| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 183.652974945091 -0.383983963036890X[t] -34.9039253829419M1[t] -43.9415014112019M2[t] -34.8759253829419M3[t] -18.8397134824402M4[t] -43.1400229154509M5[t] -79.8253983109354M6[t] + 21.4276619130444M7[t] + 9.20993699214136M8[t] + 29.9799198151845M9[t] + 11.5351919396662M10[t] -9.17372492090307M11[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) | 183.652974945091 | 15.568197 | 11.7967 | 0 | 0 |
| X | -0.383983963036890 | 0.186769 | -2.0559 | 0.045367 | 0.022683 |
| M1 | -34.9039253829419 | 8.173825 | -4.2702 | 9.4e-05 | 4.7e-05 |
| M2 | -43.9415014112019 | 8.316968 | -5.2834 | 3e-06 | 2e-06 |
| M3 | -34.8759253829419 | 8.173825 | -4.2668 | 9.5e-05 | 4.8e-05 |
| M4 | -18.8397134824402 | 7.987562 | -2.3586 | 0.022552 | 0.011276 |
| M5 | -43.1400229154509 | 7.887285 | -5.4696 | 2e-06 | 1e-06 |
| M6 | -79.8253983109354 | 7.90807 | -10.0942 | 0 | 0 |
| M7 | 21.4276619130444 | 7.955661 | 2.6934 | 0.009774 | 0.004887 |
| M8 | 9.20993699214136 | 7.949751 | 1.1585 | 0.252505 | 0.126253 |
| M9 | 29.9799198151845 | 7.899319 | 3.7953 | 0.000422 | 0.000211 |
| M10 | 11.5351919396662 | 7.857788 | 1.468 | 0.148767 | 0.074383 |
| M11 | -9.17372492090307 | 7.844008 | -1.1695 | 0.248091 | 0.124046 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.945413171743223 |
| R-squared | 0.893806065305581 |
| Adjusted R-squared | 0.866692720277218 |
| F-TEST (value) | 32.9655401932369 |
| F-TEST (DF numerator) | 12 |
| F-TEST (DF denominator) | 47 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 12.4023356200969 |
| Sum Squared Residuals | 7229.44265517568 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 100 | 110.350653258460 | -10.3506532584602 |
| 2 | 94.97 | 98.728865158962 | -3.75886515896208 |
| 3 | 107.5 | 108.531690396253 | -1.03169039625281 |
| 4 | 124.27 | 127.893203416654 | -3.62320341665409 |
| 5 | 107.06 | 106.545730659397 | 0.514269340602919 |
| 6 | 79.71 | 69.8603552639124 | 9.84964473608757 |
| 7 | 163.41 | 170.003701834716 | -6.59370183471576 |
| 8 | 144.83 | 157.417352309297 | -12.5873523092973 |
| 9 | 166.82 | 178.555959736856 | -11.7359597368558 |
| 10 | 154.26 | 161.589570119030 | -7.3295701190295 |
| 11 | 132.6 | 141.617902467491 | -9.01790246749109 |
| 12 | 157.51 | 150.423002783879 | 7.08699721612125 |
| 13 | 104.02 | 111.456527072006 | -7.4365270720065 |
| 14 | 106.03 | 101.681701834716 | 4.34829816528426 |
| 15 | 113.23 | 111.115902467491 | 2.11409753250891 |
| 16 | 117.64 | 129.367701834716 | -11.7277018347158 |
| 17 | 113.34 | 106.545730659397 | 6.79426934060295 |
| 18 | 66.62 | 69.4917306593971 | -2.87173065939706 |
| 19 | 185.99 | 170.376166278862 | 15.6138337211385 |
| 20 | 174.57 | 158.158441357958 | 16.4115586420415 |
| 21 | 208.19 | 179.665673390032 | 28.5243266099676 |
| 22 | 163.81 | 161.958194723545 | 1.85180527645510 |
| 23 | 162.46 | 141.249277862976 | 21.2107221370243 |
| 24 | 148.16 | 150.423002783879 | -2.26300278387875 |
| 25 | 113.41 | 112.566240725183 | 0.843759274816883 |
| 26 | 105.63 | 102.791415487892 | 2.83858451210764 |
| 27 | 111.79 | 112.594240725183 | -0.804240725183107 |
| 28 | 132.36 | 130.477415487892 | 1.88258451210765 |
| 29 | 110.75 | 107.282979868428 | 3.46702013157213 |
| 30 | 67.37 | 70.5976044729433 | -3.22760447294327 |
| 31 | 178.29 | 171.482040092408 | 6.80795990759222 |
| 32 | 156.38 | 159.264315171505 | -2.88431517150469 |
| 33 | 189.71 | 180.034297994548 | 9.67570200545222 |
| 34 | 152.8 | 161.220945514514 | -8.42094551451407 |
| 35 | 150.8 | 141.986527072006 | 8.81347292799352 |
| 36 | 160.4 | 153.007214855117 | 7.392785144883 |
| 37 | 127.25 | 117.734664867660 | 9.51533513234035 |
| 38 | 108.47 | 109.806802492576 | -1.33680249257633 |
| 39 | 117.09 | 120.346876938898 | -3.25687693889792 |
| 40 | 147.25 | 135.645839630369 | 11.6041603696311 |
| 41 | 116.19 | 111.345530197358 | 4.84446980264183 |
| 42 | 75.83 | 74.2915301973582 | 1.53846980264179 |
| 43 | 181.94 | 175.913215025854 | 6.0267849741465 |
| 44 | 179.12 | 164.801363918497 | 14.3186360815034 |
| 45 | 183.15 | 187.418309603747 | -4.26830960374717 |
| 46 | 197.9 | 170.083295381405 | 27.8167046185945 |
| 47 | 155.42 | 150.480252334382 | 4.93974766561748 |
| 48 | 162.54 | 158.175638997594 | 4.36436100240643 |
| 49 | 125.9 | 118.471914076690 | 7.42808592330952 |
| 50 | 105.5 | 107.591215025853 | -2.09121502585348 |
| 51 | 121.11 | 118.131289472175 | 2.97871052782493 |
| 52 | 137.51 | 135.645839630369 | 1.86416036963108 |
| 53 | 97.2 | 112.820028615420 | -15.6200286154198 |
| 54 | 69.74 | 75.028779406389 | -5.28877940638904 |
| 55 | 152.58 | 174.434876768161 | -21.8548767681614 |
| 56 | 146.59 | 161.848527242743 | -15.2585272427430 |
| 57 | 161.16 | 183.355759274817 | -22.1957592748169 |
| 58 | 152.84 | 166.757994261506 | -13.9179942615060 |
| 59 | 121.95 | 147.896040263144 | -25.9460402631442 |
| 60 | 140.12 | 156.701140579532 | -16.5811405795319 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 16 | 0.0462049157128131 | 0.0924098314256263 | 0.953795084287187 |
| 17 | 0.0205300139976160 | 0.0410600279952321 | 0.979469986002384 |
| 18 | 0.0244655583061009 | 0.0489311166122018 | 0.975534441693899 |
| 19 | 0.0854295001072718 | 0.170859000214544 | 0.914570499892728 |
| 20 | 0.214075384712602 | 0.428150769425204 | 0.785924615287398 |
| 21 | 0.55326397911564 | 0.89347204176872 | 0.44673602088436 |
| 22 | 0.450547761336154 | 0.901095522672309 | 0.549452238663846 |
| 23 | 0.639588625068107 | 0.720822749863786 | 0.360411374931893 |
| 24 | 0.551956364459396 | 0.896087271081207 | 0.448043635540604 |
| 25 | 0.454537691440005 | 0.909075382880011 | 0.545462308559995 |
| 26 | 0.373369230083308 | 0.746738460166616 | 0.626630769916692 |
| 27 | 0.303468327446582 | 0.606936654893164 | 0.696531672553418 |
| 28 | 0.226478221073379 | 0.452956442146758 | 0.773521778926621 |
| 29 | 0.166209487801753 | 0.332418975603506 | 0.833790512198247 |
| 30 | 0.121679466141774 | 0.243358932283547 | 0.878320533858226 |
| 31 | 0.0923686218723035 | 0.184737243744607 | 0.907631378127697 |
| 32 | 0.0627474729403694 | 0.125494945880739 | 0.93725252705963 |
| 33 | 0.0683408925645353 | 0.136681785129071 | 0.931659107435465 |
| 34 | 0.0442539237258365 | 0.088507847451673 | 0.955746076274164 |
| 35 | 0.0843838428730088 | 0.168767685746018 | 0.915616157126991 |
| 36 | 0.23036577454869 | 0.46073154909738 | 0.76963422545131 |
| 37 | 0.166085436997913 | 0.332170873995827 | 0.833914563002087 |
| 38 | 0.178705551680612 | 0.357411103361223 | 0.821294448319388 |
| 39 | 0.236410368984428 | 0.472820737968856 | 0.763589631015572 |
| 40 | 0.193733845820396 | 0.387467691640793 | 0.806266154179604 |
| 41 | 0.519965809110813 | 0.960068381778374 | 0.480034190889187 |
| 42 | 0.502095592632518 | 0.995808814734964 | 0.497904407367482 |
| 43 | 0.497230156102068 | 0.994460312204135 | 0.502769843897932 |
| 44 | 0.34614327425465 | 0.6922865485093 | 0.65385672574535 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 0 | 0 | OK |
| 5% type I error level | 2 | 0.0689655172413793 | NOK |
| 10% type I error level | 4 | 0.137931034482759 | NOK |
