.150156780991962 | 0.0750783904959808 |
| 45 | 0.912766481094107 | 0.174467037811787 | 0.0872335189058935 |
| 46 | 0.885240864919014 | 0.229518270161972 | 0.114759135080986 |
| 47 | 0.924108146871936 | 0.151783706256128 | 0.075891853128064 |
| 48 | 0.937275044007091 | 0.125449911985817 | 0.0627249559929086 |
| 49 | 0.93007359908734 | 0.139852801825319 | 0.0699264009126596 |
| 50 | 0.932509288981083 | 0.134981422037834 | 0.0674907110189170 |
| 51 | 0.98657196767186 | 0.0268560646562792 | 0.0134280323281396 |
| 52 | 0.986368278791666 | 0.0272634424166684 | 0.0136317212083342 |
| 53 | 0.997096261597598 | 0.00580747680480373 | 0.00290373840240187 |
| 54 | 0.99932202199446 | 0.00135595601108217 | 0.000677978005541086 |
| 55 | 0.999140906404668 | 0.00171818719066318 | 0.00085909359533159 |
| 56 | 0.99918808288195 | 0.00162383423609846 | 0.000811917118049232 |
| 57 | 0.999462107769959 | 0.00107578446008221 | 0.000537892230041104 |
| 58 | 0.999011731254067 | 0.00197653749186556 | 0.00098826874593278 |
| 59 | 0.99868969845242 | 0.00262060309516149 | 0.00131030154758075 |
| 60 | 0.997519350492559 | 0.00496129901488252 | 0.00248064950744126 |
| 61 | 0.998287169106806 | 0.00342566178638724 | 0.00171283089319362 |
| 62 | 0.999567056963 | 0.000865886074000416 | 0.000432943037000208 |
| 63 | 0.998969624488628 | 0.00206075102274397 | 0.00103037551137199 |
| 64 | 0.99857561136644 | 0.0028487772671201 | 0.00142438863356005 |
| 65 | 0.997895598670163 | 0.00420880265967331 | 0.00210440132983665 |
| 66 | 0.997092182919878 | 0.00581563416024404 | 0.00290781708012202 |
| 67 | 0.99341099218761 | 0.0131780156247784 | 0.00658900781238919 |
| 68 | 0.984007004747502 | 0.0319859905049966 | 0.0159929952524983 |
| 69 | 0.964202014869226 | 0.0715959702615476 | 0.0357979851307738 |
| 70 | 0.95092934967838 | 0.0981413006432389 | 0.0490706503216194 |
| 71 | 0.9080886523838 | 0.183822695232400 | 0.0919113476162002 |
| 72 | 0.803786511821017 | 0.392426976357965 | 0.196213488178983 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 14 | 0.25 | NOK |
| 5% type I error level | 18 | 0.321428571428571 | NOK |
| 10% type I error level | 32 | 0.571428571428571 | NOK |
