| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 2.07836940516536 -0.776305498871819X[t] + 0.482562816317725M1[t] + 0.468406500301148M2[t] + 0.548591569205598M3[t] + 0.577724418155176M4[t] + 0.7635681021386M5[t] + 0.814437505056589M6[t] + 0.820833017952014M7[t] + 0.665491976879028M8[t] + 0.562203937846657M9[t] + 0.47096890085490M10[t] + 0.143839867944373M11[t] + 0.0741563160165766t + 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) | 2.07836940516536 | 0.702856 | 2.957 | 0.004889 | 0.002445 |
| X | -0.776305498871819 | 0.379015 | -2.0482 | 0.046271 | 0.023135 |
| M1 | 0.482562816317725 | 0.675322 | 0.7146 | 0.478488 | 0.239244 |
| M2 | 0.468406500301148 | 0.670639 | 0.6984 | 0.488413 | 0.244207 |
| M3 | 0.548591569205598 | 0.67155 | 0.8169 | 0.418195 | 0.209097 |
| M4 | 0.577724418155176 | 0.669456 | 0.863 | 0.392628 | 0.196314 |
| M5 | 0.7635681021386 | 0.665421 | 1.1475 | 0.257109 | 0.128555 |
| M6 | 0.814437505056589 | 0.665572 | 1.2237 | 0.22731 | 0.113655 |
| M7 | 0.820833017952014 | 0.66731 | 1.2301 | 0.224928 | 0.112464 |
| M8 | 0.665491976879028 | 0.667132 | 0.9975 | 0.323721 | 0.16186 |
| M9 | 0.562203937846657 | 0.664419 | 0.8462 | 0.401844 | 0.200922 |
| M10 | 0.47096890085490 | 0.659911 | 0.7137 | 0.479027 | 0.239514 |
| M11 | 0.143839867944373 | 0.654187 | 0.2199 | 0.826941 | 0.41347 |
| t | 0.0741563160165766 | 0.019419 | 3.8187 | 4e-04 | 2e-04 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.624576730303413 |
| R-squared | 0.390096092036502 |
| Adjusted R-squared | 0.217731944133774 |
| F-TEST (value) | 2.26320900711121 |
| F-TEST (DF numerator) | 13 |
| F-TEST (DF denominator) | 46 |
| p-value | 0.0211618067216435 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 1.03215027135484 |
| Sum Squared Residuals | 49.0053724022618 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 1.4 | 1.08247753975602 | 0.317522460243977 |
| 2 | 1.2 | 1.14247753975602 | 0.057522460243976 |
| 3 | 1 | 1.29681892467705 | -0.296818924677053 |
| 4 | 1.7 | 1.40010808964321 | 0.299891910356793 |
| 5 | 2.4 | 1.66010808964321 | 0.739891910356793 |
| 6 | 2 | 1.78513380857777 | 0.214866191422228 |
| 7 | 2.1 | 1.86568563748977 | 0.234314362510226 |
| 8 | 2 | 1.78450091243337 | 0.215499087566634 |
| 9 | 1.8 | 1.75536918941757 | 0.0446308105824288 |
| 10 | 2.7 | 1.73829046844239 | 0.961709531557609 |
| 11 | 2.3 | 1.48531775154844 | 0.81468224845156 |
| 12 | 1.9 | 1.41563419962064 | 0.484365800379356 |
| 13 | 2 | 1.97235333195495 | 0.0276466680450549 |
| 14 | 2.3 | 2.03235333195494 | 0.267646668045055 |
| 15 | 2.8 | 2.18669471687597 | 0.613305283124028 |
| 16 | 2.4 | 2.28998388184213 | 0.110016118157873 |
| 17 | 2.3 | 2.54998388184213 | -0.249983881842126 |
| 18 | 2.7 | 2.67500960077669 | 0.0249903992233081 |
| 19 | 2.7 | 2.75556142968869 | -0.0555614296886936 |
| 20 | 2.9 | 2.67437670463229 | 0.225623295367715 |
| 21 | 3 | 2.64524498161649 | 0.35475501838351 |
| 22 | 2.2 | 2.62816626064131 | -0.42816626064131 |
| 23 | 2.3 | 2.37519354374736 | -0.0751935437473595 |
| 24 | 2.8 | 2.14248583705648 | 0.657514162943519 |
| 25 | 2.8 | 2.66815274943591 | 0.13184725056409 |
| 26 | 2.8 | 2.72815274943591 | 0.0718472505640904 |
| 27 | 2.2 | 2.72723303458257 | -0.527233034582573 |
| 28 | 2.6 | 2.79170692460514 | -0.191706924605136 |
| 29 | 2.8 | 3.05170692460514 | -0.251706924605136 |
| 30 | 2.5 | 3.06804987369765 | -0.568049873697647 |
| 31 | 2.4 | 3.06320809773375 | -0.66320809773375 |
| 32 | 2.3 | 2.84228838288041 | -0.542288382880413 |
| 33 | 1.9 | 2.75881527494359 | -0.858815274943591 |
| 34 | 1.7 | 2.6097646191602 | -0.909764619160202 |
| 35 | 2 | 2.29468746235651 | -0.294687462356506 |
| 36 | 2.1 | 2.11632114058665 | -0.0163211405866546 |
| 37 | 1.7 | 2.58764666804506 | -0.887646668045056 |
| 38 | 1.8 | 2.64764666804506 | -0.847646668045056 |
| 39 | 1.8 | 2.68554222813531 | -0.88554222813531 |
| 40 | 1.8 | 2.71120084321428 | -0.911200843214282 |
| 41 | 1.3 | 2.97120084321428 | -1.67120084321428 |
| 42 | 1.3 | 2.97978073731808 | -1.67978073731808 |
| 43 | 1.3 | 2.98270201634290 | -1.68270201634290 |
| 44 | 1.2 | 2.90151729128649 | -1.70151729128649 |
| 45 | 1.4 | 2.87238556827069 | -1.47238556827069 |
| 46 | 2.2 | 2.85530684729551 | -0.655306847295512 |
| 47 | 2.9 | 2.60233413040156 | 0.297665869598439 |
| 48 | 3.1 | 2.53265057847376 | 0.567349421526235 |
| 49 | 3.5 | 3.08936971080807 | 0.410630289191934 |
| 50 | 3.6 | 3.14936971080807 | 0.450630289191934 |
| 51 | 4.4 | 3.30371109572909 | 1.09628890427091 |
| 52 | 4.1 | 3.40700026069525 | 0.692999739304753 |
| 53 | 5.1 | 3.66700026069525 | 1.43299973930475 |
| 54 | 5.8 | 3.79202597962981 | 2.00797402037019 |
| 55 | 5.9 | 3.73284281874489 | 2.16715718125511 |
| 56 | 5.4 | 3.59731670876745 | 1.80268329123255 |
| 57 | 5.5 | 3.56818498575166 | 1.93181501424834 |
| 58 | 4.8 | 3.76847180446059 | 1.03152819553941 |
| 59 | 3.2 | 3.94246711194613 | -0.742467111946135 |
| 60 | 2.7 | 4.39290824426246 | -1.69290824426246 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 17 | 0.126007541566508 | 0.252015083133016 | 0.873992458433492 |
| 18 | 0.0478674721117147 | 0.0957349442234295 | 0.952132527888285 |
| 19 | 0.0168242297793290 | 0.0336484595586581 | 0.98317577022067 |
| 20 | 0.00549332408271554 | 0.0109866481654311 | 0.994506675917284 |
| 21 | 0.0021288551483679 | 0.0042577102967358 | 0.997871144851632 |
| 22 | 0.00425287941465446 | 0.00850575882930892 | 0.995747120585346 |
| 23 | 0.00239300471201978 | 0.00478600942403955 | 0.99760699528798 |
| 24 | 0.00121621011116059 | 0.00243242022232119 | 0.99878378988884 |
| 25 | 0.000476856907977415 | 0.00095371381595483 | 0.999523143092023 |
| 26 | 0.000186682092304966 | 0.000373364184609931 | 0.999813317907695 |
| 27 | 0.000108885574722319 | 0.000217771149444639 | 0.999891114425278 |
| 28 | 4.14383915722353e-05 | 8.28767831444706e-05 | 0.999958561608428 |
| 29 | 1.72779775627681e-05 | 3.45559551255361e-05 | 0.999982722022437 |
| 30 | 6.55690455161648e-06 | 1.31138091032330e-05 | 0.999993443095448 |
| 31 | 2.50258945404973e-06 | 5.00517890809946e-06 | 0.999997497410546 |
| 32 | 1.36765347839472e-06 | 2.73530695678945e-06 | 0.999998632346522 |
| 33 | 9.789827975231e-07 | 1.9579655950462e-06 | 0.999999021017203 |
| 34 | 8.31081662289104e-07 | 1.66216332457821e-06 | 0.999999168918338 |
| 35 | 4.75537323903766e-06 | 9.51074647807532e-06 | 0.999995244626761 |
| 36 | 6.07590257616875e-05 | 0.000121518051523375 | 0.999939240974238 |
| 37 | 0.000133211746073737 | 0.000266423492147474 | 0.999866788253926 |
| 38 | 0.00169484010095296 | 0.00338968020190592 | 0.998305159899047 |
| 39 | 0.00479087739616425 | 0.0095817547923285 | 0.995209122603836 |
| 40 | 0.0527031416273246 | 0.105406283254649 | 0.947296858372675 |
| 41 | 0.0499568126140036 | 0.0999136252280071 | 0.950043187385996 |
| 42 | 0.0697986494780453 | 0.139597298956091 | 0.930201350521955 |
| 43 | 0.113031365784953 | 0.226062731569906 | 0.886968634215047 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 19 | 0.703703703703704 | NOK |
| 5% type I error level | 21 | 0.777777777777778 | NOK |
| 10% type I error level | 23 | 0.851851851851852 | NOK |
