| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 1.65596789050869 + 0.913038167653139X[t] + 1.13860134993134Y1[t] -0.542253852886171Y2[t] -0.170092084347798M1[t] + 0.37042972215349M2[t] -0.310491195601124M3[t] -0.799607124513897M4[t] -0.99811330052441M5[t] -0.577619444079062M6[t] -1.24340332230172M7[t] + 0.0569418787685395M8[t] + 3.12930286471154M9[t] -0.909771222546327M10[t] + 0.142479922141714M11[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) | 1.65596789050869 | 1.092255 | 1.5161 | 0.136812 | 0.068406 |
| X | 0.913038167653139 | 0.228758 | 3.9913 | 0.000252 | 0.000126 |
| Y1 | 1.13860134993134 | 0.127013 | 8.9645 | 0 | 0 |
| Y2 | -0.542253852886171 | 0.100297 | -5.4065 | 3e-06 | 1e-06 |
| M1 | -0.170092084347798 | 0.433788 | -0.3921 | 0.696914 | 0.348457 |
| M2 | 0.37042972215349 | 0.494138 | 0.7496 | 0.457548 | 0.228774 |
| M3 | -0.310491195601124 | 0.532876 | -0.5827 | 0.563158 | 0.281579 |
| M4 | -0.799607124513897 | 0.542691 | -1.4734 | 0.147924 | 0.073962 |
| M5 | -0.99811330052441 | 0.530749 | -1.8806 | 0.066814 | 0.033407 |
| M6 | -0.577619444079062 | 0.527891 | -1.0942 | 0.279958 | 0.139979 |
| M7 | -1.24340332230172 | 0.509301 | -2.4414 | 0.018821 | 0.00941 |
| M8 | 0.0569418787685395 | 0.520471 | 0.1094 | 0.913391 | 0.456695 |
| M9 | 3.12930286471154 | 0.55893 | 5.5987 | 1e-06 | 1e-06 |
| M10 | -0.909771222546327 | 0.640367 | -1.4207 | 0.162615 | 0.081307 |
| M11 | 0.142479922141714 | 0.461225 | 0.3089 | 0.758877 | 0.379439 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.974673811936578 |
| R-squared | 0.94998903967498 |
| Adjusted R-squared | 0.933706401429624 |
| F-TEST (value) | 58.3436802660627 |
| F-TEST (DF numerator) | 14 |
| F-TEST (DF denominator) | 43 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 0.623972228455184 |
| Sum Squared Residuals | 16.7416777009831 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 22 | 21.4368154230463 | 0.56318457695368 |
| 2 | 21.3 | 21.1633010719134 | 0.136698928086635 |
| 3 | 20.7 | 20.7897983926439 | -0.0897983926439313 |
| 4 | 20.4 | 19.9970993507927 | 0.402900649207332 |
| 5 | 20.3 | 19.7823650815345 | 0.517634918465548 |
| 6 | 20.4 | 19.9777635085566 | 0.422236491443420 |
| 7 | 19.8 | 19.4800651506157 | 0.319934849384338 |
| 8 | 19.5 | 19.6778088893772 | -0.17780888937725 |
| 9 | 23.1 | 23.0991570491338 | 0.000842950866200051 |
| 10 | 23.5 | 23.3217239774946 | 0.178276022505369 |
| 11 | 23.5 | 22.9686056085303 | 0.531394391469691 |
| 12 | 22.9 | 22.7005279619994 | 0.199472038000559 |
| 13 | 21.9 | 21.8472750676928 | 0.0527249323071645 |
| 14 | 21.5 | 21.7571554695251 | -0.257155469525107 |
| 15 | 20.5 | 21.3456554982148 | -0.845655498214755 |
| 16 | 20.2 | 20.0261435772904 | 0.173856422709579 |
| 17 | 19.4 | 20.0283108491867 | -0.628310849186675 |
| 18 | 19.2 | 19.7005997815528 | -0.500599781552799 |
| 19 | 18.8 | 18.9669872653569 | -0.166987265356861 |
| 20 | 18.8 | 19.3725197964399 | -0.572519796439939 |
| 21 | 22.6 | 22.2965670564761 | 0.303432943523851 |
| 22 | 23.3 | 22.3102666486615 | 0.989733351338549 |
| 23 | 23 | 22.1902779140993 | 0.809722085900703 |
| 24 | 21.4 | 21.5092475234885 | -0.109247523488489 |
| 25 | 19.9 | 19.7713732518817 | 0.128626748118296 |
| 26 | 18.8 | 19.5629030148692 | -0.762903014869161 |
| 27 | 18.6 | 18.5342052082846 | 0.0657947917153587 |
| 28 | 18.4 | 18.3225444307951 | 0.077455569204924 |
| 29 | 18.6 | 17.8221611218449 | 0.777838878155106 |
| 30 | 19.9 | 18.6701298356191 | 1.22987016438093 |
| 31 | 19.2 | 19.1934693081993 | 0.00653069180071754 |
| 32 | 18.4 | 18.6266482885043 | -0.226648288504332 |
| 33 | 21.1 | 21.4416173418185 | -0.341617341818513 |
| 34 | 20.5 | 20.8192661649189 | -0.319266164918905 |
| 35 | 19.1 | 19.5416634633248 | -0.441663463324846 |
| 36 | 18.1 | 18.0391901462456 | 0.0608098537543599 |
| 37 | 17 | 17.3983482892418 | -0.398348289241824 |
| 38 | 17.1 | 17.5025739140007 | -0.402573914000742 |
| 39 | 17.4 | 17.80590381971 | -0.405903819709998 |
| 40 | 16.8 | 17.604142910488 | -0.804142910488006 |
| 41 | 15.3 | 16.1945845015916 | -0.894584501591583 |
| 42 | 14.3 | 14.9586171945757 | -0.658617194575673 |
| 43 | 13.4 | 13.6937012954550 | -0.29370129545498 |
| 44 | 15.3 | 14.7854705847691 | 0.514529415230851 |
| 45 | 22.1 | 21.5135445875977 | 0.58645541240229 |
| 46 | 23.7 | 24.2779811761546 | -0.577981176154579 |
| 47 | 22.2 | 23.0994530140455 | -0.899453014045548 |
| 48 | 19.5 | 19.6510343682664 | -0.151034368266431 |
| 49 | 16.6 | 16.9461879681373 | -0.346187968137317 |
| 50 | 17.3 | 16.0140665296916 | 1.28593347030837 |
| 51 | 19.8 | 18.5244370811467 | 1.27556291885333 |
| 52 | 21.2 | 21.0500697306338 | 0.149930269366171 |
| 53 | 21.5 | 21.2725784458424 | 0.227421554157604 |
| 54 | 20.6 | 21.0928896796959 | -0.49288967969588 |
| 55 | 19.1 | 18.9657769803732 | 0.134223019626786 |
| 56 | 19.6 | 19.1375524409093 | 0.462447559090670 |
| 57 | 23.5 | 24.0491139649738 | -0.549113964973829 |
| 58 | 24 | 24.2707620327704 | -0.270762032770434 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 18 | 0.0646149345824356 | 0.129229869164871 | 0.935385065417564 |
| 19 | 0.0190470452125269 | 0.0380940904250537 | 0.980952954787473 |
| 20 | 0.00594319978651863 | 0.0118863995730373 | 0.994056800213481 |
| 21 | 0.00450870122898065 | 0.0090174024579613 | 0.99549129877102 |
| 22 | 0.00235445930502681 | 0.00470891861005362 | 0.997645540694973 |
| 23 | 0.00466928467928549 | 0.00933856935857098 | 0.995330715320714 |
| 24 | 0.0119280130975684 | 0.0238560261951368 | 0.988071986902432 |
| 25 | 0.00500543701713592 | 0.0100108740342718 | 0.994994562982864 |
| 26 | 0.00491997545722641 | 0.00983995091445282 | 0.995080024542774 |
| 27 | 0.010498156562456 | 0.020996313124912 | 0.989501843437544 |
| 28 | 0.00537353878492025 | 0.0107470775698405 | 0.99462646121508 |
| 29 | 0.00795898357881545 | 0.0159179671576309 | 0.992041016421185 |
| 30 | 0.0661694607636518 | 0.132338921527304 | 0.933830539236348 |
| 31 | 0.0642893525435106 | 0.128578705087021 | 0.93571064745649 |
| 32 | 0.0454133791841852 | 0.0908267583683704 | 0.954586620815815 |
| 33 | 0.0413120379067199 | 0.0826240758134397 | 0.95868796209328 |
| 34 | 0.0444882455017079 | 0.0889764910034158 | 0.955511754498292 |
| 35 | 0.0362337427612301 | 0.0724674855224603 | 0.96376625723877 |
| 36 | 0.0268068921465362 | 0.0536137842930725 | 0.973193107853464 |
| 37 | 0.0276660743015567 | 0.0553321486031135 | 0.972333925698443 |
| 38 | 0.620107468691911 | 0.759785062616178 | 0.379892531308089 |
| 39 | 0.919796135195981 | 0.160407729608038 | 0.0802038648040189 |
| 40 | 0.848503637892778 | 0.302992724214444 | 0.151496362107222 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 4 | 0.173913043478261 | NOK |
| 5% type I error level | 11 | 0.478260869565217 | NOK |
| 10% type I error level | 17 | 0.739130434782609 | NOK |
