| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 13.0121448258197 + 0.256102930340177X[t] + 1.61764090464894M1[t] -0.368594387114941M2[t] -1.26533457658441M3[t] + 0.947682584358821M4[t] + 1.44220586859912M5[t] + 0.81233944587344M6[t] + 0.151780623896049M7[t] + 0.213377436825695M8[t] -0.102263491369389M9[t] + 2.06583577579154M10[t] + 0.236982839056767M11[t] + 0.11686151426312t + 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) | 13.0121448258197 | 0.587842 | 22.1354 | 0 | 0 |
| X | 0.256102930340177 | 0.029271 | 8.7494 | 0 | 0 |
| M1 | 1.61764090464894 | 0.6812 | 2.3747 | 0.020834 | 0.010417 |
| M2 | -0.368594387114941 | 0.710692 | -0.5186 | 0.605951 | 0.302975 |
| M3 | -1.26533457658441 | 0.710527 | -1.7808 | 0.080087 | 0.040043 |
| M4 | 0.947682584358821 | 0.709946 | 1.3349 | 0.187049 | 0.093524 |
| M5 | 1.44220586859912 | 0.708683 | 2.0351 | 0.046346 | 0.023173 |
| M6 | 0.81233944587344 | 0.70755 | 1.1481 | 0.255561 | 0.12778 |
| M7 | 0.151780623896049 | 0.706947 | 0.2147 | 0.830743 | 0.415371 |
| M8 | 0.213377436825695 | 0.706391 | 0.3021 | 0.763663 | 0.381832 |
| M9 | -0.102263491369389 | 0.706137 | -0.1448 | 0.885346 | 0.442673 |
| M10 | 2.06583577579154 | 0.705959 | 2.9263 | 0.004864 | 0.002432 |
| M11 | 0.236982839056767 | 0.705858 | 0.3357 | 0.73826 | 0.36913 |
| t | 0.11686151426312 | 0.007561 | 15.456 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.910055945215638 |
| R-squared | 0.828201823422328 |
| Adjusted R-squared | 0.790347987905214 |
| F-TEST (value) | 21.8789407231372 |
| F-TEST (DF numerator) | 13 |
| F-TEST (DF denominator) | 59 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 1.22252474545640 |
| Sum Squared Residuals | 88.1794384419416 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 14.2 | 14.5417649004596 | -0.341764900459630 |
| 2 | 13.5 | 12.826052881163 | 0.673947118836999 |
| 3 | 11.9 | 12.1486153780927 | -0.248615378092716 |
| 4 | 14.6 | 14.6833763975712 | -0.0833763975712067 |
| 5 | 15.6 | 15.0386582657345 | 0.561341734265546 |
| 6 | 14.1 | 14.4744327712039 | -0.374432771203856 |
| 7 | 14.9 | 14.2380589798978 | 0.661941020102203 |
| 8 | 14.2 | 14.2628555488865 | -0.062855548886458 |
| 9 | 14.6 | 14.2177378931586 | 0.382262106841401 |
| 10 | 17.2 | 16.6819707258208 | 0.518029274179232 |
| 11 | 15.4 | 15.3285234058254 | 0.0714765941746366 |
| 12 | 14.3 | 15.2596226670998 | -0.959622667099753 |
| 13 | 17.5 | 16.9429044999438 | 0.557095500056226 |
| 14 | 14.5 | 15.1759718945791 | -0.675971894579086 |
| 15 | 14.4 | 15.0363505452232 | -0.636350545223174 |
| 16 | 16.6 | 17.2893983413275 | -0.689398341327476 |
| 17 | 16.7 | 17.6446802094907 | -0.944680209490723 |
| 18 | 16.6 | 17.0036238358581 | -0.403623835858072 |
| 19 | 16.9 | 16.3062647699397 | 0.593735230060303 |
| 20 | 15.7 | 16.6896054414046 | -0.989605441404605 |
| 21 | 16.4 | 16.0042304598263 | 0.395769540173696 |
| 22 | 18.4 | 17.4952721571958 | 0.904727842804195 |
| 23 | 16.9 | 15.4503469252819 | 1.44965307471808 |
| 24 | 16.5 | 15.3302256004883 | 1.16977439951172 |
| 25 | 18.3 | 17.7305956382848 | 0.56940436171521 |
| 26 | 15.1 | 15.4514571722398 | -0.351457172239753 |
| 27 | 15.7 | 14.4666961527613 | 1.23330384723874 |
| 28 | 18.1 | 16.4380307254914 | 1.66196927450864 |
| 29 | 16.8 | 17.3055184543350 | -0.505518454334962 |
| 30 | 18.9 | 17.3815502856548 | 1.51844971434519 |
| 31 | 19 | 17.0939559082807 | 1.90604409171929 |
| 32 | 18.1 | 17.9382818543579 | 0.161718145642063 |
| 33 | 17.8 | 17.790723026494 | 0.0092769735059921 |
| 34 | 21.5 | 20.7415514268025 | 0.758448573197485 |
| 35 | 17.1 | 18.6966261948886 | -1.59662619488863 |
| 36 | 18.7 | 19.1655416098774 | -0.465541609877394 |
| 37 | 19 | 20.1573455308029 | -1.15734553080294 |
| 38 | 16.4 | 18.7745673209485 | -2.37456732094852 |
| 39 | 16.9 | 17.4312621989938 | -0.531262198993776 |
| 40 | 18.6 | 19.8123614602682 | -1.21236146026816 |
| 41 | 19.3 | 20.7822903612478 | -1.48229036124783 |
| 42 | 19.4 | 19.9619619363771 | -0.561961936377062 |
| 43 | 17.6 | 19.2133822843906 | -1.61338228439065 |
| 44 | 18.6 | 19.0589068021412 | -0.458906802141183 |
| 45 | 18.1 | 18.9369582673113 | -0.836958267311272 |
| 46 | 20.4 | 21.5036322721095 | -1.10363227210951 |
| 47 | 18.1 | 19.7660305566038 | -1.66603055660384 |
| 48 | 19.6 | 19.3129754223680 | 0.287024577632032 |
| 49 | 19.9 | 21.021867548246 | -1.12186754824601 |
| 50 | 19.2 | 19.2805452359153 | -0.0805452359153402 |
| 51 | 17.8 | 18.8336003701512 | -1.03360037015121 |
| 52 | 19.2 | 20.8049349428813 | -1.60493494288133 |
| 53 | 22 | 21.1602168110446 | 0.839783188955432 |
| 54 | 21.1 | 20.4679398513439 | 0.632060148656116 |
| 55 | 19.5 | 19.9754631296976 | -0.475463129697647 |
| 56 | 22.2 | 20.1027008708224 | 2.09729912917762 |
| 57 | 20.9 | 20.3905170245367 | 0.50948297546325 |
| 58 | 22.2 | 22.3169337034845 | -0.116933703484549 |
| 59 | 23.5 | 20.9890966765232 | 2.51090332347684 |
| 60 | 21.5 | 20.2799386119471 | 1.22006138805289 |
| 61 | 24.3 | 22.3729851333354 | 1.92701486666459 |
| 62 | 22.8 | 19.9914054951543 | 2.80859450484570 |
| 63 | 20.3 | 19.0834753547779 | 1.21652464522214 |
| 64 | 23.7 | 21.7718981324605 | 1.92810186753954 |
| 65 | 23.3 | 21.7686358981475 | 1.53136410185254 |
| 66 | 19.6 | 20.4104913195623 | -0.810491319562317 |
| 67 | 18 | 19.0728749277935 | -1.0728749277935 |
| 68 | 17.3 | 18.0476494823874 | -0.747649482387438 |
| 69 | 16.8 | 17.2598333286731 | -0.459833328673067 |
| 70 | 18.2 | 19.1606397145868 | -0.960639714586848 |
| 71 | 16.5 | 17.2693762408771 | -0.769376240877074 |
| 72 | 16 | 17.2516960882195 | -1.25169608821950 |
| 73 | 18.4 | 18.8325367489274 | -0.43253674892745 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 17 | 0.183982716470532 | 0.367965432941063 | 0.816017283529468 |
| 18 | 0.089408229599902 | 0.178816459199804 | 0.910591770400098 |
| 19 | 0.0369825528045665 | 0.073965105609133 | 0.963017447195433 |
| 20 | 0.0168593194481958 | 0.0337186388963915 | 0.983140680551804 |
| 21 | 0.00606274128471611 | 0.0121254825694322 | 0.993937258715284 |
| 22 | 0.00213873367570922 | 0.00427746735141844 | 0.99786126632429 |
| 23 | 0.000877952850211543 | 0.00175590570042309 | 0.999122047149788 |
| 24 | 0.000500127227713009 | 0.00100025445542602 | 0.999499872772287 |
| 25 | 0.000175949347069217 | 0.000351898694138435 | 0.99982405065293 |
| 26 | 0.000327766353261325 | 0.000655532706522649 | 0.999672233646739 |
| 27 | 0.000176170282482571 | 0.000352340564965143 | 0.999823829717517 |
| 28 | 0.000139280419034825 | 0.00027856083806965 | 0.999860719580965 |
| 29 | 0.000387296825746611 | 0.000774593651493222 | 0.999612703174253 |
| 30 | 0.00121702507689980 | 0.00243405015379961 | 0.9987829749231 |
| 31 | 0.00966153107247792 | 0.0193230621449558 | 0.990338468927522 |
| 32 | 0.00791705079302794 | 0.0158341015860559 | 0.992082949206972 |
| 33 | 0.00881278572329983 | 0.0176255714465997 | 0.9911872142767 |
| 34 | 0.0249667376777880 | 0.0499334753555761 | 0.975033262322212 |
| 35 | 0.0631751007789455 | 0.126350201557891 | 0.936824899221054 |
| 36 | 0.0460755160593644 | 0.0921510321187288 | 0.953924483940636 |
| 37 | 0.0506429218469786 | 0.101285843693957 | 0.949357078153021 |
| 38 | 0.100352052426032 | 0.200704104852063 | 0.899647947573968 |
| 39 | 0.116760443859033 | 0.233520887718066 | 0.883239556140967 |
| 40 | 0.131330755850001 | 0.262661511700003 | 0.868669244149999 |
| 41 | 0.101606439795886 | 0.203212879591773 | 0.898393560204114 |
| 42 | 0.0967916323784512 | 0.193583264756902 | 0.903208367621549 |
| 43 | 0.208065877742286 | 0.416131755484572 | 0.791934122257714 |
| 44 | 0.155928621388159 | 0.311857242776318 | 0.844071378611841 |
| 45 | 0.135619788802747 | 0.271239577605494 | 0.864380211197253 |
| 46 | 0.126782148691516 | 0.253564297383032 | 0.873217851308484 |
| 47 | 0.171892418163188 | 0.343784836326376 | 0.828107581836812 |
| 48 | 0.176900752829718 | 0.353801505659436 | 0.823099247170282 |
| 49 | 0.141657152873211 | 0.283314305746421 | 0.85834284712679 |
| 50 | 0.148293896358292 | 0.296587792716583 | 0.851706103641708 |
| 51 | 0.144784379555341 | 0.289568759110682 | 0.85521562044466 |
| 52 | 0.518158062653828 | 0.963683874692344 | 0.481841937346172 |
| 53 | 0.574300613255084 | 0.851398773489832 | 0.425699386744916 |
| 54 | 0.47290921779597 | 0.94581843559194 | 0.52709078220403 |
| 55 | 0.405269165199608 | 0.810538330399216 | 0.594730834800392 |
| 56 | 0.627485981897932 | 0.745028036204136 | 0.372514018102068 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 9 | 0.225 | NOK |
| 5% type I error level | 15 | 0.375 | NOK |
| 10% type I error level | 17 | 0.425 | NOK |
