| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 59.5264480874317 -6.82688172043011X[t] -0.332459016393442t + 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) | 59.5264480874317 | 1.374036 | 43.3223 | 0 | 0 |
| X | -6.82688172043011 | 2.426145 | -2.8139 | 0.006672 | 0.003336 |
| t | -0.332459016393442 | 0.068889 | -4.826 | 1.1e-05 | 5e-06 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.889129937195268 |
| R-squared | 0.790552045216862 |
| Adjusted R-squared | 0.783329701948478 |
| F-TEST (value) | 109.459217852122 |
| F-TEST (DF numerator) | 2 |
| F-TEST (DF denominator) | 58 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 4.73656273647105 |
| Sum Squared Residuals | 1301.23154027851 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 56.6 | 59.1939890710383 | -2.59398907103832 |
| 2 | 56 | 58.8615300546448 | -2.86153005464482 |
| 3 | 54.8 | 58.5290710382514 | -3.72907103825137 |
| 4 | 52.7 | 58.1966120218579 | -5.49661202185791 |
| 5 | 50.9 | 57.8641530054645 | -6.96415300546448 |
| 6 | 50.6 | 57.531693989071 | -6.93169398907103 |
| 7 | 52.1 | 57.1992349726776 | -5.09923497267759 |
| 8 | 53.3 | 56.8667759562841 | -3.56677595628415 |
| 9 | 53.9 | 56.5343169398907 | -2.63431693989071 |
| 10 | 54.3 | 56.2018579234973 | -1.90185792349727 |
| 11 | 54.2 | 55.8693989071038 | -1.66939890710382 |
| 12 | 54.2 | 55.5369398907104 | -1.33693989071037 |
| 13 | 53.5 | 55.204480874317 | -1.70448087431694 |
| 14 | 51.4 | 54.8720218579235 | -3.47202185792349 |
| 15 | 50.5 | 54.5395628415300 | -4.03956284153005 |
| 16 | 50.3 | 54.2071038251366 | -3.90710382513661 |
| 17 | 49.8 | 53.8746448087432 | -4.07464480874317 |
| 18 | 50.7 | 53.5421857923497 | -2.84218579234972 |
| 19 | 52.8 | 53.2097267759563 | -0.409726775956284 |
| 20 | 55.3 | 52.8772677595628 | 2.42273224043716 |
| 21 | 57.3 | 52.5448087431694 | 4.7551912568306 |
| 22 | 57.5 | 52.212349726776 | 5.28765027322405 |
| 23 | 56.8 | 51.8798907103825 | 4.92010928961749 |
| 24 | 56.4 | 51.5474316939891 | 4.85256830601093 |
| 25 | 56.3 | 51.2149726775956 | 5.08502732240437 |
| 26 | 56.4 | 50.8825136612022 | 5.51748633879781 |
| 27 | 57 | 50.5500546448087 | 6.44994535519126 |
| 28 | 57.9 | 50.2175956284153 | 7.6824043715847 |
| 29 | 58.9 | 49.8851366120219 | 9.01486338797814 |
| 30 | 58.8 | 49.5526775956284 | 9.24732240437158 |
| 31 | 56.5 | 42.3933368588049 | 14.1066631411951 |
| 32 | 51.9 | 42.0608778424114 | 9.83912215758858 |
| 33 | 47.4 | 41.728418826018 | 5.67158117398202 |
| 34 | 44.9 | 41.3959598096245 | 3.50404019037546 |
| 35 | 43.9 | 41.0635007932311 | 2.83649920676891 |
| 36 | 43.4 | 40.7310417768376 | 2.66895822316235 |
| 37 | 42.9 | 40.3985827604442 | 2.50141723955579 |
| 38 | 42.6 | 40.0661237440508 | 2.53387625594924 |
| 39 | 42.2 | 39.7336647276573 | 2.46633527234268 |
| 40 | 41.2 | 39.4012057112639 | 1.79879428873612 |
| 41 | 40.2 | 39.0687466948704 | 1.13125330512957 |
| 42 | 39.3 | 38.736287678477 | 0.563712321523002 |
| 43 | 38.5 | 38.4038286620836 | 0.0961713379164476 |
| 44 | 38.3 | 38.0713696456901 | 0.228630354309887 |
| 45 | 37.9 | 37.7389106292967 | 0.161089370703331 |
| 46 | 37.6 | 37.4064516129032 | 0.193548387096776 |
| 47 | 37.3 | 37.0739925965098 | 0.226007403490214 |
| 48 | 36 | 36.7415335801163 | -0.74153358011634 |
| 49 | 34.5 | 36.4090745637229 | -1.90907456372290 |
| 50 | 33.5 | 36.0766155473295 | -2.57661554732946 |
| 51 | 32.9 | 35.744156530936 | -2.84415653093601 |
| 52 | 32.9 | 35.4116975145426 | -2.51169751454257 |
| 53 | 32.8 | 35.0792384981491 | -2.27923849814913 |
| 54 | 31.9 | 34.7467794817557 | -2.84677948175569 |
| 55 | 30.5 | 34.4143204653622 | -3.91432046536224 |
| 56 | 29.2 | 34.0818614489688 | -4.8818614489688 |
| 57 | 28.7 | 33.7494024325754 | -5.04940243257536 |
| 58 | 28.4 | 33.4169434161819 | -5.01694341618192 |
| 59 | 28 | 33.0844843997885 | -5.08448439978848 |
| 60 | 27.4 | 32.7520253833950 | -5.35202538339503 |
| 61 | 26.9 | 32.4195663670016 | -5.51956636700159 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 6 | 0.00377096022939169 | 0.00754192045878337 | 0.996229039770608 |
| 7 | 0.0138452218493712 | 0.0276904436987424 | 0.986154778150629 |
| 8 | 0.0261988986077832 | 0.0523977972155665 | 0.973801101392217 |
| 9 | 0.028903627041348 | 0.057807254082696 | 0.971096372958652 |
| 10 | 0.0249323656331431 | 0.0498647312662862 | 0.975067634366857 |
| 11 | 0.0167079535486792 | 0.0334159070973584 | 0.98329204645132 |
| 12 | 0.0101089694240895 | 0.0202179388481790 | 0.98989103057591 |
| 13 | 0.00540460417068657 | 0.0108092083413731 | 0.994595395829313 |
| 14 | 0.00434926065613839 | 0.00869852131227678 | 0.995650739343862 |
| 15 | 0.00508673706585306 | 0.0101734741317061 | 0.994913262934147 |
| 16 | 0.00684055219726758 | 0.0136811043945352 | 0.993159447802732 |
| 17 | 0.0146255397083463 | 0.0292510794166926 | 0.985374460291654 |
| 18 | 0.0351390009741941 | 0.0702780019483882 | 0.964860999025806 |
| 19 | 0.107204950931757 | 0.214409901863514 | 0.892795049068243 |
| 20 | 0.357239695961125 | 0.71447939192225 | 0.642760304038875 |
| 21 | 0.688163865287569 | 0.623672269424863 | 0.311836134712431 |
| 22 | 0.831571325060838 | 0.336857349878324 | 0.168428674939162 |
| 23 | 0.882565816154924 | 0.234868367690152 | 0.117434183845076 |
| 24 | 0.910361636012744 | 0.179276727974511 | 0.0896383639872557 |
| 25 | 0.92934467961954 | 0.141310640760919 | 0.0706553203804593 |
| 26 | 0.942952190438796 | 0.114095619122408 | 0.0570478095612038 |
| 27 | 0.948548396850819 | 0.102903206298362 | 0.0514516031491811 |
| 28 | 0.94664130894065 | 0.106717382118699 | 0.0533586910593494 |
| 29 | 0.940742134286733 | 0.118515731426534 | 0.0592578657132672 |
| 30 | 0.926111161892818 | 0.147777676214365 | 0.0738888381071825 |
| 31 | 0.999943847260043 | 0.000112305479913166 | 5.61527399565828e-05 |
| 32 | 0.999999999956288 | 8.74234017493661e-11 | 4.37117008746830e-11 |
| 33 | 0.999999999999357 | 1.28592547458165e-12 | 6.42962737290823e-13 |
| 34 | 0.999999999999593 | 8.13360907797723e-13 | 4.06680453898861e-13 |
| 35 | 0.99999999999972 | 5.58146056209201e-13 | 2.79073028104601e-13 |
| 36 | 0.999999999999616 | 7.67643050327044e-13 | 3.83821525163522e-13 |
| 37 | 0.999999999999166 | 1.66772828386272e-12 | 8.33864141931358e-13 |
| 38 | 0.999999999997258 | 5.48321706618679e-12 | 2.74160853309340e-12 |
| 39 | 0.999999999992086 | 1.58281732782637e-11 | 7.91408663913185e-12 |
| 40 | 0.999999999973194 | 5.36121284965216e-11 | 2.68060642482608e-11 |
| 41 | 0.999999999917361 | 1.65277732924871e-10 | 8.26388664624354e-11 |
| 42 | 0.999999999808153 | 3.83694812259176e-10 | 1.91847406129588e-10 |
| 43 | 0.99999999968975 | 6.20497878330422e-10 | 3.10248939165211e-10 |
| 44 | 0.999999998863029 | 2.27394251997572e-09 | 1.13697125998786e-09 |
| 45 | 0.99999999479187 | 1.04162583974537e-08 | 5.20812919872685e-09 |
| 46 | 0.99999998069463 | 3.86107393863849e-08 | 1.93053696931924e-08 |
| 47 | 0.999999981185573 | 3.76288546090544e-08 | 1.88144273045272e-08 |
| 48 | 0.999999953324416 | 9.33511676786104e-08 | 4.66755838393052e-08 |
| 49 | 0.999999730413843 | 5.39172314394677e-07 | 2.69586157197338e-07 |
| 50 | 0.999998899345238 | 2.20130952438051e-06 | 1.10065476219025e-06 |
| 51 | 0.999995943193881 | 8.1136122375806e-06 | 4.0568061187903e-06 |
| 52 | 0.999971270239141 | 5.7459521717566e-05 | 2.8729760858783e-05 |
| 53 | 0.999920402852088 | 0.000159194295824794 | 7.95971479123969e-05 |
| 54 | 0.99994671657612 | 0.000106566847758278 | 5.32834238791391e-05 |
| 55 | 0.999981293268923 | 3.74134621533131e-05 | 1.87067310766566e-05 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 27 | 0.54 | NOK |
| 5% type I error level | 35 | 0.7 | NOK |
| 10% type I error level | 38 | 0.76 | NOK |
