| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 1.00534172096945 + 0.104125740041533X[t] + 0.953792248854353`y(t-1)`[t] -0.353608708255487`y(t-2)`[t] -0.120038817733203M1[t] -0.0200034714829910M2[t] -0.083701842016721M3[t] -0.093534271571743M4[t] + 0.120752434670518M5[t] -0.3598303808755M6[t] -0.287254502541916M7[t] -0.287172802964734M8[t] -0.217506131383949M9[t] + 0.0272760961556319M10[t] + 0.126370704489030M11[t] -0.000124744305243137t + 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) | 1.00534172096945 | 0.380607 | 2.6414 | 0.010933 | 0.005466 |
| X | 0.104125740041533 | 0.024644 | 4.2251 | 9.9e-05 | 4.9e-05 |
| `y(t-1)` | 0.953792248854353 | 0.154434 | 6.1761 | 0 | 0 |
| `y(t-2)` | -0.353608708255487 | 0.12094 | -2.9238 | 0.005146 | 0.002573 |
| M1 | -0.120038817733203 | 0.125125 | -0.9594 | 0.341907 | 0.170953 |
| M2 | -0.0200034714829910 | 0.129414 | -0.1546 | 0.877771 | 0.438886 |
| M3 | -0.083701842016721 | 0.132667 | -0.6309 | 0.530911 | 0.265456 |
| M4 | -0.093534271571743 | 0.134679 | -0.6945 | 0.490522 | 0.245261 |
| M5 | 0.120752434670518 | 0.169183 | 0.7137 | 0.478642 | 0.239321 |
| M6 | -0.3598303808755 | 0.127765 | -2.8164 | 0.00689 | 0.003445 |
| M7 | -0.287254502541916 | 0.143099 | -2.0074 | 0.050022 | 0.025011 |
| M8 | -0.287172802964734 | 0.137875 | -2.0828 | 0.042298 | 0.021149 |
| M9 | -0.217506131383949 | 0.149302 | -1.4568 | 0.151296 | 0.075648 |
| M10 | 0.0272760961556319 | 0.146293 | 0.1864 | 0.852833 | 0.426416 |
| M11 | 0.126370704489030 | 0.129964 | 0.9723 | 0.335466 | 0.167733 |
| t | -0.000124744305243137 | 0.001499 | -0.0832 | 0.934009 | 0.467004 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.963304547754958 |
| R-squared | 0.927955651725384 |
| Adjusted R-squared | 0.906766137526968 |
| F-TEST (value) | 43.7931536813967 |
| F-TEST (DF numerator) | 15 |
| F-TEST (DF denominator) | 51 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 0.199820452761184 |
| Sum Squared Residuals | 2.03633888042591 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 7.5 | 7.72967726491395 | -0.22967726491395 |
| 2 | 6.8 | 6.95484765389596 | -0.154847653895955 |
| 3 | 6.5 | 6.40017431898668 | 0.0998256810133238 |
| 4 | 6.6 | 6.35160556624895 | 0.248394433751053 |
| 5 | 7.6 | 7.53775984185539 | 0.0622401581446084 |
| 6 | 8 | 7.97548366003293 | 0.0245163399670651 |
| 7 | 8.1 | 8.07584298534753 | 0.0241570146524692 |
| 8 | 7.7 | 7.79024648010718 | -0.0902464801071824 |
| 9 | 7.5 | 7.44291063701543 | 0.0570893629845652 |
| 10 | 7.6 | 7.6382531537811 | -0.0382531537810969 |
| 11 | 7.8 | 7.7887856703001 | 0.0112143296999025 |
| 12 | 7.8 | 7.81768780045115 | -0.0176878004511470 |
| 13 | 7.8 | 7.6268024967616 | 0.173197503238397 |
| 14 | 7.5 | 7.8100136907398 | -0.310013690739799 |
| 15 | 7.5 | 7.46005290124452 | 0.0399470987554803 |
| 16 | 7.1 | 7.5561783398609 | -0.456178339860901 |
| 17 | 7.5 | 7.44088627227694 | 0.0591137277230566 |
| 18 | 7.5 | 7.48313909526962 | 0.0168609047303809 |
| 19 | 7.6 | 7.41414674599577 | 0.185853254004235 |
| 20 | 7.7 | 7.64484638820713 | 0.0551536117928682 |
| 21 | 7.7 | 7.77440666954256 | -0.0744066695425606 |
| 22 | 7.9 | 7.98370328195135 | -0.0837032819513493 |
| 23 | 8.1 | 8.07559268967146 | 0.0244073103285375 |
| 24 | 8.2 | 8.06913394899696 | 0.130866051003037 |
| 25 | 8.2 | 7.97362787019285 | 0.226372129807146 |
| 26 | 8.2 | 7.81951354722505 | 0.380486452774946 |
| 27 | 7.9 | 7.75569043238608 | 0.14430956761392 |
| 28 | 7.3 | 7.45959558386951 | -0.159595583869511 |
| 29 | 6.9 | 7.12426421693733 | -0.224264216937335 |
| 30 | 6.6 | 6.47420498249763 | 0.125795017502374 |
| 31 | 6.7 | 6.40196192517185 | 0.298038074828145 |
| 32 | 6.9 | 6.69709388384326 | 0.202906116156745 |
| 33 | 7 | 6.92203339006412 | 0.0779666099358808 |
| 34 | 7.1 | 7.1913483565328 | -0.0913483565327949 |
| 35 | 7.2 | 7.225385686571 | -0.0253856865709956 |
| 36 | 7.1 | 7.15890859183661 | -0.0589085918366104 |
| 37 | 6.9 | 6.90800493408718 | -0.00800493408717858 |
| 38 | 7 | 6.73797964304114 | 0.262020356958860 |
| 39 | 6.8 | 6.8402574947387 | -0.0402574947386995 |
| 40 | 6.4 | 6.60418100028201 | -0.204181000282014 |
| 41 | 6.7 | 6.74703700642392 | -0.0470370064239158 |
| 42 | 6.6 | 6.69391060453116 | -0.0939106045311558 |
| 43 | 6.4 | 6.56489990119741 | -0.164899901197414 |
| 44 | 6.3 | 6.18038264943266 | 0.119617350567341 |
| 45 | 6.2 | 6.22526709347386 | -0.0252670934738619 |
| 46 | 6.5 | 6.40990622264831 | 0.0900937773516862 |
| 47 | 6.8 | 6.88243750217909 | -0.0824375021790897 |
| 48 | 6.8 | 6.93599711556448 | -0.135997115564476 |
| 49 | 6.4 | 6.70975094104938 | -0.309750941049384 |
| 50 | 6.1 | 6.21989316336955 | -0.119893163369546 |
| 51 | 5.8 | 6.01137585717646 | -0.211375857176461 |
| 52 | 6.1 | 5.82136362113654 | 0.278636378863464 |
| 53 | 7.2 | 7.11497575448062 | 0.085024245519375 |
| 54 | 7.3 | 7.5773570558925 | -0.277357055892507 |
| 55 | 6.9 | 7.35621783572525 | -0.456217835725247 |
| 56 | 6.1 | 6.38743059840977 | -0.287430598409771 |
| 57 | 5.8 | 5.83538220990402 | -0.0353822099040236 |
| 58 | 6.2 | 6.07678898508644 | 0.123211014913555 |
| 59 | 7.1 | 7.02779845127835 | 0.0722015487216452 |
| 60 | 7.7 | 7.6182725431508 | 0.0817274568491964 |
| 61 | 7.9 | 7.75213649299503 | 0.147863507004969 |
| 62 | 7.7 | 7.7577523017285 | -0.0577523017285054 |
| 63 | 7.4 | 7.43244899546756 | -0.0324489954675638 |
| 64 | 7.5 | 7.20707588860209 | 0.292924111397909 |
| 65 | 8 | 7.93507690802579 | 0.0649230919742107 |
| 66 | 8.1 | 7.89590460177616 | 0.204095398223843 |
| 67 | 8 | 7.88693060656219 | 0.113069393437811 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 19 | 0.332229881297581 | 0.664459762595162 | 0.667770118702419 |
| 20 | 0.188239028032669 | 0.376478056065338 | 0.811760971967331 |
| 21 | 0.281226203205016 | 0.562452406410031 | 0.718773796794984 |
| 22 | 0.198039274471929 | 0.396078548943859 | 0.80196072552807 |
| 23 | 0.120925082598873 | 0.241850165197746 | 0.879074917401127 |
| 24 | 0.0985220455025425 | 0.197044091005085 | 0.901477954497458 |
| 25 | 0.0706106224314515 | 0.141221244862903 | 0.929389377568548 |
| 26 | 0.169664683165319 | 0.339329366330637 | 0.830335316834681 |
| 27 | 0.181585675886515 | 0.363171351773031 | 0.818414324113485 |
| 28 | 0.145696791788923 | 0.291393583577846 | 0.854303208211077 |
| 29 | 0.359500901624064 | 0.719001803248128 | 0.640499098375936 |
| 30 | 0.278762929323195 | 0.557525858646389 | 0.721237070676805 |
| 31 | 0.442465027247184 | 0.884930054494368 | 0.557534972752816 |
| 32 | 0.427682299674425 | 0.85536459934885 | 0.572317700325575 |
| 33 | 0.420640315736847 | 0.841280631473694 | 0.579359684263153 |
| 34 | 0.419922416055795 | 0.83984483211159 | 0.580077583944205 |
| 35 | 0.357794674660713 | 0.715589349321426 | 0.642205325339287 |
| 36 | 0.311997520699315 | 0.623995041398631 | 0.688002479300684 |
| 37 | 0.259969487158367 | 0.519938974316734 | 0.740030512841633 |
| 38 | 0.359580776380143 | 0.719161552760287 | 0.640419223619857 |
| 39 | 0.369297732500309 | 0.738595465000619 | 0.63070226749969 |
| 40 | 0.403752068603968 | 0.807504137207936 | 0.596247931396032 |
| 41 | 0.309537602621365 | 0.61907520524273 | 0.690462397378635 |
| 42 | 0.257727750703199 | 0.515455501406399 | 0.7422722492968 |
| 43 | 0.278482008842884 | 0.556964017685768 | 0.721517991157116 |
| 44 | 0.574906676795454 | 0.850186646409093 | 0.425093323204546 |
| 45 | 0.498458312705182 | 0.996916625410364 | 0.501541687294818 |
| 46 | 0.566118724190153 | 0.867762551619694 | 0.433881275809847 |
| 47 | 0.552672427027186 | 0.894655145945629 | 0.447327572972814 |
| 48 | 0.919504750405178 | 0.160990499189644 | 0.0804952495948221 |
| 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 | 0 | 0 | OK |
| 10% type I error level | 0 | 0 | OK |
