| Multiple Linear Regression - Estimated Regression Equation |
| Yt[t] = + 103.814355265646 -10.6915674040462Xt_dummy[t] + 3.38103374929093M1[t] -5.04782803932688M2[t] -13.0891898279448M3[t] -10.3441056910569M4[t] -9.9354674796748M5[t] + 1.84817073170732M6[t] -5.68069105691055M7[t] -7.55955284552844M8[t] + 1.99908536585367M9[t] -18.5172764227642M10[t] -20.8961382113821M11[t] + 0.366361788617887t + 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) | 103.814355265646 | 3.429858 | 30.2678 | 0 | 0 |
| Xt_dummy | -10.6915674040462 | 2.89231 | -3.6965 | 0.000394 | 0.000197 |
| M1 | 3.38103374929093 | 4.070678 | 0.8306 | 0.408621 | 0.204311 |
| M2 | -5.04782803932688 | 4.068623 | -1.2407 | 0.218265 | 0.109132 |
| M3 | -13.0891898279448 | 4.067024 | -3.2184 | 0.001847 | 0.000924 |
| M4 | -10.3441056910569 | 4.071745 | -2.5405 | 0.012957 | 0.006478 |
| M5 | -9.9354674796748 | 4.06832 | -2.4422 | 0.01675 | 0.008375 |
| M6 | 1.84817073170732 | 4.06535 | 0.4546 | 0.650587 | 0.325294 |
| M7 | -5.68069105691055 | 4.062834 | -1.3982 | 0.165821 | 0.08291 |
| M8 | -7.55955284552844 | 4.060775 | -1.8616 | 0.066242 | 0.033121 |
| M9 | 1.99908536585367 | 4.059173 | 0.4925 | 0.623692 | 0.311846 |
| M10 | -18.5172764227642 | 4.058028 | -4.5631 | 1.7e-05 | 9e-06 |
| M11 | -20.8961382113821 | 4.057341 | -5.1502 | 2e-06 | 1e-06 |
| t | 0.366361788617887 | 0.043112 | 8.4979 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.817912848421904 |
| R-squared | 0.668981427613633 |
| Adjusted R-squared | 0.616502873454818 |
| F-TEST (value) | 12.7477107236818 |
| F-TEST (DF numerator) | 13 |
| F-TEST (DF denominator) | 82 |
| p-value | 9.43689570931383e-15 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 8.1142235003832 |
| Sum Squared Residuals | 5398.93108716203 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 111.6 | 107.561750803555 | 4.03824919644507 |
| 2 | 104.6 | 99.4992508035545 | 5.10074919644548 |
| 3 | 91.6 | 91.8242508035545 | -0.224250803554514 |
| 4 | 98.3 | 94.9356967290603 | 3.36430327093967 |
| 5 | 97.7 | 95.7106967290603 | 1.98930327093968 |
| 6 | 106.3 | 107.860696729060 | -1.56069672906033 |
| 7 | 102.3 | 100.698196729060 | 1.60180327093973 |
| 8 | 106.6 | 99.1856967290603 | 7.41430327093971 |
| 9 | 108.1 | 109.110696729060 | -1.01069672906031 |
| 10 | 93.8 | 88.9606967290603 | 4.83930327093968 |
| 11 | 88.2 | 86.9481967290603 | 1.25180327093970 |
| 12 | 108.9 | 108.210696729060 | 0.689303270939719 |
| 13 | 114.2 | 111.958092266969 | 2.24190773303092 |
| 14 | 102.5 | 103.895592266969 | -1.39559226696918 |
| 15 | 94.2 | 96.2205922669692 | -2.02059226696917 |
| 16 | 97.4 | 99.332038192475 | -1.93203819247493 |
| 17 | 98.5 | 100.107038192475 | -1.60703819247493 |
| 18 | 106.5 | 112.257038192475 | -5.75703819247493 |
| 19 | 102.9 | 105.094538192475 | -2.19453819247494 |
| 20 | 97.1 | 103.582038192475 | -6.48203819247494 |
| 21 | 103.7 | 113.507038192475 | -9.80703819247493 |
| 22 | 93.4 | 93.357038192475 | 0.0429618075250712 |
| 23 | 85.8 | 91.344538192475 | -5.54453819247494 |
| 24 | 108.6 | 112.607038192475 | -4.00703819247494 |
| 25 | 110.2 | 116.354433730384 | -6.15443373038376 |
| 26 | 101.2 | 108.291933730384 | -7.0919337303838 |
| 27 | 101.2 | 100.616933730384 | 0.583066269616191 |
| 28 | 96.9 | 103.728379655890 | -6.82837965588957 |
| 29 | 99.4 | 104.503379655890 | -5.10337965588957 |
| 30 | 118.7 | 116.653379655890 | 2.04662034411043 |
| 31 | 108 | 109.490879655890 | -1.49087965588958 |
| 32 | 101.2 | 107.978379655890 | -6.77837965588957 |
| 33 | 119.9 | 117.903379655890 | 1.99662034411043 |
| 34 | 94.8 | 97.7533796558896 | -2.95337965588958 |
| 35 | 95.3 | 95.7408796558896 | -0.440879655889577 |
| 36 | 118 | 117.003379655890 | 0.99662034411042 |
| 37 | 115.9 | 120.750775193798 | -4.85077519379839 |
| 38 | 111.4 | 112.688275193798 | -1.28827519379844 |
| 39 | 108.2 | 105.013275193798 | 3.18672480620155 |
| 40 | 108.8 | 108.124721119304 | 0.675278880695782 |
| 41 | 109.5 | 108.899721119304 | 0.600278880695786 |
| 42 | 124.8 | 121.049721119304 | 3.75027888069579 |
| 43 | 115.3 | 113.887221119304 | 1.41277888069578 |
| 44 | 109.5 | 112.374721119304 | -2.87472111930422 |
| 45 | 124.2 | 122.299721119304 | 1.90027888069578 |
| 46 | 92.9 | 102.149721119304 | -9.24972111930421 |
| 47 | 98.4 | 100.137221119304 | -1.73722111930421 |
| 48 | 120.9 | 121.399721119304 | -0.499721119304216 |
| 49 | 111.7 | 125.147116657213 | -13.4471166572130 |
| 50 | 116.1 | 117.084616657213 | -0.984616657213097 |
| 51 | 109.4 | 109.409616657213 | -0.00961665721308802 |
| 52 | 111.7 | 112.521062582719 | -0.821062582718852 |
| 53 | 114.3 | 113.296062582719 | 1.00393741728114 |
| 54 | 133.7 | 125.446062582719 | 8.25393741728114 |
| 55 | 114.3 | 118.283562582719 | -3.98356258271886 |
| 56 | 126.5 | 116.771062582719 | 9.72893741728114 |
| 57 | 131 | 126.696062582719 | 4.30393741728113 |
| 58 | 104 | 106.546062582719 | -2.54606258271886 |
| 59 | 108.9 | 104.533562582719 | 4.36643741728115 |
| 60 | 128.5 | 125.796062582719 | 2.70393741728114 |
| 61 | 132.4 | 129.543458120628 | 2.85654187937232 |
| 62 | 128 | 121.480958120628 | 6.51904187937227 |
| 63 | 116.4 | 113.805958120628 | 2.59404187937227 |
| 64 | 120.9 | 116.917404046133 | 3.98259595386651 |
| 65 | 118.6 | 117.692404046133 | 0.9075959538665 |
| 66 | 133.1 | 129.842404046133 | 3.25759595386650 |
| 67 | 121.1 | 122.679904046134 | -1.57990404613351 |
| 68 | 127.6 | 121.167404046133 | 6.4325959538665 |
| 69 | 135.4 | 131.092404046134 | 4.3075959538665 |
| 70 | 114.9 | 110.942404046133 | 3.95759595386651 |
| 71 | 114.3 | 108.929904046134 | 5.3700959538665 |
| 72 | 128.9 | 130.192404046134 | -1.2924040461335 |
| 73 | 138.9 | 133.939799584042 | 4.96020041595768 |
| 74 | 129.4 | 125.877299584042 | 3.52270041595763 |
| 75 | 115 | 118.202299584042 | -3.20229958404237 |
| 76 | 128 | 110.622178105502 | 17.3778218944980 |
| 77 | 127 | 111.397178105502 | 15.6028218944980 |
| 78 | 128.8 | 123.547178105502 | 5.25282189449803 |
| 79 | 137.9 | 116.384678105502 | 21.515321894498 |
| 80 | 128.4 | 114.872178105502 | 13.5278218944980 |
| 81 | 135.9 | 124.797178105502 | 11.1028218944980 |
| 82 | 122.2 | 104.647178105502 | 17.5528218944980 |
| 83 | 113.1 | 102.634678105502 | 10.465321894498 |
| 84 | 136.2 | 123.897178105502 | 12.302821894498 |
| 85 | 138 | 127.644573643411 | 10.3554263565892 |
| 86 | 115.2 | 119.582073643411 | -4.38207364341086 |
| 87 | 111 | 111.907073643411 | -0.907073643410865 |
| 88 | 99.2 | 115.018519568917 | -15.8185195689166 |
| 89 | 102.4 | 115.793519568917 | -13.3935195689166 |
| 90 | 112.7 | 127.943519568917 | -15.2435195689166 |
| 91 | 105.5 | 120.781019568917 | -15.2810195689166 |
| 92 | 98.3 | 119.268519568917 | -20.9685195689166 |
| 93 | 116.4 | 129.193519568917 | -12.7935195689166 |
| 94 | 97.4 | 109.043519568917 | -11.6435195689166 |
| 95 | 93.3 | 107.031019568917 | -13.7310195689166 |
| 96 | 117.4 | 128.293519568917 | -10.8935195689166 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 17 | 0.00958825817779522 | 0.0191765163555904 | 0.990411741822205 |
| 18 | 0.00151295130037155 | 0.0030259026007431 | 0.998487048699628 |
| 19 | 0.000211035520379756 | 0.000422071040759512 | 0.99978896447962 |
| 20 | 0.0046862017915729 | 0.0093724035831458 | 0.995313798208427 |
| 21 | 0.00201818016707644 | 0.00403636033415288 | 0.997981819832924 |
| 22 | 0.000582984406437064 | 0.00116596881287413 | 0.999417015593563 |
| 23 | 0.000169318227838988 | 0.000338636455677976 | 0.99983068177216 |
| 24 | 4.50921391838976e-05 | 9.01842783677952e-05 | 0.999954907860816 |
| 25 | 1.19242550379534e-05 | 2.38485100759068e-05 | 0.999988075744962 |
| 26 | 3.01272000662773e-06 | 6.02544001325546e-06 | 0.999996987279993 |
| 27 | 4.02382399537543e-05 | 8.04764799075087e-05 | 0.999959761760046 |
| 28 | 1.32931689006513e-05 | 2.65863378013026e-05 | 0.9999867068311 |
| 29 | 4.61625019143791e-06 | 9.23250038287582e-06 | 0.999995383749809 |
| 30 | 7.26256187722001e-05 | 0.000145251237544400 | 0.999927374381228 |
| 31 | 3.92193297369082e-05 | 7.84386594738164e-05 | 0.999960780670263 |
| 32 | 1.7539687621392e-05 | 3.5079375242784e-05 | 0.999982460312379 |
| 33 | 0.000101943578444070 | 0.000203887156888139 | 0.999898056421556 |
| 34 | 4.37601635753008e-05 | 8.75203271506017e-05 | 0.999956239836425 |
| 35 | 3.17577386308187e-05 | 6.35154772616374e-05 | 0.99996824226137 |
| 36 | 2.46862913784352e-05 | 4.93725827568704e-05 | 0.999975313708622 |
| 37 | 1.15587860567240e-05 | 2.31175721134479e-05 | 0.999988441213943 |
| 38 | 7.06308652081117e-06 | 1.41261730416223e-05 | 0.99999293691348 |
| 39 | 7.76459352460209e-06 | 1.55291870492042e-05 | 0.999992235406475 |
| 40 | 5.61517115662545e-06 | 1.12303423132509e-05 | 0.999994384828843 |
| 41 | 3.53962307994491e-06 | 7.07924615988981e-06 | 0.99999646037692 |
| 42 | 3.70598624524423e-06 | 7.41197249048846e-06 | 0.999996294013755 |
| 43 | 1.95460446103235e-06 | 3.90920892206470e-06 | 0.99999804539554 |
| 44 | 9.83385089960234e-07 | 1.96677017992047e-06 | 0.99999901661491 |
| 45 | 7.83529387547875e-07 | 1.56705877509575e-06 | 0.999999216470612 |
| 46 | 1.81683930665354e-06 | 3.63367861330709e-06 | 0.999998183160693 |
| 47 | 1.12914920837435e-06 | 2.25829841674869e-06 | 0.999998870850792 |
| 48 | 6.95580323733278e-07 | 1.39116064746656e-06 | 0.999999304419676 |
| 49 | 1.46366329276573e-05 | 2.92732658553146e-05 | 0.999985363367072 |
| 50 | 1.77152318480656e-05 | 3.54304636961313e-05 | 0.999982284768152 |
| 51 | 1.90743644987284e-05 | 3.81487289974567e-05 | 0.999980925635501 |
| 52 | 1.83889201701135e-05 | 3.67778403402271e-05 | 0.99998161107983 |
| 53 | 1.79221244334448e-05 | 3.58442488668895e-05 | 0.999982077875567 |
| 54 | 3.08605686653066e-05 | 6.17211373306133e-05 | 0.999969139431335 |
| 55 | 6.1493113790906e-05 | 0.000122986227581812 | 0.99993850688621 |
| 56 | 0.000179741668081528 | 0.000359483336163056 | 0.999820258331918 |
| 57 | 0.000235422355356991 | 0.000470844710713983 | 0.999764577644643 |
| 58 | 0.00116271324468839 | 0.00232542648937677 | 0.998837286755312 |
| 59 | 0.00278397921195035 | 0.00556795842390069 | 0.99721602078805 |
| 60 | 0.0110975725509069 | 0.0221951451018139 | 0.988902427449093 |
| 61 | 0.102932241663000 | 0.205864483326001 | 0.897067758337 |
| 62 | 0.190911542719038 | 0.381823085438077 | 0.809088457280962 |
| 63 | 0.464529502779494 | 0.929059005558988 | 0.535470497220506 |
| 64 | 0.407784417131028 | 0.815568834262057 | 0.592215582868972 |
| 65 | 0.383858129975445 | 0.76771625995089 | 0.616141870024555 |
| 66 | 0.318377642378613 | 0.636755284757227 | 0.681622357621386 |
| 67 | 0.446469208214303 | 0.892938416428606 | 0.553530791785697 |
| 68 | 0.400463948849024 | 0.800927897698048 | 0.599536051150976 |
| 69 | 0.332057065757936 | 0.664114131515871 | 0.667942934242064 |
| 70 | 0.34287362649683 | 0.68574725299366 | 0.65712637350317 |
| 71 | 0.276733009258908 | 0.553466018517817 | 0.723266990741092 |
| 72 | 0.595921494694762 | 0.808157010610476 | 0.404078505305238 |
| 73 | 0.610091460711672 | 0.779817078576656 | 0.389908539288328 |
| 74 | 0.630760183379063 | 0.738479633241874 | 0.369239816620937 |
| 75 | 0.5324511149799 | 0.9350977700402 | 0.4675488850201 |
| 76 | 0.482005478878709 | 0.964010957757418 | 0.517994521121291 |
| 77 | 0.359300010340625 | 0.718600020681249 | 0.640699989659375 |
| 78 | 0.41745469628268 | 0.83490939256536 | 0.58254530371732 |
| 79 | 0.561187234727816 | 0.877625530544369 | 0.438812765272184 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 42 | 0.666666666666667 | NOK |
| 5% type I error level | 44 | 0.698412698412698 | NOK |
| 10% type I error level | 44 | 0.698412698412698 | NOK |
