| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = -2.29101830970334 + 1.18227381282826X[t] -0.528396202113022M1[t] -1.09215623702356M2[t] -1.41384671982294M3[t] -1.40672834794418M4[t] -1.51707239523279M5[t] -1.67619740018946M6[t] -1.85649345552018M7[t] + 0.152145441079096M8[t] -1.98138135702689M9[t] -1.75420734980634M10[t] -1.10066825881478M11[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) | -2.29101830970334 | 0.577156 | -3.9695 | 0.000183 | 9.1e-05 |
| X | 1.18227381282826 | 0.031166 | 37.9353 | 0 | 0 |
| M1 | -0.528396202113022 | 0.324777 | -1.627 | 0.108586 | 0.054293 |
| M2 | -1.09215623702356 | 0.324961 | -3.3609 | 0.001305 | 0.000652 |
| M3 | -1.41384671982294 | 0.333002 | -4.2458 | 7.1e-05 | 3.5e-05 |
| M4 | -1.40672834794418 | 0.326229 | -4.3121 | 5.6e-05 | 2.8e-05 |
| M5 | -1.51707239523279 | 0.325948 | -4.6543 | 1.6e-05 | 8e-06 |
| M6 | -1.67619740018946 | 0.3332 | -5.0306 | 4e-06 | 2e-06 |
| M7 | -1.85649345552018 | 0.338322 | -5.4874 | 1e-06 | 0 |
| M8 | 0.152145441079096 | 0.339771 | 0.4478 | 0.655795 | 0.327897 |
| M9 | -1.98138135702689 | 0.345001 | -5.7431 | 0 | 0 |
| M10 | -1.75420734980634 | 0.346507 | -5.0625 | 4e-06 | 2e-06 |
| M11 | -1.10066825881478 | 0.34011 | -3.2362 | 0.001907 | 0.000954 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.980495588337264 |
| R-squared | 0.961371598748837 |
| Adjusted R-squared | 0.954240201594776 |
| F-TEST (value) | 134.808310066057 |
| F-TEST (DF numerator) | 12 |
| F-TEST (DF denominator) | 65 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 0.583743276693048 |
| Sum Squared Residuals | 22.1491538504819 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 14.5 | 14.6782379180418 | -0.178237918041825 |
| 2 | 14.3 | 13.9962505018485 | 0.303749498151452 |
| 3 | 15.3 | 15.2115159757259 | 0.0884840242741036 |
| 4 | 14.4 | 14.5092700599077 | -0.109270059907701 |
| 5 | 13.7 | 13.9260164874878 | -0.226016487487795 |
| 6 | 14.2 | 14.3580283889452 | -0.158028388945250 |
| 7 | 13.5 | 13.7048228084832 | -0.204822808483219 |
| 8 | 11.9 | 11.6937307414664 | 0.206269258533592 |
| 9 | 14.6 | 14.9986634823704 | -0.398663482370433 |
| 10 | 15.6 | 15.6987470147223 | -0.0987470147222814 |
| 11 | 14.1 | 14.3424206239058 | -0.242420623905796 |
| 12 | 14.9 | 15.3248615014378 | -0.424861501437754 |
| 13 | 14.2 | 14.4417831554763 | -0.241783155476253 |
| 14 | 14.6 | 14.7056147895455 | -0.105614789545495 |
| 15 | 17.2 | 17.4578362200996 | -0.257836220099595 |
| 16 | 15.4 | 15.6915438727360 | -0.29154387273596 |
| 17 | 14.3 | 14.3989260126191 | -0.0989260126190978 |
| 18 | 17.5 | 17.1954855397331 | 0.304514460266929 |
| 19 | 14.5 | 14.6506418587458 | -0.150641858745832 |
| 20 | 14.4 | 14.2947331296886 | 0.105266870311413 |
| 21 | 16.6 | 16.7720742016128 | -0.172074201612825 |
| 22 | 16.7 | 17.1174755901162 | -0.417475590116195 |
| 23 | 16.6 | 17.1798777746936 | -0.57987777469362 |
| 24 | 16.9 | 17.4529543645286 | -0.552954364528624 |
| 25 | 15.7 | 16.0969664934358 | -0.39696649343582 |
| 26 | 16.4 | 16.2425707462222 | 0.157429253777763 |
| 27 | 18.4 | 18.8765647954935 | -0.476564795493512 |
| 28 | 16.9 | 17.3467272106955 | -0.44672721069553 |
| 29 | 16.5 | 16.5270188757100 | -0.0270188757099678 |
| 30 | 18.3 | 18.0230772087129 | 0.276922791287143 |
| 31 | 15.1 | 15.1235513838771 | -0.0235513838771379 |
| 32 | 15.7 | 15.7134617050825 | -0.0134617050825008 |
| 33 | 18.1 | 18.4272575395724 | -0.327257539572389 |
| 34 | 16.8 | 16.8810208275505 | -0.0810208275505417 |
| 35 | 18.9 | 19.1897432565017 | -0.289743256501670 |
| 36 | 19 | 18.9899103212054 | 0.0100896787946367 |
| 37 | 18.1 | 17.8703772126782 | 0.22962278732179 |
| 38 | 17.8 | 17.6612993216161 | 0.138700678383852 |
| 39 | 21.5 | 21.2411124211500 | 0.258887578849966 |
| 40 | 17.1 | 16.6373629229986 | 0.462637077001431 |
| 41 | 18.7 | 19.1280212639321 | -0.428021263932143 |
| 42 | 19 | 19.4418057841068 | -0.44180578410677 |
| 43 | 16.4 | 16.6605073405539 | -0.26050734055388 |
| 44 | 16.9 | 17.0139628991936 | -0.113962899193588 |
| 45 | 18.6 | 18.7819396834209 | -0.181939683420869 |
| 46 | 19.3 | 19.4820232157727 | -0.182023215772716 |
| 47 | 19.4 | 20.2537896880471 | -0.853789688047104 |
| 48 | 17.6 | 18.1623186522256 | -0.56231865222558 |
| 49 | 18.6 | 19.5255605506378 | -0.925560550637774 |
| 50 | 18.1 | 18.6071183718788 | -0.507118371878757 |
| 51 | 20.4 | 21.5957945649985 | -1.19579456499851 |
| 52 | 18.1 | 18.2925462609581 | -0.192546260958137 |
| 53 | 19.6 | 19.6009307890634 | -0.000930789063447662 |
| 54 | 19.9 | 20.6240795969350 | -0.724079596935033 |
| 55 | 19.2 | 19.0250549662104 | 0.174945033789598 |
| 56 | 17.8 | 18.7873736184360 | -0.987373618435979 |
| 57 | 19.2 | 19.1366218272693 | 0.0633781727306502 |
| 58 | 22 | 22.2012529852777 | -0.201252985277720 |
| 59 | 21.1 | 21.0813813570269 | 0.0186186429731163 |
| 60 | 19.5 | 18.8716829399225 | 0.628317060077465 |
| 61 | 22.2 | 21.8901081762943 | 0.309891823705701 |
| 62 | 20.9 | 21.6810302852322 | -0.781030285232237 |
| 63 | 22.2 | 21.5957945649985 | 0.60420543500149 |
| 64 | 23.5 | 23.4945510374025 | 0.00544896259751321 |
| 65 | 21.5 | 21.3743415083058 | 0.125658491694158 |
| 66 | 24.3 | 24.2891284167026 | 0.0108715832973603 |
| 67 | 22.8 | 22.3354216421295 | 0.464578357870471 |
| 68 | 20.3 | 19.4967379061329 | 0.803262093867063 |
| 69 | 23.7 | 22.6834432657541 | 1.01655673424587 |
| 70 | 23.3 | 22.3194803665605 | 0.980519633439453 |
| 71 | 19.6 | 17.6527872998249 | 1.94721270017507 |
| 72 | 18 | 17.0982722206801 | 0.901727779319857 |
| 73 | 17.3 | 16.0969664934358 | 1.20303350656418 |
| 74 | 16.8 | 16.0061159836566 | 0.793884016343421 |
| 75 | 18.2 | 17.2213814575339 | 0.978618542466057 |
| 76 | 16.5 | 15.9279986353016 | 0.572001364698384 |
| 77 | 16 | 15.3447450628817 | 0.655254937118294 |
| 78 | 18.4 | 17.6683950648644 | 0.73160493513562 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 16 | 0.00973249266085412 | 0.0194649853217082 | 0.990267507339146 |
| 17 | 0.00316813748861622 | 0.00633627497723244 | 0.996831862511384 |
| 18 | 0.0141462552180820 | 0.0282925104361641 | 0.985853744781918 |
| 19 | 0.00437235940415554 | 0.00874471880831108 | 0.995627640595844 |
| 20 | 0.00130629874418729 | 0.00261259748837459 | 0.998693701255813 |
| 21 | 0.000477810631727827 | 0.000955621263455653 | 0.999522189368272 |
| 22 | 0.000253311448983821 | 0.000506622897967642 | 0.999746688551016 |
| 23 | 0.000126204986224539 | 0.000252409972449078 | 0.999873795013775 |
| 24 | 3.99824145091164e-05 | 7.99648290182327e-05 | 0.99996001758549 |
| 25 | 1.37223613160377e-05 | 2.74447226320754e-05 | 0.999986277638684 |
| 26 | 4.04688491923357e-06 | 8.09376983846715e-06 | 0.99999595311508 |
| 27 | 2.45605398836595e-06 | 4.9121079767319e-06 | 0.999997543946012 |
| 28 | 8.3617539185452e-07 | 1.67235078370904e-06 | 0.999999163824608 |
| 29 | 3.94283250540627e-07 | 7.88566501081254e-07 | 0.99999960571675 |
| 30 | 2.16129265549682e-07 | 4.32258531099365e-07 | 0.999999783870734 |
| 31 | 7.79334161734906e-08 | 1.55866832346981e-07 | 0.999999922066584 |
| 32 | 2.01028992086117e-08 | 4.02057984172234e-08 | 0.9999999798971 |
| 33 | 6.03859113494223e-09 | 1.20771822698845e-08 | 0.999999993961409 |
| 34 | 2.42324259855201e-09 | 4.84648519710403e-09 | 0.999999997576757 |
| 35 | 1.09233485250410e-09 | 2.18466970500819e-09 | 0.999999998907665 |
| 36 | 3.4271187090009e-09 | 6.8542374180018e-09 | 0.999999996572881 |
| 37 | 6.68598564873209e-09 | 1.33719712974642e-08 | 0.999999993314014 |
| 38 | 1.76701960503517e-09 | 3.53403921007034e-09 | 0.99999999823298 |
| 39 | 1.59424344158696e-09 | 3.18848688317391e-09 | 0.999999998405757 |
| 40 | 1.16794497268976e-08 | 2.33588994537951e-08 | 0.99999998832055 |
| 41 | 1.02323293318461e-08 | 2.04646586636922e-08 | 0.99999998976767 |
| 42 | 2.21494860165548e-08 | 4.42989720331096e-08 | 0.999999977850514 |
| 43 | 1.23356324898483e-08 | 2.46712649796967e-08 | 0.999999987664367 |
| 44 | 4.63360642107868e-09 | 9.26721284215737e-09 | 0.999999995366394 |
| 45 | 2.52194452470515e-09 | 5.04388904941031e-09 | 0.999999997478055 |
| 46 | 1.24834160879368e-09 | 2.49668321758737e-09 | 0.999999998751658 |
| 47 | 7.94686583862144e-09 | 1.58937316772429e-08 | 0.999999992053134 |
| 48 | 1.18727878670707e-08 | 2.37455757341414e-08 | 0.999999988127212 |
| 49 | 3.25961854170414e-07 | 6.51923708340828e-07 | 0.999999674038146 |
| 50 | 4.26473317970132e-07 | 8.52946635940265e-07 | 0.999999573526682 |
| 51 | 4.44654527463367e-05 | 8.89309054926733e-05 | 0.999955534547254 |
| 52 | 2.87118929357833e-05 | 5.74237858715666e-05 | 0.999971288107064 |
| 53 | 1.70232491362704e-05 | 3.40464982725408e-05 | 0.999982976750864 |
| 54 | 6.35280041356182e-05 | 0.000127056008271236 | 0.999936471995864 |
| 55 | 6.98944357101535e-05 | 0.000139788871420307 | 0.99993010556429 |
| 56 | 0.00326335854511175 | 0.0065267170902235 | 0.996736641454888 |
| 57 | 0.0204970877363935 | 0.040994175472787 | 0.979502912263607 |
| 58 | 0.0682010151446982 | 0.136402030289396 | 0.931798984855302 |
| 59 | 0.620329826398652 | 0.759340347202695 | 0.379670173601348 |
| 60 | 0.575239879778304 | 0.849520240443391 | 0.424760120221696 |
| 61 | 0.481990251912681 | 0.963980503825362 | 0.518009748087319 |
| 62 | 0.991550547067767 | 0.0168989058644659 | 0.00844945293223293 |
| 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 | 43 | 0.914893617021277 | NOK |
