| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 1.02531885999819 + 1.14700986268801X[t] + 0.0378092542034817M1[t] -0.058801305622438M2[t] -0.0393603860451528M3[t] -0.0652699596022685M4[t] + 0.096871946243817M5[t] + 0.00361187955230062M6[t] + 0.0463518128607841M7[t] + 0.104442239303668M8[t] + 0.0911821726121515M9[t] + 0.0292211196518342M10[t] -0.00338944017408287M11[t] -0.0127399333084835t + 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) | 1.02531885999819 | 0.068224 | 15.0287 | 0 | 0 |
| X | 1.14700986268801 | 0.017166 | 66.8186 | 0 | 0 |
| M1 | 0.0378092542034817 | 0.078967 | 0.4788 | 0.634352 | 0.317176 |
| M2 | -0.058801305622438 | 0.078894 | -0.7453 | 0.459868 | 0.229934 |
| M3 | -0.0393603860451528 | 0.078646 | -0.5005 | 0.619128 | 0.309564 |
| M4 | -0.0652699596022685 | 0.078493 | -0.8315 | 0.409966 | 0.204983 |
| M5 | 0.096871946243817 | 0.07834 | 1.2366 | 0.222527 | 0.111264 |
| M6 | 0.00361187955230062 | 0.078269 | 0.0461 | 0.963393 | 0.481696 |
| M7 | 0.0463518128607841 | 0.078211 | 0.5927 | 0.556315 | 0.278157 |
| M8 | 0.104442239303668 | 0.078184 | 1.3359 | 0.188169 | 0.094085 |
| M9 | 0.0911821726121515 | 0.078154 | 1.1667 | 0.249344 | 0.124672 |
| M10 | 0.0292211196518342 | 0.078093 | 0.3742 | 0.709987 | 0.354993 |
| M11 | -0.00338944017408287 | 0.07807 | -0.0434 | 0.965558 | 0.482779 |
| t | -0.0127399333084835 | 0.000988 | -12.8966 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.995059924204524 |
| R-squared | 0.990144252757913 |
| Adjusted R-squared | 0.98735893288515 |
| F-TEST (value) | 355.486729707429 |
| F-TEST (DF numerator) | 13 |
| F-TEST (DF denominator) | 46 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 0.123427738668546 |
| Sum Squared Residuals | 0.70078270695022 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 2.05 | 2.19739804358119 | -0.147398043581186 |
| 2 | 2.11 | 2.08804755044680 | 0.0219524495532044 |
| 3 | 2.09 | 2.09474853671559 | -0.00474853671559424 |
| 4 | 2.05 | 2.05609902985000 | -0.00609902984999507 |
| 5 | 2.08 | 2.20550100238760 | -0.125501002387597 |
| 6 | 2.06 | 2.09950100238760 | -0.039501002387597 |
| 7 | 2.06 | 2.12950100238760 | -0.0695010023875966 |
| 8 | 2.08 | 2.17485149552200 | -0.0948514955219974 |
| 9 | 2.07 | 2.14885149552200 | -0.0788514955219975 |
| 10 | 2.06 | 2.07415050925320 | -0.0141505092531963 |
| 11 | 2.07 | 2.02880001611880 | 0.0411999838812042 |
| 12 | 2.06 | 2.01944952298440 | 0.0405504770156049 |
| 13 | 2.09 | 2.04451884387939 | 0.0454811561206067 |
| 14 | 2.07 | 1.93516835074499 | 0.134831649255009 |
| 15 | 2.09 | 1.94186933701379 | 0.148130662986208 |
| 16 | 2.28 | 2.18997229582019 | 0.090027704179805 |
| 17 | 2.33 | 2.33937426835780 | -0.00937426835779695 |
| 18 | 2.35 | 2.23337426835780 | 0.116625731642203 |
| 19 | 2.52 | 2.5501267340298 | -0.0301267340297997 |
| 20 | 2.63 | 2.5954772271642 | 0.0345227728357997 |
| 21 | 2.58 | 2.5694772271642 | 0.0105227728357999 |
| 22 | 2.7 | 2.7815287065674 | -0.0815287065674017 |
| 23 | 2.81 | 2.736178213433 | 0.0738217865669988 |
| 24 | 2.97 | 3.01358018597060 | -0.0435801859706031 |
| 25 | 3.04 | 3.0386495068656 | 0.00135049313439872 |
| 26 | 3.28 | 3.2160514794032 | 0.0639485205967992 |
| 27 | 3.33 | 3.222752465672 | 0.107247534327998 |
| 28 | 3.5 | 3.47085542447841 | 0.0291445755215942 |
| 29 | 3.56 | 3.62025739701601 | -0.0602573970160078 |
| 30 | 3.57 | 3.51425739701601 | 0.0557426029839919 |
| 31 | 3.69 | 3.83100986268801 | -0.141009862688011 |
| 32 | 3.82 | 3.87636035582241 | -0.0563603558224113 |
| 33 | 3.79 | 3.85036035582241 | -0.060360355822411 |
| 34 | 3.96 | 4.06241183522561 | -0.102411835225613 |
| 35 | 4.06 | 4.01706134209121 | 0.0429386579087876 |
| 36 | 4.05 | 4.00771084895681 | 0.0422891510431884 |
| 37 | 4.03 | 4.03278016985181 | -0.00278016985180923 |
| 38 | 3.94 | 3.92342967671741 | 0.0165703232825938 |
| 39 | 4.02 | 3.93013066298621 | 0.0898693370137916 |
| 40 | 3.88 | 3.89148115612061 | -0.0114811561206087 |
| 41 | 4.02 | 4.04088312865821 | -0.0208831286582112 |
| 42 | 4.03 | 3.93488312865821 | 0.0951168713417895 |
| 43 | 4.09 | 3.96488312865821 | 0.125116871341789 |
| 44 | 3.99 | 4.01023362179261 | -0.0202336217926110 |
| 45 | 4.01 | 3.98423362179261 | 0.0257663782073885 |
| 46 | 4.01 | 3.90953263552381 | 0.100467364476189 |
| 47 | 4.19 | 4.15093460806141 | 0.0390653919385879 |
| 48 | 4.3 | 4.14158411492701 | 0.158415885072988 |
| 49 | 4.27 | 4.16665343582201 | 0.103346564177990 |
| 50 | 3.82 | 4.05730294268761 | -0.237302942687607 |
| 51 | 3.15 | 3.4904989976124 | -0.340498997612403 |
| 52 | 2.49 | 2.59159209373080 | -0.101592093730795 |
| 53 | 1.81 | 1.59398420358039 | 0.216015796419613 |
| 54 | 1.26 | 1.48798420358039 | -0.227984203580388 |
| 55 | 1.06 | 0.944479272236382 | 0.115520727763618 |
| 56 | 0.84 | 0.70307729969878 | 0.13692270030122 |
| 57 | 0.78 | 0.67707729969878 | 0.102922700301220 |
| 58 | 0.7 | 0.602376313429979 | 0.0976236865700213 |
| 59 | 0.36 | 0.557025820295578 | -0.197025820295578 |
| 60 | 0.35 | 0.547675327161178 | -0.197675327161178 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 17 | 0.00713835350722497 | 0.0142767070144499 | 0.992861646492775 |
| 18 | 0.00222830067598725 | 0.00445660135197451 | 0.997771699324013 |
| 19 | 0.000543770866821013 | 0.00108754173364203 | 0.999456229133179 |
| 20 | 0.000261231990809338 | 0.000522463981618676 | 0.99973876800919 |
| 21 | 4.39060857313712e-05 | 8.78121714627423e-05 | 0.999956093914269 |
| 22 | 8.97928776559758e-05 | 0.000179585755311952 | 0.999910207122344 |
| 23 | 2.19361789408474e-05 | 4.38723578816948e-05 | 0.99997806382106 |
| 24 | 5.77702443458515e-06 | 1.15540488691703e-05 | 0.999994222975565 |
| 25 | 1.31741492290457e-06 | 2.63482984580914e-06 | 0.999998682585077 |
| 26 | 2.66549760711689e-07 | 5.33099521423377e-07 | 0.99999973345024 |
| 27 | 1.64503545518321e-07 | 3.29007091036641e-07 | 0.999999835496455 |
| 28 | 3.52479716541826e-08 | 7.04959433083652e-08 | 0.999999964752028 |
| 29 | 1.03452813189296e-08 | 2.06905626378592e-08 | 0.999999989654719 |
| 30 | 3.28529159324842e-09 | 6.57058318649684e-09 | 0.999999996714708 |
| 31 | 3.54568571908232e-09 | 7.09137143816464e-09 | 0.999999996454314 |
| 32 | 9.63104737599223e-10 | 1.92620947519845e-09 | 0.999999999036895 |
| 33 | 3.18236964335805e-10 | 6.3647392867161e-10 | 0.999999999681763 |
| 34 | 3.83574746934388e-10 | 7.67149493868776e-10 | 0.999999999616425 |
| 35 | 1.50585916153623e-10 | 3.01171832307245e-10 | 0.999999999849414 |
| 36 | 2.44480367735108e-10 | 4.88960735470215e-10 | 0.99999999975552 |
| 37 | 3.68956398894838e-10 | 7.37912797789676e-10 | 0.999999999631044 |
| 38 | 1.04919676085456e-09 | 2.09839352170912e-09 | 0.999999998950803 |
| 39 | 1.80643518488933e-09 | 3.61287036977866e-09 | 0.999999998193565 |
| 40 | 8.30657425768722e-09 | 1.66131485153744e-08 | 0.999999991693426 |
| 41 | 3.14811410889581e-08 | 6.29622821779161e-08 | 0.99999996851886 |
| 42 | 4.43310060738692e-05 | 8.86620121477385e-05 | 0.999955668993926 |
| 43 | 0.119346217303749 | 0.238692434607498 | 0.880653782696251 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 25 | 0.925925925925926 | NOK |
| 5% type I error level | 26 | 0.962962962962963 | NOK |
| 10% type I error level | 26 | 0.962962962962963 | NOK |
