| Multiple Linear Regression - Estimated Regression Equation |
| Yt[t] = + 64.6987662633607 -0.132646690016129`Yt-1`[t] + 0.169440930713412`Yt-2`[t] + 0.153212945603548`Yt-3`[t] -0.0442066950446977`Yt-4`[t] -4.85820399237455M1[t] + 1.78511364782675M2[t] -6.45172660810019M3[t] -15.9451711714370M4[t] -14.9994820948072M5[t] -9.12649588972515M6[t] -17.5219597850958M7[t] -30.1652515478012M8[t] -7.32381920473443M9[t] -2.70606622771052M10[t] + 4.85219699734078M11[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) | 64.6987662633607 | 19.510584 | 3.3161 | 0.001949 | 0.000975 |
| `Yt-1` | -0.132646690016129 | 0.158219 | -0.8384 | 0.406803 | 0.203401 |
| `Yt-2` | 0.169440930713412 | 0.156908 | 1.0799 | 0.286667 | 0.143333 |
| `Yt-3` | 0.153212945603548 | 0.152758 | 1.003 | 0.321901 | 0.16095 |
| `Yt-4` | -0.0442066950446977 | 0.153921 | -0.2872 | 0.775439 | 0.387719 |
| M1 | -4.85820399237455 | 4.656622 | -1.0433 | 0.303079 | 0.151539 |
| M2 | 1.78511364782675 | 4.846324 | 0.3683 | 0.714559 | 0.35728 |
| M3 | -6.45172660810019 | 5.736756 | -1.1246 | 0.26745 | 0.133725 |
| M4 | -15.9451711714370 | 5.814409 | -2.7424 | 0.009081 | 0.00454 |
| M5 | -14.9994820948072 | 6.200785 | -2.419 | 0.020206 | 0.010103 |
| M6 | -9.12649588972515 | 6.976841 | -1.3081 | 0.198303 | 0.099151 |
| M7 | -17.5219597850958 | 5.414095 | -3.2364 | 0.002434 | 0.001217 |
| M8 | -30.1652515478012 | 5.390629 | -5.5959 | 2e-06 | 1e-06 |
| M9 | -7.32381920473443 | 7.269757 | -1.0074 | 0.319781 | 0.15989 |
| M10 | -2.70606622771052 | 6.500739 | -0.4163 | 0.679437 | 0.339719 |
| M11 | 4.85219699734078 | 5.128084 | 0.9462 | 0.349727 | 0.174864 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.923623163761997 |
| R-squared | 0.853079748637721 |
| Adjusted R-squared | 0.797984654376866 |
| F-TEST (value) | 15.4837696546758 |
| F-TEST (DF numerator) | 15 |
| F-TEST (DF denominator) | 40 |
| p-value | 3.78119757726836e-12 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 4.4772364972384 |
| Sum Squared Residuals | 801.825866088144 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 68.848 | 68.8576618037653 | -0.00966180376527437 |
| 2 | 77.056 | 78.2161732926101 | -1.16017329261011 |
| 3 | 62.246 | 67.6902780271788 | -5.44427802717881 |
| 4 | 60.777 | 60.8675968583704 | -0.0905968583704075 |
| 5 | 64.513 | 60.9468706586199 | 3.56612934138012 |
| 6 | 58.353 | 63.4434478252682 | -5.09044782526823 |
| 7 | 56.511 | 56.9277501940626 | -0.416750194062605 |
| 8 | 44.554 | 44.1223807009678 | 0.431619299032193 |
| 9 | 71.414 | 67.1288113645785 | 4.28518863542152 |
| 10 | 65.719 | 66.1477640349025 | -0.428764034902504 |
| 11 | 80.997 | 77.2620951002486 | 3.73490489975138 |
| 12 | 69.826 | 74.0622350439893 | -4.23623504398927 |
| 13 | 65.386 | 71.2146062111117 | -5.82860621111166 |
| 14 | 75.589 | 79.1465950291956 | -3.55759502919558 |
| 15 | 65.52 | 66.4171111604364 | -0.897111160436408 |
| 16 | 59.003 | 59.8016594468055 | -0.798659446805518 |
| 17 | 63.961 | 61.6652156809085 | 2.29578431909145 |
| 18 | 59.716 | 63.7825509926081 | -4.06655099260812 |
| 19 | 57.52 | 56.2368888767398 | 1.28311112326023 |
| 20 | 42.886 | 44.21333731034 | -1.32733731034004 |
| 21 | 69.805 | 67.7542632831375 | 2.05073671686247 |
| 22 | 64.656 | 66.1729032234765 | -1.51690322347653 |
| 23 | 80.353 | 76.8303043256511 | 3.52269567434893 |
| 24 | 71.321 | 73.7947609408698 | -2.47376094086976 |
| 25 | 76.577 | 70.8154426613084 | 5.76155733869157 |
| 26 | 81.58 | 77.8637826925055 | 3.71621730749454 |
| 27 | 71.127 | 67.7761607614497 | 3.35083923855034 |
| 28 | 63.478 | 61.7215471369466 | 1.75645286305339 |
| 29 | 48.152 | 62.4448586744621 | -14.2928586744621 |
| 30 | 69.236 | 67.232033356002 | 2.00396664399806 |
| 31 | 57.038 | 52.7331617065981 | 4.30483829340185 |
| 32 | 43.621 | 43.270382257948 | 0.350617742052007 |
| 33 | 69.551 | 69.7325483214792 | -0.181548321479206 |
| 34 | 72.009 | 65.8364381902086 | 6.17256180979145 |
| 35 | 72.14 | 75.9458343595914 | -3.80583435959141 |
| 36 | 81.519 | 76.0586793604668 | 5.46032063953321 |
| 37 | 73.31 | 69.208896642139 | 4.10110335786108 |
| 38 | 80.406 | 78.441708289298 | 1.96429171070208 |
| 39 | 70.697 | 69.303859660555 | 1.39314033944504 |
| 40 | 59.328 | 60.6282949916434 | -1.30029499164338 |
| 41 | 68.281 | 62.8870341123948 | 5.39396588760526 |
| 42 | 70.041 | 63.8448253635796 | 6.19617463642044 |
| 43 | 51.244 | 55.4202327700799 | -4.17623277007994 |
| 44 | 46.538 | 47.442818295615 | -0.904818295615059 |
| 45 | 61.443 | 67.5973770308048 | -6.15437703080479 |
| 46 | 62.256 | 66.4828945514124 | -4.22689455141241 |
| 47 | 73.117 | 76.5687662145089 | -3.45176621450890 |
| 48 | 74.155 | 72.9053246546742 | 1.24967534532583 |
| 49 | 65.191 | 69.2153926816757 | -4.02439268167572 |
| 50 | 77.889 | 78.851740696391 | -0.962740696390921 |
| 51 | 68.688 | 67.0905903903802 | 1.59740960961984 |
| 52 | 59.983 | 59.5499015662341 | 0.433098433765919 |
| 53 | 65.47 | 62.4330208736147 | 3.03697912638529 |
| 54 | 65.089 | 64.1321424625422 | 0.956857537457838 |
| 55 | 54.795 | 55.7899664525195 | -0.994966452519525 |
| 56 | 47.123 | 45.6730814351291 | 1.44991856487089 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 19 | 0.0217754929702136 | 0.0435509859404272 | 0.978224507029786 |
| 20 | 0.00500204943031435 | 0.0100040988606287 | 0.994997950569686 |
| 21 | 0.00159376518445082 | 0.00318753036890163 | 0.99840623481555 |
| 22 | 0.00062338625067163 | 0.00124677250134326 | 0.999376613749328 |
| 23 | 0.000304210274025256 | 0.000608420548050512 | 0.999695789725975 |
| 24 | 9.5528673106095e-05 | 0.00019105734621219 | 0.999904471326894 |
| 25 | 0.0556659335374381 | 0.111331867074876 | 0.944334066462562 |
| 26 | 0.0278023330809941 | 0.0556046661619883 | 0.972197666919006 |
| 27 | 0.0181613190567343 | 0.0363226381134686 | 0.981838680943266 |
| 28 | 0.00815917186808435 | 0.0163183437361687 | 0.991840828131916 |
| 29 | 0.88292685282883 | 0.23414629434234 | 0.11707314717117 |
| 30 | 0.971358495012105 | 0.0572830099757898 | 0.0286415049878949 |
| 31 | 0.949171677334019 | 0.101656645331962 | 0.0508283226659811 |
| 32 | 0.952405566101108 | 0.0951888677977845 | 0.0475944338988923 |
| 33 | 0.93989114882068 | 0.12021770235864 | 0.06010885117932 |
| 34 | 0.923474371518591 | 0.153051256962817 | 0.0765256284814086 |
| 35 | 0.869321744376011 | 0.261356511247977 | 0.130678255623989 |
| 36 | 0.8890059000544 | 0.221988199891198 | 0.110994099945599 |
| 37 | 0.812867567589952 | 0.374264864820096 | 0.187132432410048 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 4 | 0.210526315789474 | NOK |
| 5% type I error level | 8 | 0.421052631578947 | NOK |
| 10% type I error level | 11 | 0.578947368421053 | NOK |
