| Multiple Linear Regression - Estimated Regression Equation |
| Soldiers[t] = + 82.19825815463 -48.8422479664777Dummy[t] -4.8590042294134M1[t] -9.68968586530826M2[t] -24.3324383487682M3[t] -15.4262982655884M4[t] -12.5426941871975M5[t] -14.8997323849432M6[t] -5.27930658747765M7[t] -13.1099882233725M8[t] -13.3136583447774M9[t] -12.9839117965813M10[t] -24.075289231624M11[t] -0.0489972260369107t + 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) | 82.19825815463 | 10.234328 | 8.0316 | 0 | 0 |
| Dummy | -48.8422479664777 | 6.778625 | -7.2053 | 0 | 0 |
| M1 | -4.8590042294134 | 12.205622 | -0.3981 | 0.691845 | 0.345922 |
| M2 | -9.68968586530826 | 12.32179 | -0.7864 | 0.434456 | 0.217228 |
| M3 | -24.3324383487682 | 12.182607 | -1.9973 | 0.049917 | 0.024959 |
| M4 | -15.4262982655884 | 12.173329 | -1.2672 | 0.209529 | 0.104765 |
| M5 | -12.5426941871975 | 12.274483 | -1.0219 | 0.310582 | 0.155291 |
| M6 | -14.8997323849432 | 12.159246 | -1.2254 | 0.224786 | 0.112393 |
| M7 | -5.27930658747765 | 12.154448 | -0.4344 | 0.66545 | 0.332725 |
| M8 | -13.1099882233725 | 12.240395 | -1.071 | 0.288051 | 0.144026 |
| M9 | -13.3136583447774 | 12.596936 | -1.0569 | 0.294412 | 0.147206 |
| M10 | -12.9839117965813 | 12.823909 | -1.0125 | 0.315008 | 0.157504 |
| M11 | -24.075289231624 | 12.649201 | -1.9033 | 0.061363 | 0.030682 |
| t | -0.0489972260369107 | 0.134976 | -0.363 | 0.71776 | 0.35888 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.781049808513339 |
| R-squared | 0.610038803378723 |
| Adjusted R-squared | 0.53322826465029 |
| F-TEST (value) | 7.94212374340375 |
| F-TEST (DF numerator) | 13 |
| F-TEST (DF denominator) | 66 |
| p-value | 3.04937552986217e-09 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 21.8072579105914 |
| Sum Squared Residuals | 31386.7288402174 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 37 | 77.2902566991794 | -40.2902566991794 |
| 2 | 30 | 23.5683298707702 | 6.43167012922982 |
| 3 | 47 | 57.7188281277509 | -10.7188281277509 |
| 4 | 35 | 66.5759709848939 | -31.5759709848939 |
| 5 | 30 | 20.5683298707701 | 9.4316701292299 |
| 6 | 43 | 67.0045424134652 | -24.0045424134652 |
| 7 | 82 | 76.5759709848938 | 5.42402901510618 |
| 8 | 40 | 68.6962921229621 | -28.6962921229621 |
| 9 | 47 | 68.4436247755203 | -21.4436247755203 |
| 10 | 19 | 19.8821261312018 | -0.88212613120179 |
| 11 | 52 | 57.5839994365999 | -5.58399943659992 |
| 12 | 136 | 81.6102914421869 | 54.3897085578131 |
| 13 | 80 | 76.7022899867367 | 3.29771001326335 |
| 14 | 42 | 71.8226111248048 | -29.8226111248048 |
| 15 | 54 | 57.130861415308 | -3.13086141530805 |
| 16 | 66 | 65.9880042724509 | 0.0119957275490812 |
| 17 | 81 | 68.8226111248049 | 12.1773888751951 |
| 18 | 63 | 66.4165757010223 | -3.41657570102233 |
| 19 | 137 | 75.9880042724509 | 61.0119957275491 |
| 20 | 72 | 68.1083254105192 | 3.89167458948085 |
| 21 | 107 | 67.8556580630773 | 39.1443419369227 |
| 22 | 58 | 68.1364073852366 | -10.1364073852366 |
| 23 | 36 | 56.996032724157 | -20.9960327241570 |
| 24 | 52 | 81.022324729744 | -29.022324729744 |
| 25 | 79 | 76.1143232742937 | 2.88567672570628 |
| 26 | 77 | 71.2346444123619 | 5.76535558763807 |
| 27 | 54 | 56.5428947028651 | -2.54289470286513 |
| 28 | 84 | 65.400037560008 | 18.599962439992 |
| 29 | 48 | 68.234644412362 | -20.2346444123619 |
| 30 | 96 | 65.8286089885794 | 30.1713910114206 |
| 31 | 83 | 75.400037560008 | 7.59996243999201 |
| 32 | 66 | 67.5203586980762 | -1.52035869807623 |
| 33 | 61 | 67.2676913506344 | -6.2676913506344 |
| 34 | 53 | 67.5484406727937 | -14.5484406727937 |
| 35 | 30 | 7.56581804523631 | 22.4341819547637 |
| 36 | 74 | 80.434358017301 | -6.43435801730108 |
| 37 | 69 | 75.5263565618508 | -6.52635656185079 |
| 38 | 59 | 70.646677699919 | -11.646677699919 |
| 39 | 42 | 55.9549279904222 | -13.9549279904222 |
| 40 | 65 | 64.8120708475651 | 0.187929152434931 |
| 41 | 70 | 67.646677699919 | 2.35332230008098 |
| 42 | 100 | 65.2406422761365 | 34.7593577238635 |
| 43 | 63 | 74.812070847565 | -11.8120708475651 |
| 44 | 105 | 66.9323919856333 | 38.0676080143667 |
| 45 | 82 | 66.6797246381915 | 15.3202753618085 |
| 46 | 81 | 66.9604739603507 | 14.0395260396493 |
| 47 | 75 | 55.8200992992711 | 19.1799007007289 |
| 48 | 102 | 79.8463913048581 | 22.1536086951418 |
| 49 | 121 | 74.9383898494079 | 46.0616101505921 |
| 50 | 98 | 70.058710987476 | 27.9412890125239 |
| 51 | 76 | 55.3669612779793 | 20.6330387220207 |
| 52 | 77 | 64.2241041351221 | 12.7758958648779 |
| 53 | 63 | 67.0587109874761 | -4.0587109874761 |
| 54 | 37 | 64.6526755636936 | -27.6526755636936 |
| 55 | 35 | 74.2241041351221 | -39.2241041351221 |
| 56 | 23 | 17.5021773067127 | 5.49782269328732 |
| 57 | 40 | 66.0917579257486 | -26.0917579257485 |
| 58 | 29 | 17.5302592814301 | 11.4697407185699 |
| 59 | 37 | 55.2321325868282 | -18.2321325868282 |
| 60 | 51 | 79.2584245924152 | -28.2584245924152 |
| 61 | 20 | 25.5081751704872 | -5.50817517048724 |
| 62 | 28 | 20.6284963085554 | 7.37150369144455 |
| 63 | 13 | 5.93674659905864 | 7.06325340094136 |
| 64 | 22 | 14.7938894562015 | 7.20611054379849 |
| 65 | 25 | 17.6284963085555 | 7.37150369144453 |
| 66 | 13 | 15.2224608847729 | -2.22246088477292 |
| 67 | 16 | 24.7938894562015 | -8.7938894562015 |
| 68 | 13 | 16.9142105942697 | -3.91421059426974 |
| 69 | 16 | 16.6615432468279 | -0.661543246827923 |
| 70 | 17 | 16.9422925689872 | 0.0577074310128269 |
| 71 | 9 | 5.80191790790755 | 3.19808209209245 |
| 72 | 17 | 29.8282099134946 | -12.8282099134946 |
| 73 | 25 | 24.9202084580443 | 0.0797915419556903 |
| 74 | 14 | 20.0405295961125 | -6.04052959611253 |
| 75 | 8 | 5.34877988661572 | 2.65122011338428 |
| 76 | 7 | 14.2059227437586 | -7.20592274375858 |
| 77 | 10 | 17.0405295961125 | -7.04052959611254 |
| 78 | 7 | 14.63449417233 | -7.63449417232999 |
| 79 | 10 | 24.2059227437586 | -14.2059227437586 |
| 80 | 3 | 16.3262438818268 | -13.3262438818268 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 17 | 0.380935654138568 | 0.761871308277136 | 0.619064345861432 |
| 18 | 0.234770629908143 | 0.469541259816286 | 0.765229370091857 |
| 19 | 0.33733360782745 | 0.6746672156549 | 0.66266639217255 |
| 20 | 0.219077011543955 | 0.438154023087909 | 0.780922988456045 |
| 21 | 0.277719847770330 | 0.555439695540661 | 0.72228015222967 |
| 22 | 0.196856494022704 | 0.393712988045408 | 0.803143505977296 |
| 23 | 0.492070044286015 | 0.98414008857203 | 0.507929955713985 |
| 24 | 0.989491825224566 | 0.0210163495508683 | 0.0105081747754342 |
| 25 | 0.982600828593776 | 0.0347983428124480 | 0.0173991714062240 |
| 26 | 0.971640177264651 | 0.0567196454706976 | 0.0283598227353488 |
| 27 | 0.963924059189447 | 0.0721518816211069 | 0.0360759408105534 |
| 28 | 0.94620289996544 | 0.107594200069118 | 0.0537971000345592 |
| 29 | 0.965323643544084 | 0.0693527129118324 | 0.0346763564559162 |
| 30 | 0.959707811493314 | 0.0805843770133722 | 0.0402921885066861 |
| 31 | 0.97224733808446 | 0.0555053238310796 | 0.0277526619155398 |
| 32 | 0.961694501403296 | 0.0766109971934071 | 0.0383054985967036 |
| 33 | 0.958181060892384 | 0.083637878215232 | 0.041818939107616 |
| 34 | 0.95806743670524 | 0.0838651265895205 | 0.0419325632947603 |
| 35 | 0.93706631146336 | 0.125867377073281 | 0.0629336885366406 |
| 36 | 0.93246450206734 | 0.135070995865319 | 0.0675354979326596 |
| 37 | 0.934953616584808 | 0.130092766830383 | 0.0650463834151915 |
| 38 | 0.946836015652895 | 0.10632796869421 | 0.053163984347105 |
| 39 | 0.972028658007482 | 0.0559426839850369 | 0.0279713419925185 |
| 40 | 0.970262128337427 | 0.0594757433251466 | 0.0297378716625733 |
| 41 | 0.963145259447497 | 0.0737094811050069 | 0.0368547405525034 |
| 42 | 0.968583700693919 | 0.0628325986121623 | 0.0314162993060811 |
| 43 | 0.975620366120315 | 0.0487592677593706 | 0.0243796338796853 |
| 44 | 0.984937100144645 | 0.0301257997107097 | 0.0150628998553548 |
| 45 | 0.97881620960464 | 0.0423675807907183 | 0.0211837903953591 |
| 46 | 0.968531830301299 | 0.0629363393974025 | 0.0314681696987013 |
| 47 | 0.95883567260855 | 0.0823286547828999 | 0.0411643273914499 |
| 48 | 0.970471569336744 | 0.0590568613265124 | 0.0295284306632562 |
| 49 | 0.9984399740002 | 0.00312005199959997 | 0.00156002599979999 |
| 50 | 0.999790059211256 | 0.000419881577488941 | 0.000209940788744471 |
| 51 | 0.999958190954459 | 8.36180910824826e-05 | 4.18090455412413e-05 |
| 52 | 0.99999928666368 | 1.42667264019151e-06 | 7.13336320095755e-07 |
| 53 | 0.999999830479782 | 3.39040435264190e-07 | 1.69520217632095e-07 |
| 54 | 0.999999604303005 | 7.91393990156685e-07 | 3.95696995078342e-07 |
| 55 | 0.999999778857754 | 4.42284492457833e-07 | 2.21142246228917e-07 |
| 56 | 0.99999884568695 | 2.30862610173089e-06 | 1.15431305086545e-06 |
| 57 | 0.999996407408563 | 7.18518287461198e-06 | 3.59259143730599e-06 |
| 58 | 0.999981759712432 | 3.6480575135959e-05 | 1.82402875679795e-05 |
| 59 | 0.999921120252994 | 0.000157759494012743 | 7.88797470063716e-05 |
| 60 | 0.99964006022929 | 0.000719879541421295 | 0.000359939770710647 |
| 61 | 0.999832473543108 | 0.000335052913784384 | 0.000167526456892192 |
| 62 | 0.99906264284939 | 0.00187471430122092 | 0.000937357150610462 |
| 63 | 0.995346527242309 | 0.00930694551538237 | 0.00465347275769118 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 15 | 0.319148936170213 | NOK |
| 5% type I error level | 20 | 0.425531914893617 | NOK |
| 10% type I error level | 35 | 0.74468085106383 | NOK |
