| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = -873.66330396259 + 10.0004964841749X[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) | -873.66330396259 | 77.616918 | -11.2561 | 0 | 0 |
| X | 10.0004964841749 | 0.743018 | 13.4593 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.868517469066465 |
| R-squared | 0.754322594073617 |
| Adjusted R-squared | 0.750158570244357 |
| F-TEST (value) | 181.152324050830 |
| F-TEST (DF numerator) | 1 |
| F-TEST (DF denominator) | 59 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 22.2647862679449 |
| Sum Squared Residuals | 29247.5217458788 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 108.5 | 113.485703990315 | -4.98570399031535 |
| 2 | 112.3 | 111.785619588005 | 0.51438041199518 |
| 3 | 116.6 | 108.385450783385 | 8.21454921661466 |
| 4 | 115.5 | 95.5848152836414 | 19.9151847163585 |
| 5 | 120.1 | 116.985877759776 | 3.11412224022424 |
| 6 | 132.9 | 122.886170685439 | 10.0138293145610 |
| 7 | 128.1 | 124.586255087749 | 3.51374491225140 |
| 8 | 129.3 | 126.286339490058 | 3.01366050994167 |
| 9 | 132.5 | 129.686508294678 | 2.81349170532216 |
| 10 | 131 | 119.486001880819 | 11.5139981191805 |
| 11 | 124.9 | 137.386890587492 | -12.4868905874925 |
| 12 | 120.8 | 137.386890587492 | -16.5868905874925 |
| 13 | 122 | 135.686806185183 | -13.6868061851829 |
| 14 | 122.1 | 134.886766466449 | -12.7867664664488 |
| 15 | 127.4 | 135.686806185183 | -8.28680618518287 |
| 16 | 135.2 | 122.38614586123 | 12.8138541387699 |
| 17 | 137.3 | 145.187277845149 | -7.88727784514891 |
| 18 | 135 | 144.487243091257 | -9.48724309125675 |
| 19 | 136 | 150.187526087236 | -14.1875260872364 |
| 20 | 138.4 | 153.787704821539 | -15.3877048215393 |
| 21 | 134.7 | 154.587744540273 | -19.8877445402733 |
| 22 | 138.4 | 143.587198407681 | -5.18719840768097 |
| 23 | 133.9 | 161.088067254987 | -27.1880672549871 |
| 24 | 133.6 | 156.187823977741 | -22.5878239777414 |
| 25 | 141.2 | 153.187675032489 | -11.9876750324890 |
| 26 | 151.8 | 155.387784259007 | -3.58778425900742 |
| 27 | 155.4 | 156.687848801950 | -1.28784880195012 |
| 28 | 156.6 | 139.286984919486 | 17.3130150805142 |
| 29 | 161.6 | 163.288176481506 | -1.68817648150553 |
| 30 | 160.7 | 163.188171516664 | -2.48817151666388 |
| 31 | 156 | 168.388429688435 | -12.3884296884348 |
| 32 | 159.5 | 167.188370110334 | -7.68837011033374 |
| 33 | 168.7 | 167.988409829068 | 0.711590170932269 |
| 34 | 169.9 | 156.887858731634 | 13.0121412683664 |
| 35 | 169.9 | 172.988658071155 | -3.08865807115517 |
| 36 | 185.9 | 170.98855877432 | 14.9114412256798 |
| 37 | 190.8 | 175.888802051566 | 14.9111979484341 |
| 38 | 195.8 | 184.889248887323 | 10.9107511126767 |
| 39 | 211.9 | 188.689437551310 | 23.2105624486902 |
| 40 | 227.1 | 174.988757367990 | 52.1112426320098 |
| 41 | 251.3 | 200.790038297161 | 50.5099617028386 |
| 42 | 256.7 | 208.690430519660 | 48.0095694803403 |
| 43 | 251.9 | 210.890539746178 | 41.0094602538219 |
| 44 | 251.2 | 220.291006441303 | 30.9089935586975 |
| 45 | 270.3 | 227.891383769275 | 42.4086162307245 |
| 46 | 267.2 | 217.690877355417 | 49.509122644583 |
| 47 | 243 | 229.191448312218 | 13.8085516877818 |
| 48 | 229.9 | 228.091393698959 | 1.80860630104105 |
| 49 | 187.2 | 226.291304331807 | -39.0913043318074 |
| 50 | 178.2 | 218.99094189836 | -40.7909418983598 |
| 51 | 175.2 | 217.490867425734 | -42.2908674257335 |
| 52 | 192.4 | 196.989849633175 | -4.589849633175 |
| 53 | 187 | 221.691075949087 | -34.691075949087 |
| 54 | 184 | 215.590773093740 | -31.5907730937403 |
| 55 | 194.1 | 218.790931968676 | -24.6909319686762 |
| 56 | 212.7 | 217.590872390575 | -4.89087239057535 |
| 57 | 217.5 | 216.390812812474 | 1.10918718752570 |
| 58 | 200.5 | 198.689934035485 | 1.81006596451524 |
| 59 | 205.9 | 221.29105608972 | -15.3910560897199 |
| 60 | 196.5 | 216.790832671841 | -20.2908326718414 |
| 61 | 206.3 | 216.590822742158 | -10.2908227421577 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 5 | 0.0143647311786359 | 0.0287294623572718 | 0.985635268821364 |
| 6 | 0.0252211246729953 | 0.0504422493459907 | 0.974778875327005 |
| 7 | 0.00800843981809698 | 0.0160168796361940 | 0.991991560181903 |
| 8 | 0.00229005668505935 | 0.00458011337011871 | 0.997709943314941 |
| 9 | 0.000626141236078194 | 0.00125228247215639 | 0.999373858763922 |
| 10 | 0.000278772512765352 | 0.000557545025530705 | 0.999721227487235 |
| 11 | 0.000178858635371912 | 0.000357717270743824 | 0.999821141364628 |
| 12 | 0.000124132088793737 | 0.000248264177587473 | 0.999875867911206 |
| 13 | 4.7801849389359e-05 | 9.5603698778718e-05 | 0.99995219815061 |
| 14 | 1.59531565081441e-05 | 3.19063130162881e-05 | 0.999984046843492 |
| 15 | 4.15915919858439e-06 | 8.31831839716879e-06 | 0.999995840840801 |
| 16 | 4.71777624499913e-06 | 9.43555248999826e-06 | 0.999995282223755 |
| 17 | 1.78266967915192e-06 | 3.56533935830383e-06 | 0.99999821733032 |
| 18 | 5.15082077065081e-07 | 1.03016415413016e-06 | 0.999999484917923 |
| 19 | 1.39216197907072e-07 | 2.78432395814145e-07 | 0.999999860783802 |
| 20 | 3.80902030835625e-08 | 7.6180406167125e-08 | 0.999999961909797 |
| 21 | 1.08902535520152e-08 | 2.17805071040303e-08 | 0.999999989109746 |
| 22 | 3.84208394818238e-09 | 7.68416789636475e-09 | 0.999999996157916 |
| 23 | 1.73508238769923e-09 | 3.47016477539846e-09 | 0.999999998264918 |
| 24 | 6.11915514520135e-10 | 1.22383102904027e-09 | 0.999999999388084 |
| 25 | 2.38911529340144e-10 | 4.77823058680288e-10 | 0.999999999761088 |
| 26 | 5.60130907505944e-10 | 1.12026181501189e-09 | 0.99999999943987 |
| 27 | 1.44930997885129e-09 | 2.89861995770258e-09 | 0.99999999855069 |
| 28 | 2.11692018178332e-08 | 4.23384036356664e-08 | 0.999999978830798 |
| 29 | 2.73202714068092e-08 | 5.46405428136183e-08 | 0.999999972679729 |
| 30 | 2.29734246525285e-08 | 4.59468493050569e-08 | 0.999999977026575 |
| 31 | 1.10707523352930e-08 | 2.21415046705860e-08 | 0.999999988929248 |
| 32 | 6.53527651273406e-09 | 1.30705530254681e-08 | 0.999999993464723 |
| 33 | 8.05462982439929e-09 | 1.61092596487986e-08 | 0.99999999194537 |
| 34 | 2.65085920087019e-08 | 5.30171840174039e-08 | 0.999999973491408 |
| 35 | 2.15693688316131e-08 | 4.31387376632262e-08 | 0.999999978430631 |
| 36 | 9.50203553411203e-08 | 1.90040710682241e-07 | 0.999999904979645 |
| 37 | 2.51350481295656e-07 | 5.02700962591312e-07 | 0.999999748649519 |
| 38 | 3.20849929433431e-07 | 6.41699858866861e-07 | 0.99999967915007 |
| 39 | 8.9435072159145e-07 | 1.7887014431829e-06 | 0.999999105649278 |
| 40 | 4.20379789486717e-05 | 8.40759578973433e-05 | 0.999957962021051 |
| 41 | 0.000444152211125601 | 0.000888304422251203 | 0.999555847788874 |
| 42 | 0.00223357510906924 | 0.00446715021813849 | 0.99776642489093 |
| 43 | 0.00600666616410136 | 0.0120133323282027 | 0.993993333835899 |
| 44 | 0.00850882986701048 | 0.0170176597340210 | 0.99149117013299 |
| 45 | 0.0351453588866007 | 0.0702907177732014 | 0.9648546411134 |
| 46 | 0.353049977670235 | 0.70609995534047 | 0.646950022329765 |
| 47 | 0.606409481016483 | 0.787181037967034 | 0.393590518983517 |
| 48 | 0.832660436519391 | 0.334679126961217 | 0.167339563480608 |
| 49 | 0.877576507542923 | 0.244846984914153 | 0.122423492457077 |
| 50 | 0.927094708591794 | 0.145810582816412 | 0.0729052914082059 |
| 51 | 0.973756947942697 | 0.0524861041146052 | 0.0262430520573026 |
| 52 | 0.952395249986489 | 0.0952095000270227 | 0.0476047500135113 |
| 53 | 0.953308498489513 | 0.0933830030209749 | 0.0466915015104874 |
| 54 | 0.976746558553191 | 0.0465068828936173 | 0.0232534414468087 |
| 55 | 0.974234109445724 | 0.0515317811085522 | 0.0257658905542761 |
| 56 | 0.93306994877034 | 0.133860102459318 | 0.0669300512296592 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 35 | 0.673076923076923 | NOK |
| 5% type I error level | 40 | 0.769230769230769 | NOK |
| 10% type I error level | 46 | 0.884615384615385 | NOK |
