| Multiple Linear Regression - Estimated Regression Equation |
| y[t] = + 2589.64081632653 -318.401360544218x[t] + 285.726530612245M1[t] -141.880272108844M2[t] -205.280272108843M3[t] -177.280272108844M4[t] + 8.71972789115645M5[t] -371.080272108844M6[t] -180.680272108843M7[t] + 13.1197278911563M8[t] -133.480272108844M9[t] + 132.800000000000M10[t] + 32.7999999999998M11[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) | 2589.64081632653 | 131.781034 | 19.6511 | 0 | 0 |
| x | -318.401360544218 | 72.543072 | -4.3891 | 6.2e-05 | 3.1e-05 |
| M1 | 285.726530612245 | 168.574865 | 1.695 | 0.096563 | 0.048282 |
| M2 | -141.880272108844 | 176.504911 | -0.8038 | 0.425457 | 0.212729 |
| M3 | -205.280272108843 | 176.504911 | -1.163 | 0.250567 | 0.125284 |
| M4 | -177.280272108844 | 176.504911 | -1.0044 | 0.320226 | 0.160113 |
| M5 | 8.71972789115645 | 176.504911 | 0.0494 | 0.960804 | 0.480402 |
| M6 | -371.080272108844 | 176.504911 | -2.1024 | 0.040791 | 0.020395 |
| M7 | -180.680272108843 | 176.504911 | -1.0237 | 0.311129 | 0.155565 |
| M8 | 13.1197278911563 | 176.504911 | 0.0743 | 0.941056 | 0.470528 |
| M9 | -133.480272108844 | 176.504911 | -0.7562 | 0.4532 | 0.2266 |
| M10 | 132.800000000000 | 175.9076 | 0.7549 | 0.453972 | 0.226986 |
| M11 | 32.7999999999998 | 175.9076 | 0.1865 | 0.852869 | 0.426434 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.668376440301656 |
| R-squared | 0.446727065950313 |
| Adjusted R-squared | 0.308408832437891 |
| F-TEST (value) | 3.22970482348008 |
| F-TEST (DF numerator) | 12 |
| F-TEST (DF denominator) | 48 |
| p-value | 0.00186216208043333 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 278.134337495171 |
| Sum Squared Residuals | 3713218.06530612 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 3016 | 2875.36734693877 | 140.632653061227 |
| 2 | 2155 | 2447.76054421769 | -292.760544217687 |
| 3 | 2172 | 2384.36054421769 | -212.360544217686 |
| 4 | 2150 | 2412.36054421769 | -262.360544217687 |
| 5 | 2533 | 2598.36054421769 | -65.3605442176871 |
| 6 | 2058 | 2218.56054421769 | -160.560544217687 |
| 7 | 2160 | 2408.96054421769 | -248.960544217687 |
| 8 | 2260 | 2602.76054421769 | -342.760544217687 |
| 9 | 2498 | 2456.16054421769 | 41.8394557823126 |
| 10 | 2695 | 2722.44081632653 | -27.4408163265305 |
| 11 | 2799 | 2622.44081632653 | 176.559183673469 |
| 12 | 2946 | 2589.64081632653 | 356.359183673469 |
| 13 | 2930 | 2875.36734693878 | 54.6326530612238 |
| 14 | 2318 | 2447.76054421769 | -129.760544217687 |
| 15 | 2540 | 2384.36054421769 | 155.639455782313 |
| 16 | 2570 | 2412.36054421769 | 157.639455782313 |
| 17 | 2669 | 2598.36054421769 | 70.6394557823127 |
| 18 | 2450 | 2218.56054421769 | 231.439455782313 |
| 19 | 2842 | 2408.96054421769 | 433.039455782313 |
| 20 | 3440 | 2602.76054421769 | 837.239455782313 |
| 21 | 2678 | 2456.16054421769 | 221.839455782313 |
| 22 | 2981 | 2722.44081632653 | 258.559183673469 |
| 23 | 2260 | 2622.44081632653 | -362.440816326531 |
| 24 | 2844 | 2589.64081632653 | 254.359183673469 |
| 25 | 2546 | 2875.36734693878 | -329.367346938776 |
| 26 | 2456 | 2447.76054421769 | 8.23945578231283 |
| 27 | 2295 | 2384.36054421769 | -89.3605442176873 |
| 28 | 2379 | 2412.36054421769 | -33.3605442176871 |
| 29 | 2479 | 2598.36054421769 | -119.360544217687 |
| 30 | 2057 | 2218.56054421769 | -161.560544217687 |
| 31 | 2280 | 2408.96054421769 | -128.960544217687 |
| 32 | 2351 | 2602.76054421769 | -251.760544217687 |
| 33 | 2276 | 2456.16054421769 | -180.160544217687 |
| 34 | 2548 | 2404.03945578231 | 143.960544217687 |
| 35 | 2311 | 2304.03945578231 | 6.96054421768714 |
| 36 | 2201 | 2271.23945578231 | -70.239455782313 |
| 37 | 2725 | 2556.96598639456 | 168.034013605442 |
| 38 | 2408 | 2129.35918367347 | 278.640816326531 |
| 39 | 2139 | 2065.95918367347 | 73.0408163265305 |
| 40 | 1898 | 2093.95918367347 | -195.959183673469 |
| 41 | 2537 | 2279.95918367347 | 257.040816326531 |
| 42 | 2068 | 1900.15918367347 | 167.840816326531 |
| 43 | 2063 | 2090.55918367347 | -27.5591836734693 |
| 44 | 2520 | 2284.35918367347 | 235.640816326531 |
| 45 | 2434 | 2137.75918367347 | 296.240816326531 |
| 46 | 2190 | 2404.03945578231 | -214.039455782313 |
| 47 | 2794 | 2304.03945578231 | 489.960544217687 |
| 48 | 2070 | 2271.23945578231 | -201.239455782313 |
| 49 | 2615 | 2556.96598639456 | 58.0340136054416 |
| 50 | 2265 | 2129.35918367347 | 135.640816326531 |
| 51 | 2139 | 2065.95918367347 | 73.0408163265305 |
| 52 | 2428 | 2093.95918367347 | 334.040816326531 |
| 53 | 2137 | 2279.95918367347 | -142.959183673469 |
| 54 | 1823 | 1900.15918367347 | -77.1591836734694 |
| 55 | 2063 | 2090.55918367347 | -27.5591836734693 |
| 56 | 1806 | 2284.35918367347 | -478.359183673469 |
| 57 | 1758 | 2137.75918367347 | -379.759183673469 |
| 58 | 2243 | 2404.03945578231 | -161.039455782313 |
| 59 | 1993 | 2304.03945578231 | -311.039455782313 |
| 60 | 1932 | 2271.23945578231 | -339.239455782313 |
| 61 | 2465 | 2556.96598639456 | -91.9659863945585 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 16 | 0.405071279018884 | 0.810142558037769 | 0.594928720981116 |
| 17 | 0.257128781594800 | 0.514257563189599 | 0.7428712184052 |
| 18 | 0.261586775669138 | 0.523173551338276 | 0.738413224330862 |
| 19 | 0.489501291843967 | 0.979002583687934 | 0.510498708156033 |
| 20 | 0.964647663358868 | 0.0707046732822645 | 0.0353523366411322 |
| 21 | 0.951693750654695 | 0.0966124986906091 | 0.0483062493453046 |
| 22 | 0.94930925419321 | 0.101381491613580 | 0.0506907458067902 |
| 23 | 0.953688452997632 | 0.0926230940047352 | 0.0463115470023676 |
| 24 | 0.966362832117088 | 0.0672743357658242 | 0.0336371678829121 |
| 25 | 0.964210395491895 | 0.0715792090162093 | 0.0357896045081047 |
| 26 | 0.944981243223733 | 0.110037513552534 | 0.0550187567762668 |
| 27 | 0.912141472789958 | 0.175717054420084 | 0.0878585272100422 |
| 28 | 0.866559125826477 | 0.266881748347047 | 0.133440874173523 |
| 29 | 0.810261225170478 | 0.379477549659044 | 0.189738774829522 |
| 30 | 0.749662402331894 | 0.500675195336213 | 0.250337597668106 |
| 31 | 0.681061825501475 | 0.63787634899705 | 0.318938174498525 |
| 32 | 0.66421273832309 | 0.671574523353822 | 0.335787261676911 |
| 33 | 0.598290304130007 | 0.803419391739985 | 0.401709695869993 |
| 34 | 0.549681424948808 | 0.900637150102384 | 0.450318575051192 |
| 35 | 0.453237961303298 | 0.906475922606595 | 0.546762038696702 |
| 36 | 0.40682603215476 | 0.81365206430952 | 0.59317396784524 |
| 37 | 0.341917219104340 | 0.683834438208681 | 0.65808278089566 |
| 38 | 0.289154246547123 | 0.578308493094247 | 0.710845753452877 |
| 39 | 0.204276211329097 | 0.408552422658195 | 0.795723788670903 |
| 40 | 0.208809895661752 | 0.417619791323504 | 0.791190104338248 |
| 41 | 0.181750602305841 | 0.363501204611683 | 0.818249397694159 |
| 42 | 0.12633226134003 | 0.25266452268006 | 0.87366773865997 |
| 43 | 0.0731834807906737 | 0.146366961581347 | 0.926816519209326 |
| 44 | 0.115764348601026 | 0.231528697202051 | 0.884235651398974 |
| 45 | 0.196524679852474 | 0.393049359704949 | 0.803475320147526 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 0 | 0 | OK |
| 5% type I error level | 0 | 0 | OK |
| 10% type I error level | 5 | 0.166666666666667 | NOK |
