| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 2718.53693396615 -143.325735825476X[t] + 149.357889865432M1[t] + 79.583054198158M2[t] + 308.876265971366M3[t] + 174.909067479149M4[t] + 155.408839553913M5[t] + 443.408839553913M6[t] + 8.6416410616967M7[t] -52.0585868635391M8[t] -25.2585868635390M9[t] + 169.654305814339M10[t] -198.166286791274M11[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) | 2718.53693396615 | 165.418184 | 16.4343 | 0 | 0 |
| X | -143.325735825476 | 38.433263 | -3.7292 | 0.000507 | 0.000254 |
| M1 | 149.357889865432 | 158.881256 | 0.9401 | 0.351894 | 0.175947 |
| M2 | 79.583054198158 | 166.538384 | 0.4779 | 0.634915 | 0.317457 |
| M3 | 308.876265971366 | 166.482461 | 1.8553 | 0.069699 | 0.034849 |
| M4 | 174.909067479149 | 166.264321 | 1.052 | 0.29807 | 0.149035 |
| M5 | 155.408839553913 | 166.184078 | 0.9352 | 0.354386 | 0.177193 |
| M6 | 443.408839553913 | 166.184078 | 2.6682 | 0.01037 | 0.005185 |
| M7 | 8.6416410616967 | 166.027835 | 0.052 | 0.958705 | 0.479353 |
| M8 | -52.0585868635391 | 165.974178 | -0.3137 | 0.755142 | 0.377571 |
| M9 | -25.2585868635390 | 165.974178 | -0.1522 | 0.87968 | 0.43984 |
| M10 | 169.654305814339 | 165.893118 | 1.0227 | 0.311589 | 0.155795 |
| M11 | -198.166286791274 | 165.831295 | -1.195 | 0.237963 | 0.118982 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.677027504049389 |
| R-squared | 0.458366241239345 |
| Adjusted R-squared | 0.322957801549182 |
| F-TEST (value) | 3.38506404983442 |
| F-TEST (DF numerator) | 12 |
| F-TEST (DF denominator) | 48 |
| p-value | 0.00125516766011968 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 262.184694437486 |
| Sum Squared Residuals | 3299559.07186933 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 2360 | 2581.24335218062 | -221.243352180622 |
| 2 | 2214 | 2511.46851651335 | -297.468516513352 |
| 3 | 2825 | 2740.76172828656 | 84.23827171344 |
| 4 | 2355 | 2606.79452979434 | -251.794529794343 |
| 5 | 2333 | 2587.29430186911 | -254.294301869108 |
| 6 | 3016 | 2875.29430186911 | 140.705698130893 |
| 7 | 2155 | 2440.52710337689 | -285.527103376891 |
| 8 | 2172 | 2379.82687545165 | -207.826875451655 |
| 9 | 2150 | 2406.62687545165 | -256.626875451655 |
| 10 | 2533 | 2601.53976812953 | -68.5397681295326 |
| 11 | 2058 | 2233.71917552392 | -175.71917552392 |
| 12 | 2160 | 2431.88546231519 | -271.885462315194 |
| 13 | 2260 | 2581.24335218063 | -321.243352180626 |
| 14 | 2498 | 2511.46851651335 | -13.4685165133519 |
| 15 | 2695 | 2740.76172828656 | -45.7617282865597 |
| 16 | 2799 | 2606.79452979434 | 192.205470205657 |
| 17 | 2947 | 2587.29430186911 | 359.705698130893 |
| 18 | 2930 | 2875.29430186911 | 54.7056981308925 |
| 19 | 2318 | 2440.52710337689 | -122.527103376891 |
| 20 | 2540 | 2379.82687545165 | 160.173124548345 |
| 21 | 2570 | 2406.62687545165 | 163.373124548345 |
| 22 | 2669 | 2601.53976812953 | 67.4602318704673 |
| 23 | 2450 | 2233.71917552392 | 216.280824476080 |
| 24 | 2842 | 2431.88546231519 | 410.114537684806 |
| 25 | 3440 | 2581.24335218063 | 858.756647819374 |
| 26 | 2678 | 2511.46851651335 | 166.531483486648 |
| 27 | 2981 | 2740.76172828656 | 240.238271713440 |
| 28 | 2260 | 2576.69612527099 | -316.696125270993 |
| 29 | 2844 | 2551.46286791274 | 292.537132087262 |
| 30 | 2546 | 2839.46286791274 | -293.462867912738 |
| 31 | 2456 | 2376.03052225543 | 79.9694777445737 |
| 32 | 2295 | 2308.16400753892 | -13.1640075389167 |
| 33 | 2379 | 2334.96400753892 | 44.0359924610832 |
| 34 | 2479 | 2509.81129720123 | -30.8112972012277 |
| 35 | 2057 | 2126.22487365481 | -69.2248736548125 |
| 36 | 2280 | 2298.5925279975 | -18.5925279975007 |
| 37 | 2351 | 2437.91761635515 | -86.9176163551494 |
| 38 | 2276 | 2343.77740559754 | -67.7774055975444 |
| 39 | 2548 | 2561.60455850471 | -13.6045585047140 |
| 40 | 2311 | 2407.57175699693 | -96.5717569969307 |
| 41 | 2201 | 2372.30569813089 | -171.305698130893 |
| 42 | 2725 | 2660.30569813089 | 64.6943018691073 |
| 43 | 2408 | 2204.03963926485 | 203.960360735145 |
| 44 | 2139 | 2129.00683775707 | 9.9931622429289 |
| 45 | 1898 | 2155.80683775707 | -257.806837757071 |
| 46 | 2537 | 2329.22087006113 | 207.779129938873 |
| 47 | 2069 | 1947.06770387297 | 121.932296127033 |
| 48 | 2063 | 2145.23399066424 | -82.2339906642408 |
| 49 | 2524 | 2294.59188052967 | 229.408119470327 |
| 50 | 2437 | 2224.8170448624 | 212.182955137601 |
| 51 | 2189 | 2454.11025663561 | -265.110256635607 |
| 52 | 2793 | 2320.14305814339 | 472.85694185661 |
| 53 | 2074 | 2300.64283021815 | -226.642830218154 |
| 54 | 2622 | 2588.64283021815 | 33.3571697818456 |
| 55 | 2278 | 2153.87563172594 | 124.124368274062 |
| 56 | 2144 | 2093.1754038007 | 50.824596199298 |
| 57 | 2427 | 2119.9754038007 | 307.024596199298 |
| 58 | 2139 | 2314.88829647858 | -175.888296478580 |
| 59 | 1828 | 1921.26907142438 | -93.2690714243812 |
| 60 | 2072 | 2109.40255670787 | -37.4025567078717 |
| 61 | 1800 | 2258.76044657330 | -458.760446573304 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 16 | 0.473008451142425 | 0.94601690228485 | 0.526991548857575 |
| 17 | 0.696647234174036 | 0.606705531651929 | 0.303352765825964 |
| 18 | 0.561486930091036 | 0.877026139817928 | 0.438513069908964 |
| 19 | 0.473286422109878 | 0.946572844219755 | 0.526713577890122 |
| 20 | 0.450255996155234 | 0.900511992310467 | 0.549744003844766 |
| 21 | 0.450911106048382 | 0.901822212096764 | 0.549088893951618 |
| 22 | 0.350202486683407 | 0.700404973366814 | 0.649797513316593 |
| 23 | 0.336242730367431 | 0.672485460734862 | 0.663757269632569 |
| 24 | 0.496316087284258 | 0.992632174568516 | 0.503683912715742 |
| 25 | 0.97483569161869 | 0.0503286167626209 | 0.0251643083813104 |
| 26 | 0.964367321088165 | 0.0712653578236699 | 0.0356326789118350 |
| 27 | 0.964416677022926 | 0.0711666459541487 | 0.0355833229770743 |
| 28 | 0.966604763403013 | 0.0667904731939735 | 0.0333952365969867 |
| 29 | 0.983555442586086 | 0.0328891148278272 | 0.0164445574139136 |
| 30 | 0.981332000788403 | 0.037335998423194 | 0.018667999211597 |
| 31 | 0.972852252736674 | 0.0542954945266524 | 0.0271477472633262 |
| 32 | 0.952903453957414 | 0.0941930920851721 | 0.0470965460425861 |
| 33 | 0.923372004897764 | 0.153255990204472 | 0.076627995102236 |
| 34 | 0.880164326957626 | 0.239671346084749 | 0.119835673042374 |
| 35 | 0.82319537435589 | 0.353609251288219 | 0.176804625644109 |
| 36 | 0.751349077168062 | 0.497301845663876 | 0.248650922831938 |
| 37 | 0.67053439752496 | 0.658931204950079 | 0.329465602475039 |
| 38 | 0.596532193966851 | 0.806935612066298 | 0.403467806033149 |
| 39 | 0.534210602351874 | 0.931578795296253 | 0.465789397648126 |
| 40 | 0.614490732838302 | 0.771018534323397 | 0.385509267161698 |
| 41 | 0.504602856183196 | 0.990794287633608 | 0.495397143816804 |
| 42 | 0.390842871997775 | 0.78168574399555 | 0.609157128002225 |
| 43 | 0.292795325839024 | 0.585590651678047 | 0.707204674160976 |
| 44 | 0.189023960671303 | 0.378047921342606 | 0.810976039328697 |
| 45 | 0.515444256287256 | 0.969111487425488 | 0.484555743712744 |
| 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 | 2 | 0.0666666666666667 | NOK |
| 10% type I error level | 8 | 0.266666666666667 | NOK |
