| Multiple Linear Regression - Estimated Regression Equation |
| Y_t[t] = -9.98541379884652 + 0.067304159536628X_1t[t] + 0.0945037736898523X_2t[t] + 2.9820486319068X_3t[t] -0.595169646316401X_4t[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) | -9.98541379884652 | 3.233891 | -3.0877 | 0.002804 | 0.001402 |
| X_1t | 0.067304159536628 | 0.087322 | 0.7708 | 0.44321 | 0.221605 |
| X_2t | 0.0945037736898523 | 0.058296 | 1.6211 | 0.109086 | 0.054543 |
| X_3t | 2.9820486319068 | 0.475311 | 6.2739 | 0 | 0 |
| X_4t | -0.595169646316401 | 0.287469 | -2.0704 | 0.041769 | 0.020885 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.709084608415898 |
| R-squared | 0.502800981892327 |
| Adjusted R-squared | 0.476972461471149 |
| F-TEST (value) | 19.4668906191026 |
| F-TEST (DF numerator) | 4 |
| F-TEST (DF denominator) | 77 |
| p-value | 4.2183923021355e-11 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 7.01797102937249 |
| Sum Squared Residuals | 3792.39763742159 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | -3 | 0.999342807284715 | -3.99934280728472 |
| 2 | -4 | 3.51462971162356 | -7.51462971162356 |
| 3 | -7 | 1.99118962047202 | -8.99118962047202 |
| 4 | -7 | 0.76169317247988 | -7.76169317247988 |
| 5 | -7 | -3.06607967177834 | -3.93392032822166 |
| 6 | -3 | 0.206628071546876 | -3.20662807154688 |
| 7 | 0 | 0.89630149155313 | -0.89630149155313 |
| 8 | -5 | 2.10049310544017 | -7.10049310544017 |
| 9 | -3 | -4.76809498821974 | 1.76809498821974 |
| 10 | 3 | 2.81394614043525 | 0.186053859564746 |
| 11 | 2 | 6.55733974107339 | -4.55733974107339 |
| 12 | -7 | 0.62955746254695 | -7.62955746254695 |
| 13 | -1 | 5.69200606658642 | -6.69200606658642 |
| 14 | 0 | -0.143240019035246 | 0.143240019035246 |
| 15 | -3 | -2.30100691186254 | -0.698993088137465 |
| 16 | 4 | 4.29311153335014 | -0.293111533350136 |
| 17 | 2 | -0.197639247341693 | 2.19763924734169 |
| 18 | 3 | -1.72013194846918 | 4.72013194846918 |
| 19 | 0 | -2.66035993451044 | 2.66035993451044 |
| 20 | -10 | -5.17266920135371 | -4.82733079864629 |
| 21 | -10 | -3.0927742575763 | -6.9072257424237 |
| 22 | -9 | -6.18362134609599 | -2.81637865390401 |
| 23 | -22 | -9.68107379299585 | -12.3189262070041 |
| 24 | -16 | -9.6701991092372 | -6.3298008907628 |
| 25 | -18 | -13.6597798867219 | -4.34022011327811 |
| 26 | -14 | -4.72559153220762 | -9.27440846779238 |
| 27 | -12 | -14.2645699325275 | 2.26456993252748 |
| 28 | -17 | -11.992247442206 | -5.00775255779403 |
| 29 | -23 | -14.2263601671922 | -8.77363983280779 |
| 30 | -28 | -24.8840063114198 | -3.11599368858021 |
| 31 | -31 | -18.7590485044038 | -12.2409514955962 |
| 32 | -21 | -12.8986330521004 | -8.10136694789958 |
| 33 | -19 | -11.5045482697214 | -7.4954517302786 |
| 34 | -22 | -20.5498731203402 | -1.45012687965984 |
| 35 | -22 | -14.4721676490564 | -7.52783235094359 |
| 36 | -25 | -17.5058360058839 | -7.49416399411607 |
| 37 | -16 | -9.86414263862176 | -6.13585736137824 |
| 38 | -22 | -10.3189468249836 | -11.6810531750164 |
| 39 | -21 | -15.9441861493971 | -5.0558138506029 |
| 40 | -10 | -4.55005750887448 | -5.44994249112552 |
| 41 | -7 | 0.26380500768972 | -7.26380500768972 |
| 42 | -5 | -2.80654699758214 | -2.19345300241786 |
| 43 | -4 | -11.4682341822089 | 7.46823418220891 |
| 44 | 7 | -5.13093157449317 | 12.1309315744932 |
| 45 | 6 | -5.45688458266306 | 11.4568845826631 |
| 46 | 3 | 0.978341797906937 | 2.02165820209306 |
| 47 | 10 | 2.03640991318341 | 7.96359008681659 |
| 48 | 0 | -3.51051510051144 | 3.51051510051144 |
| 49 | -2 | -4.69028660363099 | 2.69028660363099 |
| 50 | -1 | -6.71110803566809 | 5.71110803566809 |
| 51 | 2 | -1.51828303432042 | 3.51828303432042 |
| 52 | 8 | 0.120217682680609 | 7.87978231731939 |
| 53 | -6 | -9.23442745369341 | 3.23442745369341 |
| 54 | -4 | -6.05388634234112 | 2.05388634234112 |
| 55 | 4 | -6.38275521909482 | 10.3827552190948 |
| 56 | 7 | -4.82388486599372 | 11.8238848659937 |
| 57 | 3 | -5.90447831198956 | 8.90447831198956 |
| 58 | 3 | -1.68578544174177 | 4.68578544174177 |
| 59 | 8 | -4.77429538854454 | 12.7742953885445 |
| 60 | 3 | -10.4963756283648 | 13.4963756283648 |
| 61 | -3 | -10.2543586043716 | 7.25435860437155 |
| 62 | 4 | -1.76782664587024 | 5.76782664587024 |
| 63 | -5 | -14.1097734244518 | 9.10977342445179 |
| 64 | -1 | -8.79151814185125 | 7.79151814185125 |
| 65 | 5 | -6.30779824085407 | 11.3077982408541 |
| 66 | 0 | -11.5324971397888 | 11.5324971397888 |
| 67 | -6 | -12.5118822811894 | 6.51188228118942 |
| 68 | -13 | -7.02839906619801 | -5.97160093380199 |
| 69 | -15 | -11.6537581659631 | -3.34624183403691 |
| 70 | -8 | -5.89391052247631 | -2.10608947752369 |
| 71 | -20 | -11.909934405456 | -8.09006559454398 |
| 72 | -10 | -19.0152247438967 | 9.0152247438967 |
| 73 | -22 | -16.3404670480483 | -5.65953295195171 |
| 74 | -25 | -20.8111660049358 | -4.18883399506425 |
| 75 | -10 | -16.4499060004399 | 6.44990600043985 |
| 76 | -8 | -13.2115456616167 | 5.21154566161672 |
| 77 | -9 | -16.643280937008 | 7.64328093700802 |
| 78 | -5 | -9.50408645350872 | 4.50408645350872 |
| 79 | -7 | -8.40249379368445 | 1.40249379368445 |
| 80 | -11 | -10.6451440607124 | -0.354855939287597 |
| 81 | -11 | -12.6717226336308 | 1.67172263363083 |
| 82 | -16 | -13.9727551629247 | -2.02724483707534 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 8 | 0.0833278082141447 | 0.166655616428289 | 0.916672191785855 |
| 9 | 0.0313829238710983 | 0.0627658477421967 | 0.968617076128902 |
| 10 | 0.0224829502624926 | 0.0449659005249851 | 0.977517049737507 |
| 11 | 0.0113823966396928 | 0.0227647932793856 | 0.988617603360307 |
| 12 | 0.00675427580735426 | 0.0135085516147085 | 0.993245724192646 |
| 13 | 0.00267866208754335 | 0.0053573241750867 | 0.997321337912457 |
| 14 | 0.000961255255431925 | 0.00192251051086385 | 0.999038744744568 |
| 15 | 0.000351839894982232 | 0.000703679789964465 | 0.999648160105018 |
| 16 | 0.000158484277233357 | 0.000316968554466714 | 0.999841515722767 |
| 17 | 7.0260069030038e-05 | 0.000140520138060076 | 0.99992973993097 |
| 18 | 3.90748553598526e-05 | 7.81497107197051e-05 | 0.99996092514464 |
| 19 | 1.23111383234266e-05 | 2.46222766468532e-05 | 0.999987688861677 |
| 20 | 0.00017756935714572 | 0.000355138714291441 | 0.999822430642854 |
| 21 | 0.00150570476689293 | 0.00301140953378586 | 0.998494295233107 |
| 22 | 0.00160481817607999 | 0.00320963635215997 | 0.99839518182392 |
| 23 | 0.00640344068637691 | 0.0128068813727538 | 0.993596559313623 |
| 24 | 0.00604920591724587 | 0.0120984118344917 | 0.993950794082754 |
| 25 | 0.0038086404047654 | 0.0076172808095308 | 0.996191359595235 |
| 26 | 0.00473836922770236 | 0.00947673845540473 | 0.995261630772298 |
| 27 | 0.00453311007881083 | 0.00906622015762166 | 0.995466889921189 |
| 28 | 0.00266287350009853 | 0.00532574700019706 | 0.997337126499901 |
| 29 | 0.00355922655538855 | 0.0071184531107771 | 0.996440773444611 |
| 30 | 0.00208850633333777 | 0.00417701266667555 | 0.997911493666662 |
| 31 | 0.00397576275090184 | 0.00795152550180369 | 0.996024237249098 |
| 32 | 0.00402564198308779 | 0.00805128396617557 | 0.995974358016912 |
| 33 | 0.016308165731183 | 0.0326163314623659 | 0.983691834268817 |
| 34 | 0.0575105970771316 | 0.115021194154263 | 0.942489402922868 |
| 35 | 0.063572754082614 | 0.127145508165228 | 0.936427245917386 |
| 36 | 0.0566280714735711 | 0.113256142947142 | 0.943371928526429 |
| 37 | 0.0663764129997135 | 0.132752825999427 | 0.933623587000286 |
| 38 | 0.131764299013259 | 0.263528598026518 | 0.868235700986741 |
| 39 | 0.219778620467966 | 0.439557240935933 | 0.780221379532034 |
| 40 | 0.27567600360462 | 0.551352007209241 | 0.72432399639538 |
| 41 | 0.352065504439506 | 0.704131008879011 | 0.647934495560494 |
| 42 | 0.463161405541347 | 0.926322811082695 | 0.536838594458652 |
| 43 | 0.721706501496486 | 0.556586997007029 | 0.278293498503514 |
| 44 | 0.885261020593557 | 0.229477958812885 | 0.114738979406443 |
| 45 | 0.940698684622083 | 0.118602630755834 | 0.0593013153779168 |
| 46 | 0.929662634884723 | 0.140674730230554 | 0.0703373651152772 |
| 47 | 0.935585330072396 | 0.128829339855208 | 0.064414669927604 |
| 48 | 0.927735562144122 | 0.144528875711756 | 0.0722644378558782 |
| 49 | 0.911594809339786 | 0.176810381320428 | 0.0884051906602139 |
| 50 | 0.904361530806475 | 0.19127693838705 | 0.095638469193525 |
| 51 | 0.882763844558627 | 0.234472310882745 | 0.117236155441373 |
| 52 | 0.91117328752433 | 0.17765342495134 | 0.0888267124756699 |
| 53 | 0.893424198575486 | 0.213151602849028 | 0.106575801424514 |
| 54 | 0.88692716078999 | 0.226145678420021 | 0.11307283921001 |
| 55 | 0.902659058891421 | 0.194681882217159 | 0.0973409411085795 |
| 56 | 0.958024873156047 | 0.083950253687906 | 0.041975126843953 |
| 57 | 0.956298415249498 | 0.0874031695010049 | 0.0437015847505024 |
| 58 | 0.939987798489933 | 0.120024403020134 | 0.0600122015100672 |
| 59 | 0.957249453955553 | 0.0855010920888932 | 0.0427505460444466 |
| 60 | 0.970675715785317 | 0.0586485684293665 | 0.0293242842146832 |
| 61 | 0.960583758226567 | 0.0788324835468665 | 0.0394162417734332 |
| 62 | 0.963730408788448 | 0.0725391824231045 | 0.0362695912115523 |
| 63 | 0.959098599059573 | 0.081802801880855 | 0.0409014009404275 |
| 64 | 0.942726980949739 | 0.114546038100523 | 0.0572730190502615 |
| 65 | 0.941592268453943 | 0.116815463092115 | 0.0584077315460574 |
| 66 | 0.985726412419835 | 0.0285471751603303 | 0.0142735875801651 |
| 67 | 0.986027179608352 | 0.0279456407832957 | 0.0139728203916478 |
| 68 | 0.987021349847582 | 0.0259573003048358 | 0.0129786501524179 |
| 69 | 0.992423250734552 | 0.0151534985308954 | 0.00757674926544768 |
| 70 | 0.981890055501032 | 0.0362198889979357 | 0.0181099444989678 |
| 71 | 0.975755834958081 | 0.0484883300838384 | 0.0242441650419192 |
| 72 | 0.994631078361104 | 0.0107378432777914 | 0.00536892163889572 |
| 73 | 0.996831022742428 | 0.00633795451514485 | 0.00316897725757242 |
| 74 | 0.999241222726961 | 0.00151755454607713 | 0.000758777273038567 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 20 | 0.298507462686567 | NOK |
| 5% type I error level | 33 | 0.492537313432836 | NOK |
| 10% type I error level | 41 | 0.611940298507463 | NOK |
