| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 3.11118284867064 -0.716641311359197X[t] + 0.282084452745795Y1[t] + 0.000132132924410053Y2[t] + 0.222648311389754Y3[t] + 0.0644414775319017M1[t] -0.0712678070039426M2[t] + 0.0476062623864397M3[t] -0.472054384726602M4[t] -0.236816742333625M5[t] -0.190827334464285M6[t] + 0.0138621738001510M7[t] -0.0698831927195396M8[t] -0.0393335208239630M9[t] + 0.060031719599684M10[t] + 0.229582895721487M11[t] + 0.0142594687019964t + 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) | 3.11118284867064 | 0.482924 | 6.4424 | 0 | 0 |
| X | -0.716641311359197 | 0.098678 | -7.2625 | 0 | 0 |
| Y1 | 0.282084452745795 | 0.09946 | 2.8362 | 0.005987 | 0.002994 |
| Y2 | 0.000132132924410053 | 0.102667 | 0.0013 | 0.998977 | 0.499488 |
| Y3 | 0.222648311389754 | 0.08637 | 2.5779 | 0.01208 | 0.00604 |
| M1 | 0.0644414775319017 | 0.095342 | 0.6759 | 0.501366 | 0.250683 |
| M2 | -0.0712678070039426 | 0.095838 | -0.7436 | 0.459626 | 0.229813 |
| M3 | 0.0476062623864397 | 0.097312 | 0.4892 | 0.626242 | 0.313121 |
| M4 | -0.472054384726602 | 0.096734 | -4.8799 | 7e-06 | 3e-06 |
| M5 | -0.236816742333625 | 0.117705 | -2.012 | 0.048131 | 0.024066 |
| M6 | -0.190827334464285 | 0.11603 | -1.6446 | 0.104593 | 0.052297 |
| M7 | 0.0138621738001510 | 0.101029 | 0.1372 | 0.891265 | 0.445632 |
| M8 | -0.0698831927195396 | 0.097553 | -0.7164 | 0.476187 | 0.238093 |
| M9 | -0.0393335208239630 | 0.099091 | -0.3969 | 0.692633 | 0.346316 |
| M10 | 0.060031719599684 | 0.098767 | 0.6078 | 0.545306 | 0.272653 |
| M11 | 0.229582895721487 | 0.094592 | 2.4271 | 0.017836 | 0.008918 |
| t | 0.0142594687019964 | 0.002071 | 6.8861 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.93485058218978 |
| R-squared | 0.873945611020572 |
| Adjusted R-squared | 0.844715607778966 |
| F-TEST (value) | 29.8989228224438 |
| F-TEST (DF numerator) | 16 |
| F-TEST (DF denominator) | 69 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 0.169398627601853 |
| Sum Squared Residuals | 1.980016757304 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 6.12 | 6.17391744167092 | -0.0539174416709179 |
| 2 | 6.03 | 6.07803657969715 | -0.0480365796971522 |
| 3 | 6.25 | 6.23700880594223 | 0.0129911940577740 |
| 4 | 5.8 | 5.82259859565273 | -0.0225985956527266 |
| 5 | 5.67 | 5.92514842423038 | -0.255148424230384 |
| 6 | 5.89 | 5.99764949063453 | -0.107649490634529 |
| 7 | 5.91 | 6.17844812979947 | -0.268448129799473 |
| 8 | 5.86 | 6.0856887097994 | -0.225688709799397 |
| 9 | 6.07 | 6.16537889892391 | -0.0953788989239145 |
| 10 | 6.27 | 6.34268770270775 | -0.0726877027077505 |
| 11 | 6.68 | 6.57181057042535 | 0.108189429574653 |
| 12 | 6.77 | 6.51892434100836 | 0.251075658991638 |
| 13 | 6.71 | 6.66759672476634 | 0.0424032752336597 |
| 14 | 6.62 | 6.62051954140074 | -0.000519541400740842 |
| 15 | 6.5 | 6.74829589879561 | -0.248295898795611 |
| 16 | 5.89 | 6.19567379540849 | -0.305673795408489 |
| 17 | 6.05 | 6.25304518635252 | -0.203045186352521 |
| 18 | 6.43 | 6.33162917691252 | 0.0983708230874767 |
| 19 | 6.47 | 6.52197591724251 | -0.0519759172425134 |
| 20 | 6.62 | 6.49944733786829 | 0.120552662131713 |
| 21 | 6.77 | 6.67118079002281 | 0.098819209977187 |
| 22 | 6.7 | 6.83604391945458 | -0.136043919454576 |
| 23 | 6.95 | 7.0335257192333 | -0.083525719233295 |
| 24 | 6.73 | 6.92211140280401 | -0.192111402804007 |
| 25 | 7.07 | 6.92320142086765 | 0.146798579132349 |
| 26 | 7.28 | 6.95329332757144 | 0.326706672428559 |
| 27 | 7.32 | 7.09672689742899 | 0.223273102571010 |
| 28 | 6.76 | 6.67833727091442 | 0.0816627290855802 |
| 29 | 6.93 | 6.81662851918057 | 0.113371480819427 |
| 30 | 6.99 | 6.93366369073661 | 0.056336309263386 |
| 31 | 7.16 | 7.04487714308668 | 0.115122856913318 |
| 32 | 7.28 | 7.0612037431475 | 0.218796256852505 |
| 33 | 7.08 | 7.1532443793551 | -0.0732443793550991 |
| 34 | 7.34 | 7.24831826681877 | 0.0916817331812289 |
| 35 | 7.87 | 7.53216224013837 | 0.337837759861635 |
| 36 | 6.28 | 6.70520695399735 | -0.425206953997345 |
| 37 | 6.3 | 6.3933522117767 | -0.0933522117767033 |
| 38 | 6.36 | 6.39533759868453 | -0.0353375986845282 |
| 39 | 6.28 | 6.19138803149044 | 0.0886119685095656 |
| 40 | 5.89 | 5.66788099106299 | 0.222119008937014 |
| 41 | 6.04 | 5.82071349363653 | 0.219286506363469 |
| 42 | 5.96 | 5.90541164136804 | 0.0545883586319633 |
| 43 | 6.1 | 6.01498084061146 | 0.0850191593885366 |
| 44 | 6.26 | 6.01837344225269 | 0.241626557747309 |
| 45 | 6.02 | 6.09052272898783 | -0.070522728987828 |
| 46 | 6.25 | 6.16763907431695 | 0.0823609256830487 |
| 47 | 6.41 | 6.45192116119279 | -0.0419211611927858 |
| 48 | 6.22 | 6.2283260424517 | -0.00832604245169606 |
| 49 | 6.57 | 6.30466119555144 | 0.265338804448558 |
| 50 | 6.18 | 6.31753956274534 | -0.137539562745345 |
| 51 | 6.26 | 6.29840323162635 | -0.0384032316263541 |
| 52 | 6.1 | 5.89344418658087 | 0.206555813419133 |
| 53 | 6.02 | 6.01098551442846 | 0.0090144855715385 |
| 54 | 6.06 | 6.06645835842341 | -0.00645835842340899 |
| 55 | 6.35 | 6.26105641304336 | 0.0889435869566402 |
| 56 | 6.21 | 6.25556842692774 | -0.0455684269277418 |
| 57 | 6.48 | 6.26982999514457 | 0.210170004855428 |
| 58 | 6.74 | 6.52416701820519 | 0.215832981794808 |
| 59 | 6.53 | 6.75018453303792 | -0.220184533037923 |
| 60 | 6.8 | 6.5357727695774 | 0.264227230422604 |
| 61 | 6.75 | 6.74849733109987 | 0.00150266890013153 |
| 62 | 6.56 | 6.56622282312647 | -0.00622282312647365 |
| 63 | 6.66 | 6.70586875262616 | -0.0458687526261637 |
| 64 | 6.18 | 6.21751849866457 | -0.0375184986645732 |
| 65 | 6.4 | 6.28932510656995 | 0.110674893430048 |
| 66 | 6.43 | 6.43383397008062 | -0.00383397008062244 |
| 67 | 6.54 | 6.55440336040572 | -0.0144033604057166 |
| 68 | 6.44 | 6.56493334488354 | -0.124933344883538 |
| 69 | 6.64 | 6.58822802416991 | 0.0517719758300902 |
| 70 | 6.82 | 6.78274772480514 | 0.0372522751948566 |
| 71 | 6.97 | 6.99509516656909 | -0.0250951665690933 |
| 72 | 7 | 6.86663785366582 | 0.133362146334184 |
| 73 | 6.91 | 6.9938978494709 | -0.0838978494709051 |
| 74 | 6.74 | 6.88046164358613 | -0.140461643586131 |
| 75 | 6.98 | 6.97230838209022 | 0.00769161790977991 |
| 76 | 6.37 | 6.51454666171594 | -0.144546661715938 |
| 77 | 6.56 | 6.55415375560158 | 0.00584624439842229 |
| 78 | 6.63 | 6.72135367184427 | -0.0913536718442654 |
| 79 | 6.87 | 6.82425819581079 | 0.0457418041892087 |
| 80 | 6.68 | 6.86478499512085 | -0.18478499512085 |
| 81 | 6.75 | 6.87161518339586 | -0.121615183395863 |
| 82 | 6.84 | 7.05839629369162 | -0.218396293691615 |
| 83 | 7.15 | 7.22530060940319 | -0.0753006094031912 |
| 84 | 7.09 | 7.11302063649538 | -0.0230206364953772 |
| 85 | 6.97 | 7.19487582479617 | -0.224875824796173 |
| 86 | 7.15 | 7.10858892318819 | 0.0414110768118119 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 20 | 0.787118683545582 | 0.425762632908835 | 0.212881316454418 |
| 21 | 0.655045656562364 | 0.689908686875273 | 0.344954343437636 |
| 22 | 0.607680887516884 | 0.784638224966232 | 0.392319112483116 |
| 23 | 0.535797486173832 | 0.928405027652336 | 0.464202513826168 |
| 24 | 0.84267146350941 | 0.314657072981181 | 0.157328536490591 |
| 25 | 0.881361547464187 | 0.237276905071626 | 0.118638452535813 |
| 26 | 0.879633409134744 | 0.240733181730512 | 0.120366590865256 |
| 27 | 0.84826925020371 | 0.303461499592581 | 0.151730749796290 |
| 28 | 0.798631680640636 | 0.402736638718729 | 0.201368319359364 |
| 29 | 0.876413466414034 | 0.247173067171933 | 0.123586533585967 |
| 30 | 0.847475462380255 | 0.305049075239491 | 0.152524537619745 |
| 31 | 0.872723964227303 | 0.254552071545394 | 0.127276035772697 |
| 32 | 0.856922566184538 | 0.286154867630925 | 0.143077433815462 |
| 33 | 0.918501886511566 | 0.162996226976868 | 0.0814981134884341 |
| 34 | 0.952403926713727 | 0.0951921465725458 | 0.0475960732862729 |
| 35 | 0.944549742126838 | 0.110900515746325 | 0.0554502578731625 |
| 36 | 0.918809295280062 | 0.162381409439876 | 0.0811907047199378 |
| 37 | 0.962658678770106 | 0.0746826424597884 | 0.0373413212298942 |
| 38 | 0.96754094671819 | 0.0649181065636187 | 0.0324590532818094 |
| 39 | 0.960224356166723 | 0.079551287666555 | 0.0397756438332775 |
| 40 | 0.95335133084735 | 0.0932973383052982 | 0.0466486691526491 |
| 41 | 0.936099529633891 | 0.127800940732218 | 0.063900470366109 |
| 42 | 0.929072966682753 | 0.141854066634495 | 0.0709270333172473 |
| 43 | 0.903329107390661 | 0.193341785218678 | 0.0966708926093389 |
| 44 | 0.911778558821522 | 0.176442882356955 | 0.0882214411784775 |
| 45 | 0.923275840216021 | 0.153448319567958 | 0.076724159783979 |
| 46 | 0.903669038602447 | 0.192661922795105 | 0.0963309613975526 |
| 47 | 0.936775524999189 | 0.126448950001622 | 0.0632244750008111 |
| 48 | 0.965739718744571 | 0.0685205625108576 | 0.0342602812554288 |
| 49 | 0.957151911424515 | 0.0856961771509705 | 0.0428480885754852 |
| 50 | 0.990109044999835 | 0.0197819100003304 | 0.00989095500016522 |
| 51 | 0.989671794963133 | 0.0206564100737336 | 0.0103282050368668 |
| 52 | 0.983169251258645 | 0.0336614974827105 | 0.0168307487413552 |
| 53 | 0.983958775379748 | 0.0320824492405036 | 0.0160412246202518 |
| 54 | 0.979224048786962 | 0.0415519024260762 | 0.0207759512130381 |
| 55 | 0.978247398222339 | 0.0435052035553227 | 0.0217526017776613 |
| 56 | 0.97984007126282 | 0.0403198574743618 | 0.0201599287371809 |
| 57 | 0.9657299615288 | 0.0685400769424018 | 0.0342700384712009 |
| 58 | 0.97738955196921 | 0.0452208960615808 | 0.0226104480307904 |
| 59 | 0.987894891079697 | 0.0242102178406070 | 0.0121051089203035 |
| 60 | 0.981481804056188 | 0.0370363918876245 | 0.0185181959438123 |
| 61 | 0.96952965040018 | 0.0609406991996396 | 0.0304703495998198 |
| 62 | 0.943204254755117 | 0.113591490489767 | 0.0567957452448834 |
| 63 | 0.919936896382975 | 0.16012620723405 | 0.080063103617025 |
| 64 | 0.855738698759541 | 0.288522602480917 | 0.144261301240459 |
| 65 | 0.749316342140005 | 0.501367315719989 | 0.250683657859995 |
| 66 | 0.589286320515201 | 0.821427358969598 | 0.410713679484799 |
| 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 | 10 | 0.212765957446809 | NOK |
| 10% type I error level | 19 | 0.404255319148936 | NOK |
