| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 6.55556335362125 -0.571609540172981X[t] + 0.000561849015211116M1[t] + 0.0553358183600769M2[t] -0.163738945999203M3[t] -0.213781172039566M4[t] + 0.168542473572323M5[t] + 0.134220565537727M6[t] + 0.428593144820758M7[t] + 0.320025335624217M8[t] + 0.245728763213839M9[t] + 0.131406855179243M10[t] -0.105754098838056M11[t] + 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) | 6.55556335362125 | 1.88745 | 3.4732 | 0.001057 | 0.000529 |
| X | -0.571609540172981 | 0.255851 | -2.2341 | 0.029885 | 0.014942 |
| M1 | 0.000561849015211116 | 0.751089 | 7e-04 | 0.999406 | 0.499703 |
| M2 | 0.0553358183600769 | 0.754027 | 0.0734 | 0.941785 | 0.470893 |
| M3 | -0.163738945999203 | 0.747947 | -0.2189 | 0.827588 | 0.413794 |
| M4 | -0.213781172039566 | 0.742345 | -0.288 | 0.774528 | 0.387264 |
| M5 | 0.168542473572323 | 0.775304 | 0.2174 | 0.828773 | 0.414386 |
| M6 | 0.134220565537727 | 0.779682 | 0.1721 | 0.864003 | 0.432001 |
| M7 | 0.428593144820758 | 0.774831 | 0.5531 | 0.582582 | 0.291291 |
| M8 | 0.320025335624217 | 0.775051 | 0.4129 | 0.681404 | 0.340702 |
| M9 | 0.245728763213839 | 0.774493 | 0.3173 | 0.752329 | 0.376164 |
| M10 | 0.131406855179243 | 0.774831 | 0.1696 | 0.866 | 0.433 |
| M11 | -0.105754098838056 | 0.776266 | -0.1362 | 0.892172 | 0.446086 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.368317136159586 |
| R-squared | 0.135657512788799 |
| Adjusted R-squared | -0.0677171900844245 |
| F-TEST (value) | 0.667032383439366 |
| F-TEST (DF numerator) | 12 |
| F-TEST (DF denominator) | 51 |
| p-value | 0.774100232451549 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 1.22415323350237 |
| Sum Squared Residuals | 76.4261080938098 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 1.4 | 1.86892697321801 | -0.468926973218012 |
| 2 | 1.2 | 2.03802285059747 | -0.838022850597475 |
| 3 | 1 | 2.10475285632468 | -1.10475285632468 |
| 4 | 1.7 | 2.45483730840541 | -0.75483730840541 |
| 5 | 2.4 | 3.00864381606919 | -0.608643816069193 |
| 6 | 2 | 2.9171609540173 | -0.917160954017298 |
| 7 | 2.1 | 2.63992399312735 | -0.539923993127348 |
| 8 | 2 | 2.30271236786161 | -0.302712367861615 |
| 9 | 1.8 | 2.17125484143394 | -0.371254841433939 |
| 10 | 2.7 | 2.28557674946853 | 0.414423250531467 |
| 11 | 2.3 | 2.16273770348583 | 0.137262296514168 |
| 12 | 1.9 | 2.21133084830659 | -0.31133084830659 |
| 13 | 2 | 2.09757078928721 | -0.097570789287205 |
| 14 | 2.3 | 2.15234475863207 | 0.147655241367929 |
| 15 | 2.8 | 1.93326999427279 | 0.86673000572721 |
| 16 | 2.4 | 2.05471063028432 | 0.345289369715678 |
| 17 | 2.3 | 2.43703427589621 | -0.137034275896211 |
| 18 | 2.7 | 2.63135618393081 | 0.0686438160691928 |
| 19 | 2.7 | 2.69708494714465 | 0.00291505285535434 |
| 20 | 2.9 | 2.58851713794811 | 0.311482862051894 |
| 21 | 3 | 2.45705961152043 | 0.542940388479571 |
| 22 | 2.2 | 2.28557674946853 | -0.085576749468534 |
| 23 | 2.3 | 2.04841579545124 | 0.251584204548764 |
| 24 | 2.8 | 2.03984798625470 | 0.760152013745305 |
| 25 | 2.8 | 1.92608792723531 | 0.873912072764689 |
| 26 | 2.8 | 1.92370094256288 | 0.876299057437121 |
| 27 | 2.2 | 1.70462617820360 | 0.495373821796402 |
| 28 | 2.6 | 1.65458395216324 | 0.945416047836765 |
| 29 | 2.8 | 2.20839045982702 | 0.591609540172982 |
| 30 | 2.5 | 2.51703427589621 | -0.017034275896211 |
| 31 | 2.4 | 3.04005067124843 | -0.640050671248435 |
| 32 | 2.3 | 3.10296572410379 | -0.80296572410379 |
| 33 | 1.9 | 2.97150819767611 | -1.07150819767611 |
| 34 | 1.7 | 2.74286438160692 | -1.04286438160692 |
| 35 | 2 | 2.44854247357232 | -0.448542473572323 |
| 36 | 2.1 | 2.49713561839308 | -0.397135618393081 |
| 37 | 1.7 | 2.44053651339099 | -0.740536513390994 |
| 38 | 1.8 | 2.55247143675316 | -0.752471436753157 |
| 39 | 1.8 | 2.44771858042847 | -0.647718580428473 |
| 40 | 1.8 | 2.34051540037081 | -0.540515400370812 |
| 41 | 1.3 | 2.83716095401730 | -1.53716095401730 |
| 42 | 1.3 | 3.03148286205189 | -1.73148286205189 |
| 43 | 1.3 | 3.15437257928303 | -1.85437257928303 |
| 44 | 1.2 | 3.10296572410379 | -1.90296572410379 |
| 45 | 1.4 | 3.14299105972801 | -1.74299105972801 |
| 46 | 2.2 | 3.08583010571071 | -0.885830105710708 |
| 47 | 2.9 | 2.90583010571071 | -0.0058301057107079 |
| 48 | 3.1 | 2.84010134249687 | 0.259898657503131 |
| 49 | 3.5 | 2.66918032946019 | 0.830819670539814 |
| 50 | 3.6 | 2.72395429880505 | 0.876045701194949 |
| 51 | 4.4 | 2.73352335051496 | 1.66647664948504 |
| 52 | 4.1 | 2.85496398652650 | 1.24503601347350 |
| 53 | 5.1 | 3.40877049419028 | 1.69122950580972 |
| 54 | 5.8 | 3.20296572410379 | 2.59703427589621 |
| 55 | 5.9 | 2.86856780919654 | 3.03143219080346 |
| 56 | 5.4 | 2.70283904598270 | 2.69716095401730 |
| 57 | 5.5 | 2.85718628964151 | 2.64281371035849 |
| 58 | 4.8 | 3.20015201374531 | 1.59984798625469 |
| 59 | 3.2 | 3.1344739217799 | 0.0655260782200998 |
| 60 | 2.7 | 3.01158420454876 | -0.311584204548763 |
| 61 | 2.1 | 2.49769746740829 | -0.397697467408292 |
| 62 | 1.9 | 2.20950571264937 | -0.309505712649368 |
| 63 | 0.6 | 1.87610904025549 | -1.27610904025549 |
| 64 | 0.7 | 1.94038872224973 | -1.24038872224973 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 16 | 0.250999624610369 | 0.501999249220739 | 0.749000375389631 |
| 17 | 0.134298690750899 | 0.268597381501798 | 0.865701309249101 |
| 18 | 0.0675270237970275 | 0.135054047594055 | 0.932472976202973 |
| 19 | 0.0341317582116171 | 0.0682635164232342 | 0.965868241788383 |
| 20 | 0.0221540947594259 | 0.0443081895188518 | 0.977845905240574 |
| 21 | 0.0167895289030647 | 0.0335790578061293 | 0.983210471096935 |
| 22 | 0.00776063731442184 | 0.0155212746288437 | 0.992239362685578 |
| 23 | 0.00308720280404967 | 0.00617440560809934 | 0.99691279719595 |
| 24 | 0.00183501473543106 | 0.00367002947086212 | 0.998164985264569 |
| 25 | 0.00155482626682898 | 0.00310965253365795 | 0.998445173733171 |
| 26 | 0.00116432807710713 | 0.00232865615421426 | 0.998835671922893 |
| 27 | 0.00047760688548082 | 0.00095521377096164 | 0.99952239311452 |
| 28 | 0.000218556234601086 | 0.000437112469202172 | 0.999781443765399 |
| 29 | 9.07356060410878e-05 | 0.000181471212082176 | 0.999909264393959 |
| 30 | 3.10013810131361e-05 | 6.20027620262722e-05 | 0.999968998618987 |
| 31 | 1.18027548394712e-05 | 2.36055096789423e-05 | 0.99998819724516 |
| 32 | 4.56410593138198e-06 | 9.12821186276396e-06 | 0.999995435894069 |
| 33 | 1.70353454775037e-06 | 3.40706909550074e-06 | 0.999998296465452 |
| 34 | 6.46461819126007e-07 | 1.29292363825201e-06 | 0.99999935353818 |
| 35 | 1.81045520984456e-07 | 3.62091041968912e-07 | 0.999999818954479 |
| 36 | 4.76224967405622e-08 | 9.52449934811245e-08 | 0.999999952377503 |
| 37 | 1.26500865572980e-08 | 2.53001731145959e-08 | 0.999999987349913 |
| 38 | 3.50441040158472e-09 | 7.00882080316945e-09 | 0.99999999649559 |
| 39 | 9.23672890299638e-10 | 1.84734578059928e-09 | 0.999999999076327 |
| 40 | 2.17353995256554e-10 | 4.34707990513107e-10 | 0.999999999782646 |
| 41 | 3.21153447368962e-10 | 6.42306894737924e-10 | 0.999999999678847 |
| 42 | 1.34698530406356e-09 | 2.69397060812711e-09 | 0.999999998653015 |
| 43 | 3.81965692725504e-08 | 7.63931385451007e-08 | 0.99999996180343 |
| 44 | 1.01779936657762e-05 | 2.03559873315525e-05 | 0.999989822006334 |
| 45 | 0.080459088583182 | 0.160918177166364 | 0.919540911416818 |
| 46 | 0.526362502411322 | 0.947274995177356 | 0.473637497588678 |
| 47 | 0.519724390500221 | 0.960551218999559 | 0.480275609499779 |
| 48 | 0.735016324271627 | 0.529967351456746 | 0.264983675728373 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 22 | 0.666666666666667 | NOK |
| 5% type I error level | 25 | 0.757575757575758 | NOK |
| 10% type I error level | 26 | 0.787878787878788 | NOK |
