| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 0.599180932557525 + 0.690170760852934X[t] + 0.799964668425404`Y-1`[t] -0.415248318667088`Y-2`[t] + 0.0905745590290102M1[t] + 0.0163192906230318M2[t] + 0.105507076694788M3[t] + 0.0676117496179909M4[t] + 0.0712801719111382M5[t] + 0.0656905940929301M6[t] + 0.00799840973995277M7[t] + 0.0361116251349147M8[t] + 0.0549776843366118M9[t] -0.0445931299432913M10[t] -0.0115226106672737M11[t] -0.00761139671202985t + 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) | 0.599180932557525 | 0.116311 | 5.1515 | 7e-06 | 4e-06 |
| X | 0.690170760852934 | 0.117726 | 5.8625 | 1e-06 | 0 |
| `Y-1` | 0.799964668425404 | 0.179596 | 4.4543 | 6.6e-05 | 3.3e-05 |
| `Y-2` | -0.415248318667088 | 0.110474 | -3.7588 | 0.000546 | 0.000273 |
| M1 | 0.0905745590290102 | 0.073231 | 1.2368 | 0.223363 | 0.111682 |
| M2 | 0.0163192906230318 | 0.072225 | 0.226 | 0.82239 | 0.411195 |
| M3 | 0.105507076694788 | 0.071539 | 1.4748 | 0.148091 | 0.074046 |
| M4 | 0.0676117496179909 | 0.075284 | 0.8981 | 0.374511 | 0.187255 |
| M5 | 0.0712801719111382 | 0.074097 | 0.962 | 0.341838 | 0.170919 |
| M6 | 0.0656905940929301 | 0.072807 | 0.9023 | 0.372322 | 0.186161 |
| M7 | 0.00799840973995277 | 0.07443 | 0.1075 | 0.914959 | 0.45748 |
| M8 | 0.0361116251349147 | 0.073909 | 0.4886 | 0.627798 | 0.313899 |
| M9 | 0.0549776843366118 | 0.077543 | 0.709 | 0.482437 | 0.241218 |
| M10 | -0.0445931299432913 | 0.07592 | -0.5874 | 0.560257 | 0.280128 |
| M11 | -0.0115226106672737 | 0.075387 | -0.1528 | 0.879288 | 0.439644 |
| t | -0.00761139671202985 | 0.001516 | -5.0195 | 1.1e-05 | 6e-06 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.996738388731846 |
| R-squared | 0.993487415571757 |
| Adjusted R-squared | 0.991045196411166 |
| F-TEST (value) | 406.796994963937 |
| F-TEST (DF numerator) | 15 |
| F-TEST (DF denominator) | 40 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 0.105929688689683 |
| Sum Squared Residuals | 0.44884395783573 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 2.08 | 2.14437343998530 | -0.0643734399853037 |
| 2 | 2.06 | 2.10311564766674 | -0.0431156476667425 |
| 3 | 2.06 | 2.15623529409795 | -0.0962352940979458 |
| 4 | 2.08 | 2.11903353668246 | -0.0390335366824608 |
| 5 | 2.07 | 2.13108985563209 | -0.0610898556320865 |
| 6 | 2.06 | 2.10158426804425 | -0.0415842680442524 |
| 7 | 2.07 | 2.03243352348166 | 0.0375664765183375 |
| 8 | 2.06 | 2.06508747203552 | -0.00508747203551918 |
| 9 | 2.09 | 2.06419000465426 | 0.0258099953457381 |
| 10 | 2.07 | 1.98515921690176 | 0.0848407830982383 |
| 11 | 2.09 | 1.98216159653723 | 0.107838403462771 |
| 12 | 2.28 | 2.18291976044756 | 0.0970802395524438 |
| 13 | 2.33 | 2.40957124339202 | -0.079571243392021 |
| 14 | 2.35 | 2.28880563114854 | 0.0611943688514634 |
| 15 | 2.52 | 2.53816158815665 | -0.0181615881566496 |
| 16 | 2.63 | 2.6203438916268 | 0.00965610837320004 |
| 17 | 2.58 | 2.63380481656131 | -0.0538048165613066 |
| 18 | 2.7 | 2.70747098376965 | -0.00747098376965239 |
| 19 | 2.81 | 2.75892557884905 | 0.0510744211509518 |
| 20 | 2.97 | 2.99013640303196 | -0.0201364030319573 |
| 21 | 3.04 | 3.08370809741631 | -0.0437080974163098 |
| 22 | 3.28 | 3.13862637244065 | 0.141373627559345 |
| 23 | 3.33 | 3.32700963312004 | 0.00299036687995733 |
| 24 | 3.5 | 3.44380217422969 | 0.0561978257703104 |
| 25 | 3.56 | 3.64199691424563 | -0.081996914245634 |
| 26 | 3.57 | 3.53753591505974 | 0.0324640849402547 |
| 27 | 3.69 | 3.77473974219693 | -0.0847397421969333 |
| 28 | 3.82 | 3.82107629543248 | -0.00107629543248452 |
| 29 | 3.79 | 3.87129892966885 | -0.0812989296688536 |
| 30 | 3.96 | 3.95265942387237 | 0.0073405761276342 |
| 31 | 4.06 | 4.03580728599969 | 0.0241927140003100 |
| 32 | 4.05 | 4.06571335735176 | -0.0157133573517571 |
| 33 | 4.03 | 4.02744354129046 | 0.00255645870953857 |
| 34 | 3.94 | 3.90841452011669 | 0.0315854798833081 |
| 35 | 4.02 | 3.87018178889573 | 0.149818211104265 |
| 36 | 3.88 | 3.97546252500505 | -0.0954625250050485 |
| 37 | 4.02 | 3.91321076824911 | 0.106789231750894 |
| 38 | 4.03 | 4.00147392132405 | 0.0285260786759544 |
| 39 | 4.09 | 4.03291519275463 | 0.0570848072453656 |
| 40 | 3.99 | 4.03125386588466 | -0.0412538658846602 |
| 41 | 4.01 | 3.92239952550321 | 0.0876004744967872 |
| 42 | 4.01 | 3.96672267620819 | 0.0432773237918087 |
| 43 | 4.19 | 4.06565681898308 | 0.124343181016924 |
| 44 | 4.3 | 4.23015227798258 | 0.0698477220174186 |
| 45 | 4.27 | 4.25465835663897 | 0.0153416433610332 |
| 46 | 3.82 | 4.07779989054089 | -0.257799890540892 |
| 47 | 3.15 | 3.41064698144699 | -0.260646981446994 |
| 48 | 2.49 | 2.54781554031771 | -0.0578155403177057 |
| 49 | 1.81 | 1.69084763412794 | 0.119152365872065 |
| 50 | 1.26 | 1.33906888480093 | -0.07906888480093 |
| 51 | 1.06 | 0.917948182793837 | 0.142051817206163 |
| 52 | 0.84 | 0.768292410373594 | 0.0717075896264055 |
| 53 | 0.78 | 0.67140687263454 | 0.108593127365460 |
| 54 | 0.7 | 0.701562648105538 | -0.00156264810553799 |
| 55 | 0.36 | 0.597176792686524 | -0.237176792686524 |
| 56 | 0.35 | 0.378910489598185 | -0.028910489598185 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 19 | 0.0143384346741444 | 0.0286768693482887 | 0.985661565325856 |
| 20 | 0.00252929998960038 | 0.00505859997920076 | 0.9974707000104 |
| 21 | 0.000468839701643676 | 0.000937679403287353 | 0.999531160298356 |
| 22 | 0.000512949299928806 | 0.00102589859985761 | 0.999487050700071 |
| 23 | 9.58819342595953e-05 | 0.000191763868519191 | 0.99990411806574 |
| 24 | 2.08509321733568e-05 | 4.17018643467136e-05 | 0.999979149067827 |
| 25 | 4.62565115711951e-06 | 9.25130231423902e-06 | 0.999995374348843 |
| 26 | 7.49288453113313e-07 | 1.49857690622663e-06 | 0.999999250711547 |
| 27 | 6.8412628114168e-07 | 1.36825256228336e-06 | 0.999999315873719 |
| 28 | 1.29571307738209e-07 | 2.59142615476419e-07 | 0.999999870428692 |
| 29 | 6.43024642337561e-08 | 1.28604928467512e-07 | 0.999999935697536 |
| 30 | 2.03833527143946e-08 | 4.07667054287893e-08 | 0.999999979616647 |
| 31 | 4.24973295087452e-09 | 8.49946590174904e-09 | 0.999999995750267 |
| 32 | 2.80244334143799e-09 | 5.60488668287597e-09 | 0.999999997197557 |
| 33 | 7.76124823151533e-09 | 1.55224964630307e-08 | 0.999999992238752 |
| 34 | 2.44315118144257e-07 | 4.88630236288515e-07 | 0.999999755684882 |
| 35 | 5.04340426487219e-07 | 1.00868085297444e-06 | 0.999999495659573 |
| 36 | 1.25946645896411e-05 | 2.51893291792822e-05 | 0.99998740533541 |
| 37 | 3.73895208304896e-06 | 7.47790416609791e-06 | 0.999996261047917 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 18 | 0.947368421052632 | NOK |
| 5% type I error level | 19 | 1 | NOK |
| 10% type I error level | 19 | 1 | NOK |
