| Multiple Linear Regression - Estimated Regression Equation |
| month[t] = + 2547.65327640078 -1.29266335839508Year[t] + 0.0298364064047847robberies[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) | 2547.65327640078 | 537.615071 | 4.7388 | 6e-06 | 3e-06 |
| Year | -1.29266335839508 | 0.273404 | -4.728 | 6e-06 | 3e-06 |
| robberies | 0.0298364064047847 | 0.006081 | 4.9068 | 3e-06 | 2e-06 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.417665158837213 |
| R-squared | 0.174444184906515 |
| Adjusted R-squared | 0.160086692470106 |
| F-TEST (value) | 12.1500453981888 |
| F-TEST (DF numerator) | 2 |
| F-TEST (DF denominator) | 115 |
| p-value | 1.63275246892747e-05 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 3.14594925654832 |
| Sum Squared Residuals | 1138.15462334935 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 1 | 7.5004064586588 | -6.5004064586588 |
| 2 | 2 | 7.44073364584255 | -5.44073364584255 |
| 3 | 3 | 7.76893411629518 | -4.76893411629518 |
| 4 | 4 | 7.47057005224734 | -3.47057005224734 |
| 5 | 5 | 7.56007927146169 | -2.56007927146169 |
| 6 | 6 | 7.41089723943777 | -1.41089723943777 |
| 7 | 7 | 7.58991567786648 | -0.589915677866476 |
| 8 | 8 | 7.32138802022341 | 0.678611979776586 |
| 9 | 9 | 7.44073364584255 | 1.55926635415745 |
| 10 | 10 | 7.32138802022341 | 2.67861197977659 |
| 11 | 11 | 7.14236958179471 | 3.85763041820529 |
| 12 | 12 | 7.7390977098904 | 4.2609022901096 |
| 13 | 1 | 6.4762707579001 | -5.4762707579001 |
| 14 | 2 | 6.74479841554317 | -4.74479841554317 |
| 15 | 3 | 6.86414404116231 | -3.8641440411623 |
| 16 | 4 | 5.93921544261398 | -1.93921544261398 |
| 17 | 5 | 6.14807028744747 | -1.14807028744747 |
| 18 | 6 | 6.38676153868575 | -0.38676153868575 |
| 19 | 7 | 6.56577997711446 | 0.434220022885542 |
| 20 | 8 | 6.77463482194795 | 1.22536517805205 |
| 21 | 9 | 6.6851256027336 | 2.3148743972664 |
| 22 | 10 | 6.53594357070967 | 3.46405642929033 |
| 23 | 11 | 7.0729988859958 | 3.9270011140042 |
| 24 | 12 | 7.66972701409149 | 4.33027298590851 |
| 25 | 1 | 5.89968115321986 | -4.89968115321986 |
| 26 | 2 | 5.54164427636244 | -3.54164427636244 |
| 27 | 3 | 5.33278943152895 | -2.33278943152895 |
| 28 | 4 | 6.1980452172677 | -2.1980452172677 |
| 29 | 5 | 6.49640928131555 | -1.49640928131555 |
| 30 | 6 | 5.78033552760072 | 0.219664472399282 |
| 31 | 7 | 6.91411897098254 | 0.0858810290174644 |
| 32 | 8 | 7.83904756953086 | 0.160952430469139 |
| 33 | 9 | 7.27215584783995 | 1.72784415216005 |
| 34 | 10 | 6.58591850052991 | 3.4140814994701 |
| 35 | 11 | 7.45117428626866 | 3.54882571373134 |
| 36 | 12 | 8.13741163357871 | 3.86258836642129 |
| 37 | 1 | 7.11327593282669 | -6.11327593282669 |
| 38 | 2 | 6.09883811506401 | -4.09883811506401 |
| 39 | 3 | 6.57622061754057 | -3.57622061754057 |
| 40 | 4 | 5.65129201899224 | -1.65129201899224 |
| 41 | 5 | 5.80047405101616 | -0.800474051016164 |
| 42 | 6 | 4.69652701403913 | 1.30347298596087 |
| 43 | 7 | 5.97949248944487 | 1.02050751055513 |
| 44 | 8 | 6.36736577270707 | 1.63263422729293 |
| 45 | 9 | 5.68112842539703 | 3.31887157460297 |
| 46 | 10 | 5.1440731101109 | 4.8559268898891 |
| 47 | 11 | 5.29325514213482 | 5.70674485786518 |
| 48 | 12 | 4.72636342044391 | 7.27363657955609 |
| 49 | 1 | 4.06026459654931 | -3.06026459654931 |
| 50 | 2 | 4.29895584778759 | -2.29895584778759 |
| 51 | 3 | 4.44813787981152 | -1.44813787981151 |
| 52 | 4 | 3.79173693890625 | 0.208263061093748 |
| 53 | 5 | 4.03042819014453 | 0.96957180985547 |
| 54 | 6 | 4.83601116307372 | 1.16398883692628 |
| 55 | 7 | 5.73110335521726 | 1.26889664478274 |
| 56 | 8 | 6.77537757938472 | 1.22462242061528 |
| 57 | 9 | 8.14785227400482 | 0.852147725995184 |
| 58 | 10 | 6.74554117297994 | 3.25445882702006 |
| 59 | 11 | 6.29799507690817 | 4.70200492309183 |
| 60 | 12 | 6.4173407025273 | 5.5826592974727 |
| 61 | 1 | 3.87154827513127 | -2.87154827513127 |
| 62 | 2 | 4.61745843525089 | -2.61745843525089 |
| 63 | 3 | 4.91582249929873 | -1.91582249929873 |
| 64 | 4 | 4.25942155839347 | -0.259421558393469 |
| 65 | 5 | 5.30369578256093 | -0.303695782560933 |
| 66 | 6 | 4.43843999682218 | 1.56156000317782 |
| 67 | 7 | 8.04864517180112 | -1.04864517180112 |
| 68 | 8 | 6.49715203875232 | 1.50284796124768 |
| 69 | 9 | 6.16895156829969 | 2.83104843170031 |
| 70 | 10 | 8.13815439101548 | 1.86184560898452 |
| 71 | 11 | 7.80995392056285 | 3.19004607943715 |
| 72 | 12 | 8.37684564225376 | 3.62315435774624 |
| 73 | 1 | 5.62219837002423 | -4.62219837002423 |
| 74 | 2 | 4.87628820990461 | -2.87628820990461 |
| 75 | 3 | 6.18909009171514 | -3.18909009171514 |
| 76 | 4 | 7.26320072228738 | -3.26320072228738 |
| 77 | 5 | 4.84645180349982 | 0.153548196500175 |
| 78 | 6 | 5.8608896212625 | 0.139110378737496 |
| 79 | 7 | 9.05338510657447 | -2.05338510657447 |
| 80 | 8 | 8.63567541690748 | -0.63567541690748 |
| 81 | 9 | 7.71074681835915 | 1.28925318164085 |
| 82 | 10 | 5.89072602766729 | 4.10927397233271 |
| 83 | 11 | 6.18909009171513 | 4.81090990828487 |
| 84 | 12 | 8.12845650802614 | 3.87154349197386 |
| 85 | 1 | 6.11971939591623 | -5.11971939591623 |
| 86 | 2 | 5.37380923579661 | -3.37380923579661 |
| 87 | 3 | 6.53742908558321 | -3.53742908558321 |
| 88 | 4 | 4.65773548208178 | -0.657735482081778 |
| 89 | 5 | 5.76168251905881 | -0.761682519058812 |
| 90 | 6 | 5.55282767422532 | 0.447172325774681 |
| 91 | 7 | 6.44791986636886 | 0.552080133631141 |
| 92 | 8 | 9.19286925560905 | -1.19286925560905 |
| 93 | 9 | 6.44791986636886 | 2.55208013363114 |
| 94 | 10 | 7.01481158805977 | 2.98518841194023 |
| 95 | 11 | 7.76072174817939 | 3.23927825182061 |
| 96 | 12 | 7.79055815458417 | 4.20944184541583 |
| 97 | 1 | 5.6923118232599 | -4.6923118232599 |
| 98 | 2 | 5.60280260404555 | -3.60280260404555 |
| 99 | 3 | 4.43918275425895 | -1.43918275425895 |
| 100 | 4 | 3.18605368525799 | 0.81394631474201 |
| 101 | 5 | 3.12638087244842 | 1.87361912755158 |
| 102 | 6 | 4.49885556706852 | 1.50114443293148 |
| 103 | 7 | 6.52773120259388 | 0.472268797406125 |
| 104 | 8 | 9.66055387509627 | -1.66055387509627 |
| 105 | 9 | 6.79625886023694 | 2.20374113976306 |
| 106 | 10 | 10.4661368480255 | -0.466136848025452 |
| 107 | 11 | 9.42186262385799 | 1.57813737614201 |
| 108 | 12 | 7.60184183316612 | 4.39815816683388 |
| 109 | 1 | 9.56134677289258 | -8.56134677289258 |
| 110 | 2 | 8.09936285905813 | -6.09936285905813 |
| 111 | 3 | 5.83179597229449 | -2.83179597229449 |
| 112 | 4 | 5.74228675308014 | -1.74228675308014 |
| 113 | 5 | 3.65373830474521 | 1.34626169525479 |
| 114 | 6 | 4.07144799441219 | 1.92855200558781 |
| 115 | 7 | 6.51803331960454 | 0.481966680395461 |
| 116 | 8 | 6.3986876939854 | 1.6013123060146 |
| 117 | 9 | 7.50263473096243 | 1.49736526903757 |
| 118 | 10 | 7.50263473096243 | 2.49736526903757 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 6 | 0.396492000812851 | 0.792984001625703 | 0.603507999187149 |
| 7 | 0.445416406010992 | 0.890832812021984 | 0.554583593989008 |
| 8 | 0.453759909042885 | 0.907519818085771 | 0.546240090957115 |
| 9 | 0.520059409416524 | 0.959881181166952 | 0.479940590583476 |
| 10 | 0.51649959819879 | 0.96700080360242 | 0.48350040180121 |
| 11 | 0.427599896335431 | 0.855199792670861 | 0.572400103664569 |
| 12 | 0.860807715220188 | 0.278384569559623 | 0.139192284779812 |
| 13 | 0.826002086053892 | 0.347995827892216 | 0.173997913946108 |
| 14 | 0.800445107433108 | 0.399109785133785 | 0.199554892566892 |
| 15 | 0.778814964040288 | 0.442370071919423 | 0.221185035959711 |
| 16 | 0.72119569248777 | 0.55760861502446 | 0.27880430751223 |
| 17 | 0.662774065788194 | 0.674451868423611 | 0.337225934211806 |
| 18 | 0.635341800530262 | 0.729316398939476 | 0.364658199469738 |
| 19 | 0.650014151241981 | 0.699971697516037 | 0.349985848758018 |
| 20 | 0.698435632587052 | 0.603128734825896 | 0.301564367412948 |
| 21 | 0.738529629118733 | 0.522940741762534 | 0.261470370881267 |
| 22 | 0.784361738559193 | 0.431276522881614 | 0.215638261440807 |
| 23 | 0.83415406977549 | 0.331691860449021 | 0.16584593022451 |
| 24 | 0.833414213951592 | 0.333171572096816 | 0.166585786048408 |
| 25 | 0.882043185994598 | 0.235913628010803 | 0.117956814005402 |
| 26 | 0.871313832497651 | 0.257372335004698 | 0.128686167502349 |
| 27 | 0.845897495052529 | 0.308205009894941 | 0.154102504947471 |
| 28 | 0.82413109140324 | 0.351737817193521 | 0.17586890859676 |
| 29 | 0.793812055130573 | 0.412375889738854 | 0.206187944869427 |
| 30 | 0.762567030445552 | 0.474865939108896 | 0.237432969554448 |
| 31 | 0.715544702234802 | 0.568910595530395 | 0.284455297765198 |
| 32 | 0.670620303446639 | 0.658759393106723 | 0.329379696553361 |
| 33 | 0.621225632028465 | 0.757548735943071 | 0.378774367971535 |
| 34 | 0.626339154239388 | 0.747321691521224 | 0.373660845760612 |
| 35 | 0.593089020858401 | 0.813821958283198 | 0.406910979141599 |
| 36 | 0.548203622072799 | 0.903592755854402 | 0.451796377927201 |
| 37 | 0.793262849638373 | 0.413474300723253 | 0.206737150361627 |
| 38 | 0.821166947514541 | 0.357666104970919 | 0.178833052485459 |
| 39 | 0.841949437401567 | 0.316101125196867 | 0.158050562598433 |
| 40 | 0.824284910103252 | 0.351430179793495 | 0.175715089896748 |
| 41 | 0.801344721327572 | 0.397310557344856 | 0.198655278672428 |
| 42 | 0.805764138556792 | 0.388471722886416 | 0.194235861443208 |
| 43 | 0.778989570665413 | 0.442020858669174 | 0.221010429334587 |
| 44 | 0.749413403834598 | 0.501173192330804 | 0.250586596165402 |
| 45 | 0.757724028267166 | 0.484551943465668 | 0.242275971732834 |
| 46 | 0.812379192382507 | 0.375241615234986 | 0.187620807617493 |
| 47 | 0.868972114703018 | 0.262055770593965 | 0.131027885296982 |
| 48 | 0.941884323408464 | 0.116231353183073 | 0.0581156765915363 |
| 49 | 0.948750661733437 | 0.102498676533126 | 0.0512493382665631 |
| 50 | 0.947015019073729 | 0.105969961852543 | 0.0529849809262715 |
| 51 | 0.938802481150468 | 0.122395037699064 | 0.061197518849532 |
| 52 | 0.921863513790063 | 0.156272972419873 | 0.0781364862099366 |
| 53 | 0.901383345191778 | 0.197233309616444 | 0.0986166548082221 |
| 54 | 0.876872838917055 | 0.24625432216589 | 0.123127161082945 |
| 55 | 0.847902356518835 | 0.304195286962331 | 0.152097643481165 |
| 56 | 0.814197997243696 | 0.371604005512609 | 0.185802002756304 |
| 57 | 0.777601454945431 | 0.444797090109138 | 0.222398545054569 |
| 58 | 0.753354048911749 | 0.493291902176501 | 0.246645951088251 |
| 59 | 0.764614084268831 | 0.470771831462339 | 0.235385915731169 |
| 60 | 0.805348235666909 | 0.389303528666181 | 0.194651764333091 |
| 61 | 0.813410687269579 | 0.373178625460842 | 0.186589312730421 |
| 62 | 0.820110763231214 | 0.359778473537571 | 0.179889236768786 |
| 63 | 0.813197147584745 | 0.37360570483051 | 0.186802852415255 |
| 64 | 0.779843894007894 | 0.440312211984212 | 0.220156105992106 |
| 65 | 0.746058310189664 | 0.507883379620672 | 0.253941689810336 |
| 66 | 0.70353972729372 | 0.592920545412561 | 0.29646027270628 |
| 67 | 0.688975041526475 | 0.622049916947049 | 0.311024958473525 |
| 68 | 0.639671132367748 | 0.720657735264504 | 0.360328867632252 |
| 69 | 0.602883099002736 | 0.794233801994528 | 0.397116900997264 |
| 70 | 0.552594987898273 | 0.894810024203454 | 0.447405012101727 |
| 71 | 0.522150278318705 | 0.955699443362589 | 0.477849721681295 |
| 72 | 0.508994452122769 | 0.982011095754463 | 0.491005547877231 |
| 73 | 0.614803201565247 | 0.770393596869506 | 0.385196798434753 |
| 74 | 0.633462090746867 | 0.733075818506266 | 0.366537909253133 |
| 75 | 0.671392555181274 | 0.657214889637452 | 0.328607444818726 |
| 76 | 0.713967446851873 | 0.572065106296254 | 0.286032553148127 |
| 77 | 0.672105076132198 | 0.655789847735603 | 0.327894923867801 |
| 78 | 0.626845202565255 | 0.746309594869489 | 0.373154797434745 |
| 79 | 0.626621182179102 | 0.746757635641795 | 0.373378817820898 |
| 80 | 0.590640460247878 | 0.818719079504244 | 0.409359539752122 |
| 81 | 0.534840654573528 | 0.930318690852945 | 0.465159345426472 |
| 82 | 0.521317308556493 | 0.957365382887014 | 0.478682691443507 |
| 83 | 0.540143049462507 | 0.919713901074987 | 0.459856950537493 |
| 84 | 0.538742660988442 | 0.922514678023117 | 0.461257339011558 |
| 85 | 0.668524548907894 | 0.662950902184211 | 0.331475451092106 |
| 86 | 0.714333461509964 | 0.571333076980072 | 0.285666538490036 |
| 87 | 0.77143615387248 | 0.45712769225504 | 0.22856384612752 |
| 88 | 0.75087475596913 | 0.49825048806174 | 0.24912524403087 |
| 89 | 0.731827604532123 | 0.536344790935753 | 0.268172395467876 |
| 90 | 0.692277763974205 | 0.615444472051591 | 0.307722236025795 |
| 91 | 0.645812818065259 | 0.708374363869482 | 0.354187181934741 |
| 92 | 0.626045926678777 | 0.747908146642445 | 0.373954073321223 |
| 93 | 0.567445090213533 | 0.865109819572933 | 0.432554909786467 |
| 94 | 0.509536938425017 | 0.980926123149965 | 0.490463061574983 |
| 95 | 0.457829019462726 | 0.915658038925451 | 0.542170980537274 |
| 96 | 0.452835612453508 | 0.905671224907017 | 0.547164387546492 |
| 97 | 0.584119135089783 | 0.831761729820435 | 0.415880864910218 |
| 98 | 0.674022172362659 | 0.651955655274681 | 0.325977827637341 |
| 99 | 0.694773480869471 | 0.610453038261058 | 0.305226519130529 |
| 100 | 0.679618223224477 | 0.640763553551045 | 0.320381776775523 |
| 101 | 0.665388910438776 | 0.669222179122447 | 0.334611089561224 |
| 102 | 0.668549725115294 | 0.662900549769411 | 0.331450274884706 |
| 103 | 0.668831797303068 | 0.662336405393865 | 0.331168202696932 |
| 104 | 0.624511775798674 | 0.750976448402652 | 0.375488224201326 |
| 105 | 0.584541584850538 | 0.830916830298924 | 0.415458415149462 |
| 106 | 0.491757950468842 | 0.983515900937684 | 0.508242049531158 |
| 107 | 0.390636248103188 | 0.781272496206376 | 0.609363751896812 |
| 108 | 0.300997636884505 | 0.601995273769009 | 0.699002363115495 |
| 109 | 0.464788124610449 | 0.929576249220898 | 0.535211875389551 |
| 110 | 0.790711815877367 | 0.418576368245267 | 0.209288184122633 |
| 111 | 0.891832154511003 | 0.216335690977994 | 0.108167845488997 |
| 112 | 0.975000497372784 | 0.0499990052544321 | 0.024999502627216 |
| 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 | 1 | 0.00934579439252336 | OK |
| 10% type I error level | 1 | 0.00934579439252336 | OK |
