| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 100.335200181349 -2.32705377694079X[t] + 0.149120980679454M1[t] + 1.09636674339122M2[t] + 0.95194583943642M3[t] + 0.702524935481617M4[t] + 0.419770698193481M5[t] + 0.143683127572011M6[t] + 0.132595556950542M7[t] + 0.809350282485877M8[t] + 0.691596045197743M9[t] + 0.462175141242941M10[t] + 0.239420903954802M11[t] + 0.281087570621469t + 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) | 100.335200181349 | 1.030615 | 97.3547 | 0 | 0 |
| X | -2.32705377694079 | 0.902121 | -2.5795 | 0.01245 | 0.006225 |
| M1 | 0.149120980679454 | 1.249786 | 0.1193 | 0.905436 | 0.452718 |
| M2 | 1.09636674339122 | 1.248478 | 0.8782 | 0.383479 | 0.191739 |
| M3 | 0.95194583943642 | 1.247459 | 0.7631 | 0.448492 | 0.224246 |
| M4 | 0.702524935481617 | 1.24673 | 0.5635 | 0.575271 | 0.287635 |
| M5 | 0.419770698193481 | 1.246293 | 0.3368 | 0.737472 | 0.368736 |
| M6 | 0.143683127572011 | 1.246147 | 0.1153 | 0.908604 | 0.454302 |
| M7 | 0.132595556950542 | 1.246293 | 0.1064 | 0.915639 | 0.457819 |
| M8 | 0.809350282485877 | 1.244656 | 0.6503 | 0.518092 | 0.259046 |
| M9 | 0.691596045197743 | 1.243634 | 0.5561 | 0.580276 | 0.290138 |
| M10 | 0.462175141242941 | 1.242904 | 0.3719 | 0.711359 | 0.355679 |
| M11 | 0.239420903954802 | 1.242465 | 0.1927 | 0.847868 | 0.423934 |
| t | 0.281087570621469 | 0.019061 | 14.7469 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.93492067185643 |
| R-squared | 0.874076662664479 |
| Adjusted R-squared | 0.845852466365138 |
| F-TEST (value) | 30.9690541191741 |
| F-TEST (DF numerator) | 13 |
| F-TEST (DF denominator) | 58 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 2.15175963867601 |
| Sum Squared Residuals | 268.544033472836 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 103.52 | 100.765408732649 | 2.7545912673507 |
| 2 | 103.5 | 101.993742065983 | 1.50625793401684 |
| 3 | 103.52 | 102.130408732650 | 1.38959126735019 |
| 4 | 103.53 | 102.162075399316 | 1.36792460068352 |
| 5 | 103.53 | 102.160408732650 | 1.36959126735019 |
| 6 | 103.53 | 102.165408732650 | 1.36459126735020 |
| 7 | 103.52 | 102.435408732650 | 1.08459126735019 |
| 8 | 103.54 | 103.393251028807 | 0.146748971193397 |
| 9 | 103.59 | 103.55658436214 | 0.0334156378600615 |
| 10 | 103.59 | 103.608251028807 | -0.0182510288066067 |
| 11 | 103.59 | 103.66658436214 | -0.0765843621399367 |
| 12 | 103.59 | 103.708251028807 | -0.118251028806602 |
| 13 | 103.63 | 104.138459580108 | -0.508459580107533 |
| 14 | 103.74 | 105.366792913441 | -1.62679291344077 |
| 15 | 103.7 | 105.503459580107 | -1.80345958010743 |
| 16 | 103.72 | 105.535126246774 | -1.8151262467741 |
| 17 | 103.81 | 105.533459580107 | -1.72345958010743 |
| 18 | 103.8 | 105.538459580107 | -1.73845958010743 |
| 19 | 104.22 | 105.808459580107 | -1.58845958010743 |
| 20 | 106.91 | 104.439248099323 | 2.47075190067656 |
| 21 | 107.06 | 104.602581432657 | 2.45741856734324 |
| 22 | 107.17 | 104.654248099323 | 2.51575190067657 |
| 23 | 107.25 | 104.712581432657 | 2.53741856734324 |
| 24 | 107.28 | 104.754248099323 | 2.52575190067657 |
| 25 | 107.24 | 105.184456650624 | 2.05554334937564 |
| 26 | 107.23 | 106.412789983958 | 0.817210016042422 |
| 27 | 107.34 | 106.549456650624 | 0.790543349375747 |
| 28 | 107.34 | 106.581123317291 | 0.758876682709082 |
| 29 | 107.3 | 106.579456650624 | 0.720543349375744 |
| 30 | 107.24 | 106.584456650624 | 0.655543349375742 |
| 31 | 107.3 | 106.854456650624 | 0.445543349375744 |
| 32 | 107.32 | 107.812298946781 | -0.492298946781062 |
| 33 | 107.28 | 107.975632280114 | -0.695632280114389 |
| 34 | 107.33 | 108.027298946781 | -0.697298946781059 |
| 35 | 107.33 | 108.085632280114 | -0.755632280114389 |
| 36 | 107.33 | 108.127298946781 | -0.797298946781055 |
| 37 | 107.28 | 108.557507498082 | -1.27750749808197 |
| 38 | 107.28 | 109.785840831415 | -2.50584083141520 |
| 39 | 107.29 | 109.922507498082 | -2.63250749808187 |
| 40 | 107.29 | 109.954174164749 | -2.66417416474854 |
| 41 | 107.23 | 109.952507498082 | -2.72250749808187 |
| 42 | 107.24 | 109.957507498082 | -2.71750749808188 |
| 43 | 107.24 | 110.227507498082 | -2.98750749808188 |
| 44 | 107.2 | 111.185349794239 | -3.98534979423868 |
| 45 | 107.23 | 111.348683127572 | -4.11868312757201 |
| 46 | 107.2 | 111.400349794239 | -4.20034979423868 |
| 47 | 107.21 | 111.458683127572 | -4.24868312757202 |
| 48 | 107.24 | 111.500349794239 | -4.26034979423868 |
| 49 | 107.21 | 111.930558345540 | -4.72055834553961 |
| 50 | 113.89 | 113.158891678873 | 0.731108321127171 |
| 51 | 114.05 | 113.295558345540 | 0.754441654460494 |
| 52 | 114.05 | 113.327225012206 | 0.722774987793827 |
| 53 | 114.05 | 113.325558345540 | 0.724441654460494 |
| 54 | 114.05 | 113.330558345540 | 0.719441654460497 |
| 55 | 115.12 | 113.600558345539 | 1.51944165446050 |
| 56 | 115.68 | 114.558400641696 | 1.12159935830370 |
| 57 | 116.05 | 114.721733975030 | 1.32826602497036 |
| 58 | 116.18 | 114.773400641696 | 1.40659935830370 |
| 59 | 116.35 | 114.831733975030 | 1.51826602497036 |
| 60 | 116.44 | 114.873400641696 | 1.56659935830370 |
| 61 | 117 | 115.303609192997 | 1.69639080700277 |
| 62 | 117.61 | 116.531942526330 | 1.07805747366955 |
| 63 | 118.17 | 116.668609192997 | 1.50139080700287 |
| 64 | 118.33 | 116.700275859664 | 1.62972414033621 |
| 65 | 118.33 | 116.698609192997 | 1.63139080700287 |
| 66 | 118.42 | 116.703609192997 | 1.71639080700288 |
| 67 | 118.5 | 116.973609192997 | 1.52639080700288 |
| 68 | 118.67 | 117.931451489154 | 0.738548510846074 |
| 69 | 119.09 | 118.094784822487 | 0.995215177512742 |
| 70 | 119.14 | 118.146451489154 | 0.993548510846073 |
| 71 | 119.23 | 118.204784822487 | 1.02521517751275 |
| 72 | 119.33 | 118.246451489154 | 1.08354851084607 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 17 | 1.54955075409298e-05 | 3.09910150818596e-05 | 0.999984504492459 |
| 18 | 4.27673861299270e-07 | 8.55347722598539e-07 | 0.999999572326139 |
| 19 | 2.94340827849628e-06 | 5.88681655699257e-06 | 0.999997056591722 |
| 20 | 1.78954359541076e-07 | 3.57908719082152e-07 | 0.99999982104564 |
| 21 | 1.15789556670435e-08 | 2.31579113340871e-08 | 0.999999988421044 |
| 22 | 9.59869217606954e-10 | 1.91973843521391e-09 | 0.99999999904013 |
| 23 | 1.04205943435395e-10 | 2.08411886870791e-10 | 0.999999999895794 |
| 24 | 1.28638055784226e-11 | 2.57276111568452e-11 | 0.999999999987136 |
| 25 | 1.31242701928871e-12 | 2.62485403857742e-12 | 0.999999999998687 |
| 26 | 9.7874818907804e-14 | 1.95749637815608e-13 | 0.999999999999902 |
| 27 | 7.03301506835766e-15 | 1.40660301367153e-14 | 0.999999999999993 |
| 28 | 5.00242106693344e-16 | 1.00048421338669e-15 | 1 |
| 29 | 4.05395777031992e-17 | 8.10791554063984e-17 | 1 |
| 30 | 4.52501780906316e-18 | 9.05003561812632e-18 | 1 |
| 31 | 1.90904042905979e-18 | 3.81808085811959e-18 | 1 |
| 32 | 2.19960918995568e-19 | 4.39921837991137e-19 | 1 |
| 33 | 2.76567829207708e-20 | 5.53135658415417e-20 | 1 |
| 34 | 4.57596443666624e-21 | 9.15192887333249e-21 | 1 |
| 35 | 1.33891726382325e-21 | 2.6778345276465e-21 | 1 |
| 36 | 8.23991845632549e-22 | 1.64798369126510e-21 | 1 |
| 37 | 9.59646329539283e-22 | 1.91929265907857e-21 | 1 |
| 38 | 1.65864520190152e-22 | 3.31729040380303e-22 | 1 |
| 39 | 2.70303962986345e-23 | 5.4060792597269e-23 | 1 |
| 40 | 3.90707311348483e-24 | 7.81414622696966e-24 | 1 |
| 41 | 1.06546983322795e-24 | 2.13093966645590e-24 | 1 |
| 42 | 1.53972633725262e-25 | 3.07945267450524e-25 | 1 |
| 43 | 1.43311665075113e-25 | 2.86623330150225e-25 | 1 |
| 44 | 2.06171215882732e-26 | 4.12342431765465e-26 | 1 |
| 45 | 5.37940717330637e-27 | 1.07588143466127e-26 | 1 |
| 46 | 4.79289350038597e-27 | 9.58578700077195e-27 | 1 |
| 47 | 1.93496730183953e-26 | 3.86993460367906e-26 | 1 |
| 48 | 3.33130939550566e-24 | 6.66261879101131e-24 | 1 |
| 49 | 1.99361679206807e-09 | 3.98723358413615e-09 | 0.999999998006383 |
| 50 | 0.9686141508827 | 0.0627716982346015 | 0.0313858491173008 |
| 51 | 0.991508920567788 | 0.0169821588644248 | 0.00849107943221239 |
| 52 | 0.994999691612553 | 0.0100006167748937 | 0.00500030838744685 |
| 53 | 0.996505082957263 | 0.00698983408547404 | 0.00349491704273702 |
| 54 | 0.999883840136367 | 0.000232319727265039 | 0.000116159863632519 |
| 55 | 0.99996043910997 | 7.91217800613651e-05 | 3.95608900306826e-05 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 36 | 0.923076923076923 | NOK |
| 5% type I error level | 38 | 0.974358974358974 | NOK |
| 10% type I error level | 39 | 1 | NOK |
