| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 3.19853175831125 -0.200223337414399X[t] -0.0731380364246286M1[t] -0.0635410640368461M2[t] -0.247325814755517M3[t] -0.231129176925388M4[t] + 0.370889683425942M5[t] + 0.390427099169884M6[t] + 0.486116384355618M7[t] + 0.349702934330727M8[t] + 0.277271617312685M9[t] + 0.216809033056628M10[t] -0.0036312174579902M11[t] + 0.020417916773178t + 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) | 3.19853175831125 | 2.465007 | 1.2976 | 0.200388 | 0.100194 |
| X | -0.200223337414399 | 0.308151 | -0.6498 | 0.518823 | 0.259412 |
| M1 | -0.0731380364246286 | 0.729866 | -0.1002 | 0.92058 | 0.46029 |
| M2 | -0.0635410640368461 | 0.734145 | -0.0866 | 0.931374 | 0.465687 |
| M3 | -0.247325814755517 | 0.727078 | -0.3402 | 0.735158 | 0.367579 |
| M4 | -0.231129176925388 | 0.72053 | -0.3208 | 0.749717 | 0.374858 |
| M5 | 0.370889683425942 | 0.759008 | 0.4887 | 0.627226 | 0.313613 |
| M6 | 0.390427099169884 | 0.767117 | 0.509 | 0.613023 | 0.306512 |
| M7 | 0.486116384355618 | 0.75254 | 0.646 | 0.521254 | 0.260627 |
| M8 | 0.349702934330727 | 0.752364 | 0.4648 | 0.644089 | 0.322044 |
| M9 | 0.277271617312685 | 0.751841 | 0.3688 | 0.713841 | 0.356921 |
| M10 | 0.216809033056628 | 0.753179 | 0.2879 | 0.774645 | 0.387322 |
| M11 | -0.0036312174579902 | 0.755071 | -0.0048 | 0.996182 | 0.498091 |
| t | 0.020417916773178 | 0.010032 | 2.0353 | 0.047139 | 0.02357 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.449208059996124 |
| R-squared | 0.201787881165481 |
| Adjusted R-squared | -0.00574726973149353 |
| F-TEST (value) | 0.972307005793218 |
| F-TEST (DF numerator) | 13 |
| F-TEST (DF denominator) | 50 |
| p-value | 0.490542412898064 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 1.18809754306499 |
| Sum Squared Residuals | 70.5787885918531 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 1.4 | 1.50398027186173 | -0.103980271861729 |
| 2 | 1.2 | 1.57403982850557 | -0.374039828505567 |
| 3 | 1 | 1.51078466326727 | -0.510784663267274 |
| 4 | 1.7 | 1.68755555406066 | 0.0124444459393401 |
| 5 | 2.4 | 2.37005933240949 | 0.0299406675905115 |
| 6 | 2 | 2.38999233118517 | -0.389992331185169 |
| 7 | 2.1 | 2.30587619572968 | -0.205876195729681 |
| 8 | 2 | 2.10979132751221 | -0.109791327512209 |
| 9 | 1.8 | 2.03775559352591 | -0.237755593525906 |
| 10 | 2.7 | 2.07780026100879 | 0.622199738991215 |
| 11 | 2.3 | 1.91782259475023 | 0.382177405249775 |
| 12 | 1.9 | 1.92184939523995 | -0.0218493952399534 |
| 13 | 2 | 1.82908460810562 | 0.170915391894377 |
| 14 | 2.3 | 1.85909949726658 | 0.440900502733417 |
| 15 | 2.8 | 1.69573266332109 | 1.10426733667891 |
| 16 | 2.4 | 1.79241421914872 | 0.607585780851283 |
| 17 | 2.3 | 2.41485099627322 | -0.114850996273225 |
| 18 | 2.7 | 2.53489566375610 | 0.165104336243896 |
| 19 | 2.7 | 2.57091353074926 | 0.129086469250744 |
| 20 | 2.9 | 2.45491799749754 | 0.445082002502455 |
| 21 | 3 | 2.38288226351124 | 0.617117736488759 |
| 22 | 2.2 | 2.32281526228692 | -0.122815262286921 |
| 23 | 2.3 | 2.12279292854548 | 0.177207071454519 |
| 24 | 2.8 | 2.10679739529377 | 0.69320260470623 |
| 25 | 2.8 | 2.01403260815944 | 0.78596739184056 |
| 26 | 2.8 | 2.02402516357896 | 0.77597483642104 |
| 27 | 2.2 | 1.86065832963347 | 0.339341670366534 |
| 28 | 2.6 | 1.89727288423677 | 0.702727115763227 |
| 29 | 2.8 | 2.5797766625856 | 0.220223337414399 |
| 30 | 2.5 | 2.73986599755136 | -0.239865997551361 |
| 31 | 2.4 | 2.93606253447603 | -0.536062534476032 |
| 32 | 2.3 | 2.88013400244864 | -0.58013400244864 |
| 33 | 1.9 | 2.80809826846234 | -0.908098268462335 |
| 34 | 1.7 | 2.72800893349658 | -1.02800893349658 |
| 35 | 2 | 2.50796426601370 | -0.507964266013696 |
| 36 | 2.1 | 2.51199106650342 | -0.411991066503424 |
| 37 | 1.7 | 2.43924861311053 | -0.739248613110534 |
| 38 | 1.8 | 2.48928583601293 | -0.689285836012934 |
| 39 | 1.8 | 2.36596366955032 | -0.56596366955032 |
| 40 | 1.8 | 2.38255589041219 | -0.582555890412187 |
| 41 | 1.3 | 3.04503733501958 | -1.74503733501958 |
| 42 | 1.3 | 3.16508200250246 | -1.86508200250245 |
| 43 | 1.3 | 3.22112220323705 | -1.92112220323705 |
| 44 | 1.2 | 3.12514900372677 | -1.92514900372678 |
| 45 | 1.4 | 3.11318027096479 | -1.71318027096479 |
| 46 | 2.2 | 3.09315793722335 | -0.893157937223351 |
| 47 | 2.9 | 2.91315793722335 | -0.0131579372233512 |
| 48 | 3.1 | 2.8771400702302 | 0.222859929769801 |
| 49 | 3.5 | 2.76435294935443 | 0.73564705064557 |
| 50 | 3.6 | 2.79436783851539 | 0.805632161484611 |
| 51 | 4.4 | 2.71109033953566 | 1.68890966046434 |
| 52 | 4.1 | 2.80777189536328 | 1.29222810463672 |
| 53 | 5.1 | 3.49027567371211 | 1.60972432628789 |
| 54 | 5.8 | 3.47016400500491 | 2.32983599499509 |
| 55 | 5.9 | 3.36602553580798 | 2.53397446419202 |
| 56 | 5.4 | 3.23000766881483 | 2.16999233118517 |
| 57 | 5.5 | 3.25808360353573 | 2.24191639646427 |
| 58 | 4.8 | 3.37821760598437 | 1.42178239401563 |
| 59 | 3.2 | 3.23826227346725 | -0.0382622734672462 |
| 60 | 2.7 | 3.18222207273265 | -0.482222072732654 |
| 61 | 2.1 | 2.94930094940824 | -0.849300949408245 |
| 62 | 1.9 | 2.85918183612057 | -0.959181836120567 |
| 63 | 0.6 | 2.65577033469219 | -2.05577033469219 |
| 64 | 0.7 | 2.73242955677838 | -2.03242955677838 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 17 | 0.0600373187173287 | 0.120074637434657 | 0.939962681282671 |
| 18 | 0.0171496024352501 | 0.0342992048705002 | 0.98285039756475 |
| 19 | 0.00523332764629523 | 0.0104666552925905 | 0.994766672353705 |
| 20 | 0.00131956573917313 | 0.00263913147834625 | 0.998680434260827 |
| 21 | 0.00031787983766048 | 0.00063575967532096 | 0.99968212016234 |
| 22 | 0.000783736742613174 | 0.00156747348522635 | 0.999216263257387 |
| 23 | 0.000332817470904682 | 0.000665634941809364 | 0.999667182529095 |
| 24 | 0.000109057872006419 | 0.000218115744012838 | 0.999890942127994 |
| 25 | 3.26511036663507e-05 | 6.53022073327015e-05 | 0.999967348896334 |
| 26 | 9.92324251880837e-06 | 1.98464850376167e-05 | 0.999990076757481 |
| 27 | 4.83146507837474e-06 | 9.66293015674947e-06 | 0.999995168534922 |
| 28 | 1.99254256937857e-06 | 3.98508513875715e-06 | 0.99999800745743 |
| 29 | 7.5952923354468e-07 | 1.51905846708936e-06 | 0.999999240470766 |
| 30 | 4.62514090971134e-07 | 9.25028181942269e-07 | 0.999999537485909 |
| 31 | 7.47901855831481e-07 | 1.49580371166296e-06 | 0.999999252098144 |
| 32 | 5.74943995003683e-07 | 1.14988799000737e-06 | 0.999999425056005 |
| 33 | 4.20206737185008e-07 | 8.40413474370015e-07 | 0.999999579793263 |
| 34 | 3.74734427182479e-07 | 7.49468854364957e-07 | 0.999999625265573 |
| 35 | 1.90317590760419e-07 | 3.80635181520837e-07 | 0.99999980968241 |
| 36 | 1.04633919411434e-07 | 2.09267838822868e-07 | 0.99999989536608 |
| 37 | 4.48920499259087e-08 | 8.97840998518173e-08 | 0.99999995510795 |
| 38 | 1.34617346537585e-08 | 2.6923469307517e-08 | 0.999999986538265 |
| 39 | 3.63797319526439e-09 | 7.27594639052878e-09 | 0.999999996362027 |
| 40 | 2.81727894498358e-09 | 5.63455788996715e-09 | 0.99999999718272 |
| 41 | 5.31720823324365e-09 | 1.06344164664873e-08 | 0.999999994682792 |
| 42 | 7.49651005109034e-09 | 1.49930201021807e-08 | 0.99999999250349 |
| 43 | 1.01025409233999e-07 | 2.02050818467999e-07 | 0.99999989897459 |
| 44 | 1.29035586785711e-05 | 2.58071173571422e-05 | 0.999987096441321 |
| 45 | 0.0539955911259929 | 0.107991182251986 | 0.946004408874007 |
| 46 | 0.861571711324773 | 0.276856577350453 | 0.138428288675227 |
| 47 | 0.795204949780818 | 0.409590100438364 | 0.204795050219182 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 25 | 0.806451612903226 | NOK |
| 5% type I error level | 27 | 0.870967741935484 | NOK |
| 10% type I error level | 27 | 0.870967741935484 | NOK |
