| Multiple Linear Regression - Estimated Regression Equation |
| y[t] = + 84.7854609929078 -33.9867021276596x[t] -7.365142688281M1[t] -19.1876055386694M2[t] -26.8672112462006M3[t] -17.9753883823033M4[t] -22.0835655184059M5[t] -17.4774569402229M6[t] -7.87134836203985M7[t] -22.6938112124282M8[t] -13.2707066869301M9[t] -29.2360266801756M10[t] -32.2013466734211M11[t] -0.0346800067544744t + 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) | 84.7854609929078 | 13.625221 | 6.2227 | 0 | 0 |
| x | -33.9867021276596 | 12.189533 | -2.7882 | 0.006918 | 0.003459 |
| M1 | -7.365142688281 | 15.519574 | -0.4746 | 0.636659 | 0.31833 |
| M2 | -19.1876055386694 | 15.483608 | -1.2392 | 0.219653 | 0.109826 |
| M3 | -26.8672112462006 | 15.451885 | -1.7388 | 0.086739 | 0.043369 |
| M4 | -17.9753883823033 | 15.424432 | -1.1654 | 0.248058 | 0.124029 |
| M5 | -22.0835655184059 | 15.40127 | -1.4339 | 0.156328 | 0.078164 |
| M6 | -17.4774569402229 | 15.382421 | -1.1362 | 0.259983 | 0.129992 |
| M7 | -7.87134836203985 | 15.367898 | -0.5122 | 0.610225 | 0.305112 |
| M8 | -22.6938112124282 | 15.357716 | -1.4777 | 0.144249 | 0.072125 |
| M9 | -13.2707066869301 | 15.936455 | -0.8327 | 0.408002 | 0.204001 |
| M10 | -29.2360266801756 | 15.925964 | -1.8357 | 0.070901 | 0.03545 |
| M11 | -32.2013466734211 | 15.919667 | -2.0227 | 0.047155 | 0.023577 |
| t | -0.0346800067544744 | 0.258555 | -0.1341 | 0.893708 | 0.446854 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.613762687419943 |
| R-squared | 0.376704636468951 |
| Adjusted R-squared | 0.253934337591623 |
| F-TEST (value) | 3.06836946650553 |
| F-TEST (DF numerator) | 13 |
| F-TEST (DF denominator) | 66 |
| p-value | 0.00135859852503972 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 27.5700345856201 |
| Sum Squared Residuals | 50167.0492654509 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 37 | 77.3856382978724 | -40.3856382978724 |
| 2 | 30 | 65.5284954407294 | -35.5284954407295 |
| 3 | 47 | 57.8142097264437 | -10.8142097264438 |
| 4 | 35 | 66.6713525835866 | -31.6713525835866 |
| 5 | 30 | 62.5284954407295 | -32.5284954407295 |
| 6 | 43 | 67.099924012158 | -24.0999240121581 |
| 7 | 82 | 76.6713525835866 | 5.32864741641338 |
| 8 | 40 | 61.8142097264438 | -21.8142097264438 |
| 9 | 47 | 71.2026342451874 | -24.2026342451874 |
| 10 | 19 | 55.2026342451874 | -36.2026342451874 |
| 11 | 52 | 52.2026342451874 | -0.202634245187440 |
| 12 | 136 | 84.369300911854 | 51.6306990881459 |
| 13 | 80 | 76.9694782168186 | 3.03052178318137 |
| 14 | 42 | 65.1123353596758 | -23.1123353596758 |
| 15 | 54 | 57.3980496453901 | -3.39804964539007 |
| 16 | 66 | 66.2551925025329 | -0.255192502532925 |
| 17 | 81 | 62.1123353596758 | 18.8876646403242 |
| 18 | 63 | 66.6837639311044 | -3.68376393110436 |
| 19 | 137 | 76.255192502533 | 60.744807497467 |
| 20 | 72 | 61.3980496453901 | 10.6019503546099 |
| 21 | 107 | 70.7864741641337 | 36.2135258358663 |
| 22 | 58 | 54.7864741641337 | 3.21352583586626 |
| 23 | 36 | 51.7864741641337 | -15.7864741641337 |
| 24 | 52 | 83.9531408308004 | -31.9531408308004 |
| 25 | 79 | 76.553318135765 | 2.44668186423506 |
| 26 | 77 | 64.6961752786221 | 12.3038247213779 |
| 27 | 54 | 56.9818895643364 | -2.98188956433638 |
| 28 | 84 | 65.8390324214792 | 18.1609675785208 |
| 29 | 48 | 61.6961752786221 | -13.6961752786221 |
| 30 | 96 | 66.2676038500507 | 29.7323961499493 |
| 31 | 83 | 75.8390324214792 | 7.16096757852078 |
| 32 | 66 | 60.9818895643364 | 5.01811043566362 |
| 33 | 61 | 70.37031408308 | -9.37031408308004 |
| 34 | 53 | 54.37031408308 | -1.37031408308004 |
| 35 | 30 | 51.37031408308 | -21.3703140830800 |
| 36 | 74 | 83.5369807497467 | -9.53698074974671 |
| 37 | 69 | 76.1371580547112 | -7.13715805471124 |
| 38 | 59 | 64.2800151975684 | -5.2800151975684 |
| 39 | 42 | 56.5657294832827 | -14.5657294832827 |
| 40 | 65 | 65.4228723404255 | -0.42287234042554 |
| 41 | 70 | 61.2800151975684 | 8.7199848024316 |
| 42 | 100 | 65.851443768997 | 34.1485562310030 |
| 43 | 63 | 75.4228723404255 | -12.4228723404255 |
| 44 | 105 | 60.5657294832827 | 44.4342705167173 |
| 45 | 82 | 69.9541540020263 | 12.0458459979737 |
| 46 | 81 | 53.9541540020264 | 27.0458459979736 |
| 47 | 75 | 50.9541540020263 | 24.0458459979737 |
| 48 | 102 | 83.120820668693 | 18.879179331307 |
| 49 | 121 | 41.7342958459979 | 79.265704154002 |
| 50 | 98 | 29.8771529888551 | 68.1228470111449 |
| 51 | 76 | 22.1628672745694 | 53.8371327254306 |
| 52 | 77 | 31.0200101317122 | 45.9799898682878 |
| 53 | 63 | 26.8771529888551 | 36.1228470111449 |
| 54 | 37 | 31.4485815602837 | 5.55141843971632 |
| 55 | 35 | 41.0200101317122 | -6.02001013171225 |
| 56 | 23 | 26.1628672745694 | -3.16286727456939 |
| 57 | 40 | 35.5512917933131 | 4.44870820668694 |
| 58 | 29 | 19.5512917933131 | 9.44870820668693 |
| 59 | 37 | 16.5512917933131 | 20.4487082066869 |
| 60 | 51 | 48.7179584599797 | 2.28204154002026 |
| 61 | 20 | 41.3181357649443 | -21.3181357649443 |
| 62 | 28 | 29.4609929078014 | -1.46099290780141 |
| 63 | 13 | 21.7467071935157 | -8.74670719351572 |
| 64 | 22 | 30.6038500506586 | -8.60385005065856 |
| 65 | 25 | 26.4609929078014 | -1.46099290780142 |
| 66 | 13 | 31.03242147923 | -18.03242147923 |
| 67 | 16 | 40.6038500506586 | -24.6038500506586 |
| 68 | 13 | 25.7467071935157 | -12.7467071935157 |
| 69 | 16 | 35.1351317122594 | -19.1351317122594 |
| 70 | 17 | 19.1351317122594 | -2.13513171225938 |
| 71 | 9 | 16.1351317122594 | -7.13513171225938 |
| 72 | 17 | 48.301798378926 | -31.3017983789260 |
| 73 | 25 | 40.9019756838906 | -15.9019756838906 |
| 74 | 14 | 29.0448328267477 | -15.0448328267477 |
| 75 | 8 | 21.330547112462 | -13.3305471124620 |
| 76 | 7 | 30.1876899696049 | -23.1876899696049 |
| 77 | 10 | 26.0448328267477 | -16.0448328267477 |
| 78 | 7 | 30.6162613981763 | -23.6162613981763 |
| 79 | 10 | 40.1876899696049 | -30.1876899696049 |
| 80 | 3 | 25.330547112462 | -22.330547112462 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 17 | 0.255075575634882 | 0.510151151269765 | 0.744924424365118 |
| 18 | 0.141699077080418 | 0.283398154160837 | 0.858300922919582 |
| 19 | 0.151050411313659 | 0.302100822627319 | 0.84894958868634 |
| 20 | 0.07975174856508 | 0.15950349713016 | 0.92024825143492 |
| 21 | 0.0843841902944365 | 0.168768380588873 | 0.915615809705563 |
| 22 | 0.0473000124798995 | 0.094600024959799 | 0.9526999875201 |
| 23 | 0.160874120996143 | 0.321748241992286 | 0.839125879003857 |
| 24 | 0.885926490520633 | 0.228147018958734 | 0.114073509479367 |
| 25 | 0.848585881225292 | 0.302828237549417 | 0.151414118774708 |
| 26 | 0.80118219002806 | 0.397635619943881 | 0.198817809971940 |
| 27 | 0.787019709116876 | 0.425960581766247 | 0.212980290883124 |
| 28 | 0.719815802069943 | 0.560368395860115 | 0.280184197930057 |
| 29 | 0.76745059920079 | 0.465098801598419 | 0.232549400799209 |
| 30 | 0.715565319637854 | 0.568869360724291 | 0.284434680362146 |
| 31 | 0.765095689549464 | 0.469808620901071 | 0.234904310450536 |
| 32 | 0.718768080632905 | 0.56246383873419 | 0.281231919367095 |
| 33 | 0.72978054993053 | 0.54043890013894 | 0.27021945006947 |
| 34 | 0.702078154173809 | 0.595843691652382 | 0.297921845826191 |
| 35 | 0.799151954890256 | 0.401696090219487 | 0.200848045109743 |
| 36 | 0.820548738853849 | 0.358902522292303 | 0.179451261146151 |
| 37 | 0.82726539217651 | 0.345469215646981 | 0.172734607823491 |
| 38 | 0.850934371837349 | 0.298131256325302 | 0.149065628162651 |
| 39 | 0.916488712065918 | 0.167022575868164 | 0.0835112879340822 |
| 40 | 0.927482373366724 | 0.145035253266552 | 0.072517626633276 |
| 41 | 0.933277051898339 | 0.133445896203322 | 0.0667229481016611 |
| 42 | 0.91462911790366 | 0.170741764192679 | 0.0853708820963394 |
| 43 | 0.953810184109267 | 0.0923796317814669 | 0.0461898158907334 |
| 44 | 0.95357675767042 | 0.0928464846591595 | 0.0464232423295797 |
| 45 | 0.930314010467917 | 0.139371979064166 | 0.0696859895320828 |
| 46 | 0.907702801629286 | 0.184594396741429 | 0.0922971983707143 |
| 47 | 0.882472075813098 | 0.235055848373803 | 0.117527924186902 |
| 48 | 0.83478213451145 | 0.330435730977098 | 0.165217865488549 |
| 49 | 0.962269850359773 | 0.0754602992804548 | 0.0377301496402274 |
| 50 | 0.98909870864649 | 0.0218025827070216 | 0.0109012913535108 |
| 51 | 0.997015342096484 | 0.00596931580703152 | 0.00298465790351576 |
| 52 | 0.999803550978705 | 0.000392898042590588 | 0.000196449021295294 |
| 53 | 0.99995458921153 | 9.08215769417236e-05 | 4.54107884708618e-05 |
| 54 | 0.999946228442393 | 0.000107543115213212 | 5.37715576066058e-05 |
| 55 | 0.999917708498355 | 0.000164583003289346 | 8.22915016446731e-05 |
| 56 | 0.99982149404688 | 0.000357011906239281 | 0.000178505953119641 |
| 57 | 0.999633226123644 | 0.000733547752711485 | 0.000366773876355743 |
| 58 | 0.998795714836937 | 0.00240857032612686 | 0.00120428516306343 |
| 59 | 0.998237731290312 | 0.00352453741937499 | 0.00176226870968749 |
| 60 | 0.999705575039137 | 0.000588849921726148 | 0.000294424960863074 |
| 61 | 0.999880016018994 | 0.000239967962011429 | 0.000119983981005715 |
| 62 | 0.999310605280909 | 0.00137878943818254 | 0.00068939471909127 |
| 63 | 0.996465129142593 | 0.00706974171481499 | 0.00353487085740750 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 13 | 0.276595744680851 | NOK |
| 5% type I error level | 14 | 0.297872340425532 | NOK |
| 10% type I error level | 18 | 0.382978723404255 | NOK |
