| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 0.697386631716908 + 1.07821756225426X[t] + 0.188267365661863M1[t] + 0.0823564875491473M2[t] + 0.0821782437745737M3[t] + 0.040089121887287M4[t] + 0.175732634338139M5[t] + 0.069732634338139M6[t] + 0.099732634338139M7[t] + 0.141643512450852M8[t] + 0.115643512450852M9[t] + 0.047821756225426M10[t] + 0.00591087811271298M11[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) | 0.697386631716908 | 0.134558 | 5.1828 | 5e-06 | 2e-06 |
| X | 1.07821756225426 | 0.034679 | 31.0911 | 0 | 0 |
| M1 | 0.188267365661863 | 0.165999 | 1.1341 | 0.262485 | 0.131242 |
| M2 | 0.0823564875491473 | 0.166063 | 0.4959 | 0.62225 | 0.311125 |
| M3 | 0.0821782437745737 | 0.165954 | 0.4952 | 0.622775 | 0.311388 |
| M4 | 0.040089121887287 | 0.165927 | 0.2416 | 0.810135 | 0.405068 |
| M5 | 0.175732634338139 | 0.165999 | 1.0586 | 0.295176 | 0.147588 |
| M6 | 0.069732634338139 | 0.165999 | 0.4201 | 0.676343 | 0.338171 |
| M7 | 0.099732634338139 | 0.165999 | 0.6008 | 0.550858 | 0.275429 |
| M8 | 0.141643512450852 | 0.166063 | 0.853 | 0.398011 | 0.199006 |
| M9 | 0.115643512450852 | 0.166063 | 0.6964 | 0.489617 | 0.244809 |
| M10 | 0.047821756225426 | 0.165954 | 0.2882 | 0.774489 | 0.387245 |
| M11 | 0.00591087811271298 | 0.165927 | 0.0356 | 0.971733 | 0.485867 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.97698956501841 |
| R-squared | 0.954508610154864 |
| Adjusted R-squared | 0.94289378721568 |
| F-TEST (value) | 82.1802118855151 |
| F-TEST (DF numerator) | 12 |
| F-TEST (DF denominator) | 47 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 0.262338833659341 |
| Sum Squared Residuals | 3.23461819134993 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 2.05 | 1.96387155963302 | 0.0861284403669798 |
| 2 | 2.11 | 1.85796068152032 | 0.252039318479683 |
| 3 | 2.09 | 1.85778243774574 | 0.232217562254259 |
| 4 | 2.05 | 1.81569331585845 | 0.234306684141546 |
| 5 | 2.08 | 1.95133682830931 | 0.128663171690695 |
| 6 | 2.06 | 1.84533682830931 | 0.214663171690695 |
| 7 | 2.06 | 1.87533682830931 | 0.184663171690695 |
| 8 | 2.08 | 1.91724770642202 | 0.162752293577982 |
| 9 | 2.07 | 1.89124770642202 | 0.178752293577981 |
| 10 | 2.06 | 1.82342595019659 | 0.236574049803407 |
| 11 | 2.07 | 1.78151507208388 | 0.288484927916120 |
| 12 | 2.06 | 1.77560419397117 | 0.284395806028833 |
| 13 | 2.09 | 1.96387155963303 | 0.126128440366970 |
| 14 | 2.07 | 1.85796068152031 | 0.212039318479686 |
| 15 | 2.09 | 1.85778243774574 | 0.232217562254259 |
| 16 | 2.28 | 2.08524770642202 | 0.194752293577981 |
| 17 | 2.33 | 2.22089121887287 | 0.109108781127130 |
| 18 | 2.35 | 2.11489121887287 | 0.23510878112713 |
| 19 | 2.52 | 2.41444560943644 | 0.105554390563565 |
| 20 | 2.63 | 2.45635648754915 | 0.173643512450852 |
| 21 | 2.58 | 2.43035648754915 | 0.149643512450852 |
| 22 | 2.7 | 2.63208912188729 | 0.0679108781127131 |
| 23 | 2.81 | 2.59017824377457 | 0.219821756225426 |
| 24 | 2.97 | 2.85382175622543 | 0.116178243774574 |
| 25 | 3.04 | 3.04208912188729 | -0.00208912188728887 |
| 26 | 3.28 | 3.20573263433814 | 0.0742673656618617 |
| 27 | 3.33 | 3.20555439056356 | 0.124445609436436 |
| 28 | 3.5 | 3.43301965923984 | 0.0669803407601573 |
| 29 | 3.56 | 3.56866317169069 | -0.00866317169069452 |
| 30 | 3.57 | 3.46266317169069 | 0.107336828309305 |
| 31 | 3.69 | 3.76221756225426 | -0.0722175622542595 |
| 32 | 3.82 | 3.80412844036697 | 0.0158715596330275 |
| 33 | 3.79 | 3.77812844036697 | 0.0118715596330278 |
| 34 | 3.96 | 3.97986107470511 | -0.0198610747051113 |
| 35 | 4.06 | 3.9379501965924 | 0.122049803407601 |
| 36 | 4.05 | 3.93203931847969 | 0.117960681520315 |
| 37 | 4.03 | 4.12030668414155 | -0.090306684141548 |
| 38 | 3.94 | 4.01439580602883 | -0.0743958060288326 |
| 39 | 4.02 | 4.01421756225426 | 0.00578243774574043 |
| 40 | 3.88 | 3.97212844036697 | -0.0921284403669724 |
| 41 | 4.02 | 4.10777195281782 | -0.0877719528178247 |
| 42 | 4.03 | 4.00177195281782 | 0.028228047182176 |
| 43 | 4.09 | 4.03177195281782 | 0.0582280471821756 |
| 44 | 3.99 | 4.07368283093054 | -0.0836828309305369 |
| 45 | 4.01 | 4.04768283093054 | -0.0376828309305373 |
| 46 | 4.01 | 3.97986107470511 | 0.0301389252948886 |
| 47 | 4.19 | 4.20750458715596 | -0.0175045871559628 |
| 48 | 4.3 | 4.20159370904325 | 0.0984062909567495 |
| 49 | 4.27 | 4.38986107470511 | -0.119861074705114 |
| 50 | 3.82 | 4.2839501965924 | -0.463950196592398 |
| 51 | 3.15 | 3.74466317169069 | -0.594663171690695 |
| 52 | 2.49 | 2.89391087811271 | -0.403910878112713 |
| 53 | 1.81 | 1.95133682830931 | -0.141336828309305 |
| 54 | 1.26 | 1.84533682830931 | -0.585336828309306 |
| 55 | 1.06 | 1.33622804718218 | -0.276228047182176 |
| 56 | 0.84 | 1.10858453473132 | -0.268584534731324 |
| 57 | 0.78 | 1.08258453473132 | -0.302584534731324 |
| 58 | 0.7 | 1.01476277850590 | -0.314762778505898 |
| 59 | 0.36 | 0.972851900393185 | -0.612851900393185 |
| 60 | 0.35 | 0.966941022280472 | -0.616941022280472 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 16 | 0.00130293052395701 | 0.00260586104791403 | 0.998697069476043 |
| 17 | 0.000122735999409401 | 0.000245471998818801 | 0.99987726400059 |
| 18 | 3.20495567024431e-05 | 6.40991134048863e-05 | 0.999967950443298 |
| 19 | 5.80184528839881e-06 | 1.16036905767976e-05 | 0.999994198154712 |
| 20 | 2.36944212831141e-06 | 4.73888425662281e-06 | 0.999997630557872 |
| 21 | 3.0694626968905e-07 | 6.138925393781e-07 | 0.99999969305373 |
| 22 | 7.4878157055439e-07 | 1.49756314110878e-06 | 0.99999925121843 |
| 23 | 2.05774205941695e-07 | 4.11548411883389e-07 | 0.999999794225794 |
| 24 | 6.08229157996809e-08 | 1.21645831599362e-07 | 0.999999939177084 |
| 25 | 1.23874614883201e-08 | 2.47749229766401e-08 | 0.999999987612538 |
| 26 | 4.73477909853461e-09 | 9.46955819706923e-09 | 0.99999999526522 |
| 27 | 7.00362497182087e-09 | 1.40072499436417e-08 | 0.999999992996375 |
| 28 | 2.41042358537337e-09 | 4.82084717074674e-09 | 0.999999997589576 |
| 29 | 4.8166292083947e-10 | 9.6332584167894e-10 | 0.999999999518337 |
| 30 | 2.65902668303813e-10 | 5.31805336607625e-10 | 0.999999999734097 |
| 31 | 1.49883220209994e-10 | 2.99766440419987e-10 | 0.999999999850117 |
| 32 | 2.44924477020674e-11 | 4.89848954041348e-11 | 0.999999999975508 |
| 33 | 3.7148352069936e-12 | 7.4296704139872e-12 | 0.999999999996285 |
| 34 | 5.81288040798854e-13 | 1.16257608159771e-12 | 0.999999999999419 |
| 35 | 3.71915688163386e-13 | 7.43831376326773e-13 | 0.999999999999628 |
| 36 | 7.03787142243884e-13 | 1.40757428448777e-12 | 0.999999999999296 |
| 37 | 1.03731517877432e-13 | 2.07463035754864e-13 | 0.999999999999896 |
| 38 | 4.42167437494018e-12 | 8.84334874988037e-12 | 0.999999999995578 |
| 39 | 1.08885410194382e-09 | 2.17770820388763e-09 | 0.999999998911146 |
| 40 | 8.2585411691057e-09 | 1.65170823382114e-08 | 0.999999991741459 |
| 41 | 1.95898810897004e-08 | 3.91797621794007e-08 | 0.99999998041012 |
| 42 | 3.84583717314523e-07 | 7.69167434629045e-07 | 0.999999615416283 |
| 43 | 1.54454215402667e-06 | 3.08908430805333e-06 | 0.999998455457846 |
| 44 | 3.91727109508774e-05 | 7.83454219017548e-05 | 0.99996082728905 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 29 | 1 | NOK |
| 5% type I error level | 29 | 1 | NOK |
| 10% type I error level | 29 | 1 | NOK |
