| Multiple Linear Regression - Estimated Regression Equation |
| robberies[t] = -82575.7915115605 + 41.9883576729426Year[t] + 5.80231945607509month[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) | -82575.7915115605 | 2808.958693 | -29.3973 | 0 | 0 |
| Year | 41.9883576729426 | 1.4254 | 29.4572 | 0 | 0 |
| month | 5.80231945607509 | 1.182496 | 4.9068 | 3e-06 | 2e-06 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.940538975417242 |
| R-squared | 0.884613564278916 |
| Adjusted R-squared | 0.88260684365768 |
| F-TEST (value) | 440.825471626413 |
| F-TEST (DF numerator) | 2 |
| F-TEST (DF denominator) | 115 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 43.8711758008778 |
| Sum Squared Residuals | 221338.207607425 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 41 | -20.8780070994354 | 61.8780070994354 |
| 2 | 39 | -15.0756876431437 | 54.0756876431437 |
| 3 | 50 | -9.27336818706856 | 59.2733681870686 |
| 4 | 40 | -3.47104873099347 | 43.4710487309935 |
| 5 | 43 | 2.33127072508162 | 40.6687292749184 |
| 6 | 38 | 8.13359018115672 | 29.8664098188433 |
| 7 | 44 | 13.9359096372318 | 30.0640903627682 |
| 8 | 35 | 19.7382290933069 | 15.2617709066931 |
| 9 | 39 | 25.540548549382 | 13.459451450618 |
| 10 | 35 | 31.3428680054571 | 3.65713199454292 |
| 11 | 29 | 37.1451874615322 | -8.14518746153217 |
| 12 | 49 | 42.9475069176072 | 6.05249308239275 |
| 13 | 50 | 21.1103505737239 | 28.8896494262761 |
| 14 | 59 | 26.912670029799 | 32.087329970201 |
| 15 | 63 | 32.7149894858741 | 30.2850105141259 |
| 16 | 32 | 38.5173089419492 | -6.51730894194917 |
| 17 | 39 | 44.3196283980243 | -5.31962839802426 |
| 18 | 47 | 50.1219478540993 | -3.12194785409935 |
| 19 | 53 | 55.9242673101744 | -2.92426731017444 |
| 20 | 60 | 61.7265867662495 | -1.72658676624954 |
| 21 | 57 | 67.5289062223246 | -10.5289062223246 |
| 22 | 52 | 73.3312256783997 | -21.3312256783997 |
| 23 | 70 | 79.1335451344748 | -9.1335451344748 |
| 24 | 90 | 84.9358645905499 | 5.0641354094501 |
| 25 | 74 | 63.0987082466665 | 10.9012917533335 |
| 26 | 62 | 68.9010277027416 | -6.90102770274162 |
| 27 | 55 | 74.7033471588167 | -19.7033471588167 |
| 28 | 84 | 80.5056666148918 | 3.49433338510821 |
| 29 | 94 | 86.3079860709669 | 7.69201392903312 |
| 30 | 70 | 92.110305527042 | -22.110305527042 |
| 31 | 108 | 97.912624983117 | 10.0873750168829 |
| 32 | 139 | 103.714944439192 | 35.2850555608079 |
| 33 | 120 | 109.517263895267 | 10.4827361047328 |
| 34 | 97 | 115.319583351342 | -18.3195833513423 |
| 35 | 126 | 121.121902807417 | 4.87809719258258 |
| 36 | 149 | 126.924222263493 | 22.0757777365075 |
| 37 | 158 | 105.087065919609 | 52.9129340803909 |
| 38 | 124 | 110.889385375684 | 13.1106146243158 |
| 39 | 140 | 116.691704831759 | 23.3082951682407 |
| 40 | 109 | 122.494024287834 | -13.4940242878344 |
| 41 | 114 | 128.296343743909 | -14.2963437439095 |
| 42 | 77 | 134.098663199985 | -57.0986631999846 |
| 43 | 120 | 139.90098265606 | -19.9009826560597 |
| 44 | 133 | 145.703302112135 | -12.7033021121348 |
| 45 | 110 | 151.50562156821 | -41.5056215682098 |
| 46 | 92 | 157.307941024285 | -65.3079410242849 |
| 47 | 97 | 163.11026048036 | -66.11026048036 |
| 48 | 78 | 168.912579936435 | -90.912579936435 |
| 49 | 99 | 147.075423592552 | -48.0754235925517 |
| 50 | 107 | 152.877743048627 | -45.8777430486268 |
| 51 | 112 | 158.680062504702 | -46.6800625047019 |
| 52 | 90 | 164.482381960777 | -74.482381960777 |
| 53 | 98 | 170.284701416852 | -72.2847014168521 |
| 54 | 125 | 176.087020872927 | -51.0870208729272 |
| 55 | 155 | 181.889340329002 | -26.8893403290023 |
| 56 | 190 | 187.691659785077 | 2.30834021492264 |
| 57 | 236 | 193.493979241152 | 42.5060207588476 |
| 58 | 189 | 199.296298697228 | -10.2962986972275 |
| 59 | 174 | 205.098618153303 | -31.0986181533026 |
| 60 | 178 | 210.900937609378 | -32.9009376093777 |
| 61 | 136 | 189.063781265494 | -53.0637812654944 |
| 62 | 161 | 194.866100721569 | -33.8661007215694 |
| 63 | 171 | 200.668420177645 | -29.6684201776445 |
| 64 | 149 | 206.47073963372 | -57.4707396337196 |
| 65 | 184 | 212.273059089795 | -28.2730590897947 |
| 66 | 155 | 218.07537854587 | -63.0753785458698 |
| 67 | 276 | 223.877698001945 | 52.1223019980551 |
| 68 | 224 | 229.68001745802 | -5.68001745801997 |
| 69 | 213 | 235.482336914095 | -22.4823369140951 |
| 70 | 279 | 241.28465637017 | 37.7153436298299 |
| 71 | 268 | 247.086975826245 | 20.9130241737548 |
| 72 | 287 | 252.88929528232 | 34.1107047176797 |
| 73 | 238 | 231.052138938437 | 6.94786106156304 |
| 74 | 213 | 236.854458394512 | -23.854458394512 |
| 75 | 257 | 242.656777850587 | 14.3432221494129 |
| 76 | 293 | 248.459097306662 | 44.5409026933378 |
| 77 | 212 | 254.261416762737 | -42.2614167627373 |
| 78 | 246 | 260.063736218812 | -14.0637362188124 |
| 79 | 353 | 265.866055674887 | 87.1339443251125 |
| 80 | 339 | 271.668375130963 | 67.3316248690374 |
| 81 | 308 | 277.470694587038 | 30.5293054129623 |
| 82 | 247 | 283.273014043113 | -36.2730140431128 |
| 83 | 257 | 289.075333499188 | -32.0753334991878 |
| 84 | 322 | 294.877652955263 | 27.1223470447371 |
| 85 | 298 | 273.04049661138 | 24.9595033886204 |
| 86 | 273 | 278.842816067455 | -5.84281606745466 |
| 87 | 312 | 284.64513552353 | 27.3548644764703 |
| 88 | 249 | 290.447454979605 | -41.4474549796048 |
| 89 | 286 | 296.24977443568 | -10.2497744356799 |
| 90 | 279 | 302.052093891755 | -23.052093891755 |
| 91 | 309 | 307.85441334783 | 1.1455866521699 |
| 92 | 401 | 313.656732803905 | 87.3432671960948 |
| 93 | 309 | 319.45905225998 | -10.4590522599803 |
| 94 | 328 | 325.261371716055 | 2.73862828394465 |
| 95 | 353 | 331.06369117213 | 21.9363088278696 |
| 96 | 354 | 336.866010628206 | 17.1339893717945 |
| 97 | 327 | 315.028854284322 | 11.9711457156778 |
| 98 | 324 | 320.831173740397 | 3.16882625960273 |
| 99 | 285 | 326.633493196472 | -41.6334931964724 |
| 100 | 243 | 332.435812652547 | -89.4358126525475 |
| 101 | 241 | 338.238132108623 | -97.2381321086225 |
| 102 | 287 | 344.040451564698 | -57.0404515646976 |
| 103 | 355 | 349.842771020773 | 5.15722897922728 |
| 104 | 460 | 355.645090476848 | 104.354909523152 |
| 105 | 364 | 361.447409932923 | 2.55259006707711 |
| 106 | 487 | 367.249729388998 | 119.750270611002 |
| 107 | 452 | 373.052048845073 | 78.9479511549269 |
| 108 | 391 | 378.854368301148 | 12.1456316988518 |
| 109 | 500 | 357.017211957265 | 142.982788042735 |
| 110 | 451 | 362.81953141334 | 88.1804685866601 |
| 111 | 375 | 368.621850869415 | 6.37814913058509 |
| 112 | 372 | 374.42417032549 | -2.42417032549 |
| 113 | 302 | 380.226489781565 | -78.2264897815651 |
| 114 | 316 | 386.02880923764 | -70.0288092376402 |
| 115 | 398 | 391.831128693715 | 6.16887130628473 |
| 116 | 394 | 397.63344814979 | -3.63344814979036 |
| 117 | 431 | 403.435767605865 | 27.5642323941346 |
| 118 | 431 | 409.238087061941 | 21.7619129380595 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 6 | 0.00292477030546535 | 0.00584954061093069 | 0.997075229694535 |
| 7 | 0.000353180999264952 | 0.000706361998529905 | 0.999646819000735 |
| 8 | 6.65453575138491e-05 | 0.000133090715027698 | 0.999933454642486 |
| 9 | 6.85935904881883e-06 | 1.37187180976377e-05 | 0.99999314064095 |
| 10 | 7.74425316693731e-07 | 1.54885063338746e-06 | 0.999999225574683 |
| 11 | 1.81975235458974e-07 | 3.63950470917948e-07 | 0.999999818024765 |
| 12 | 4.36709292791243e-07 | 8.73418585582487e-07 | 0.999999563290707 |
| 13 | 6.05029970213779e-08 | 1.21005994042756e-07 | 0.999999939497003 |
| 14 | 1.55353879696411e-08 | 3.10707759392822e-08 | 0.999999984464612 |
| 15 | 4.62621470543248e-09 | 9.25242941086496e-09 | 0.999999995373785 |
| 16 | 4.66606283941435e-08 | 9.3321256788287e-08 | 0.999999953339372 |
| 17 | 1.53997863350435e-08 | 3.07995726700869e-08 | 0.999999984600214 |
| 18 | 2.79402996984195e-09 | 5.5880599396839e-09 | 0.99999999720597 |
| 19 | 6.75500649600914e-10 | 1.35100129920183e-09 | 0.9999999993245 |
| 20 | 3.47717264845496e-10 | 6.95434529690993e-10 | 0.999999999652283 |
| 21 | 9.13945515912589e-11 | 1.82789103182518e-10 | 0.999999999908605 |
| 22 | 1.6330578659966e-11 | 3.26611573199319e-11 | 0.99999999998367 |
| 23 | 2.468954057664e-11 | 4.93790811532801e-11 | 0.99999999997531 |
| 24 | 7.69362216814337e-10 | 1.53872443362867e-09 | 0.999999999230638 |
| 25 | 2.22125238822055e-10 | 4.4425047764411e-10 | 0.999999999777875 |
| 26 | 6.3721204741667e-11 | 1.27442409483334e-10 | 0.99999999993628 |
| 27 | 2.76395030400816e-11 | 5.52790060801632e-11 | 0.99999999997236 |
| 28 | 1.6862520284461e-11 | 3.37250405689221e-11 | 0.999999999983137 |
| 29 | 2.30092912721315e-11 | 4.6018582544263e-11 | 0.99999999997699 |
| 30 | 5.99800383708167e-12 | 1.19960076741633e-11 | 0.999999999994002 |
| 31 | 3.16210277649429e-11 | 6.32420555298858e-11 | 0.999999999968379 |
| 32 | 7.74245459858994e-09 | 1.54849091971799e-08 | 0.999999992257545 |
| 33 | 1.05057772261373e-08 | 2.10115544522746e-08 | 0.999999989494223 |
| 34 | 3.61291590090781e-09 | 7.22583180181561e-09 | 0.999999996387084 |
| 35 | 3.82767392080265e-09 | 7.6553478416053e-09 | 0.999999996172326 |
| 36 | 1.78675415717074e-08 | 3.57350831434148e-08 | 0.999999982132458 |
| 37 | 1.50015467516453e-07 | 3.00030935032906e-07 | 0.999999849984533 |
| 38 | 7.93902851540438e-08 | 1.58780570308088e-07 | 0.999999920609715 |
| 39 | 6.23223560891054e-08 | 1.24644712178211e-07 | 0.999999937677644 |
| 40 | 3.77825067684051e-08 | 7.55650135368103e-08 | 0.999999962217493 |
| 41 | 1.96603440043293e-08 | 3.93206880086586e-08 | 0.999999980339656 |
| 42 | 9.42109791532012e-08 | 1.88421958306402e-07 | 0.99999990578902 |
| 43 | 4.22450007635133e-08 | 8.44900015270267e-08 | 0.999999957755 |
| 44 | 1.88611228575846e-08 | 3.77222457151693e-08 | 0.999999981138877 |
| 45 | 1.12991762771571e-08 | 2.25983525543142e-08 | 0.999999988700824 |
| 46 | 1.89464304112469e-08 | 3.78928608224938e-08 | 0.99999998105357 |
| 47 | 2.13833829042498e-08 | 4.27667658084996e-08 | 0.999999978616617 |
| 48 | 9.75624813505618e-08 | 1.95124962701124e-07 | 0.999999902437519 |
| 49 | 1.03660502387777e-07 | 2.07321004775554e-07 | 0.999999896339498 |
| 50 | 6.91136255191801e-08 | 1.3822725103836e-07 | 0.999999930886375 |
| 51 | 3.89792546829614e-08 | 7.79585093659228e-08 | 0.999999961020745 |
| 52 | 6.34998889293332e-08 | 1.26999777858666e-07 | 0.999999936500111 |
| 53 | 6.93250275476785e-08 | 1.38650055095357e-07 | 0.999999930674973 |
| 54 | 3.65981226182556e-08 | 7.31962452365112e-08 | 0.999999963401877 |
| 55 | 2.61078872389601e-08 | 5.22157744779202e-08 | 0.999999973892113 |
| 56 | 8.68638669649579e-08 | 1.73727733929916e-07 | 0.999999913136133 |
| 57 | 4.64312055725058e-06 | 9.28624111450116e-06 | 0.999995356879443 |
| 58 | 4.51918953106398e-06 | 9.03837906212797e-06 | 0.999995480810469 |
| 59 | 3.00212406421605e-06 | 6.0042481284321e-06 | 0.999996997875936 |
| 60 | 2.11041064088647e-06 | 4.22082128177293e-06 | 0.99999788958936 |
| 61 | 1.38947193166237e-06 | 2.77894386332474e-06 | 0.999998610528068 |
| 62 | 7.39561241937532e-07 | 1.47912248387506e-06 | 0.999999260438758 |
| 63 | 4.06315996269192e-07 | 8.12631992538384e-07 | 0.999999593684004 |
| 64 | 3.11484939899968e-07 | 6.22969879799936e-07 | 0.99999968851506 |
| 65 | 1.96769381757035e-07 | 3.93538763514071e-07 | 0.999999803230618 |
| 66 | 2.06846038274131e-07 | 4.13692076548262e-07 | 0.999999793153962 |
| 67 | 6.58521844810462e-06 | 1.31704368962092e-05 | 0.999993414781552 |
| 68 | 6.30915937343214e-06 | 1.26183187468643e-05 | 0.999993690840627 |
| 69 | 4.93741810155299e-06 | 9.87483620310598e-06 | 0.999995062581898 |
| 70 | 2.09886768542911e-05 | 4.19773537085821e-05 | 0.999979011323146 |
| 71 | 3.22184234991324e-05 | 6.44368469982649e-05 | 0.999967781576501 |
| 72 | 6.27547517080073e-05 | 0.000125509503416015 | 0.999937245248292 |
| 73 | 5.05641150497002e-05 | 0.0001011282300994 | 0.99994943588495 |
| 74 | 3.10950821766762e-05 | 6.21901643533524e-05 | 0.999968904917823 |
| 75 | 2.74891201359675e-05 | 5.49782402719351e-05 | 0.999972510879864 |
| 76 | 5.77652015918534e-05 | 0.000115530403183707 | 0.999942234798408 |
| 77 | 4.45467820765714e-05 | 8.90935641531428e-05 | 0.999955453217923 |
| 78 | 2.80927131726133e-05 | 5.61854263452266e-05 | 0.999971907286827 |
| 79 | 0.000345620213034987 | 0.000691240426069975 | 0.999654379786965 |
| 80 | 0.0010640648865395 | 0.002128129773079 | 0.99893593511346 |
| 81 | 0.00102943403371108 | 0.00205886806742216 | 0.99897056596629 |
| 82 | 0.0007809154475388 | 0.0015618308950776 | 0.999219084552461 |
| 83 | 0.000604812923022352 | 0.0012096258460447 | 0.999395187076978 |
| 84 | 0.000503314416088171 | 0.00100662883217634 | 0.999496685583912 |
| 85 | 0.000432218542305866 | 0.000864437084611733 | 0.999567781457694 |
| 86 | 0.00025829275164454 | 0.00051658550328908 | 0.999741707248355 |
| 87 | 0.000228251960817269 | 0.000456503921634537 | 0.999771748039183 |
| 88 | 0.000165976559056721 | 0.000331953118113443 | 0.999834023440943 |
| 89 | 9.4436683433996e-05 | 0.000188873366867992 | 0.999905563316566 |
| 90 | 5.74711865912675e-05 | 0.000114942373182535 | 0.999942528813409 |
| 91 | 3.25884115364217e-05 | 6.51768230728435e-05 | 0.999967411588464 |
| 92 | 0.000183566177695566 | 0.000367132355391132 | 0.999816433822304 |
| 93 | 0.000104030822436622 | 0.000208061644873244 | 0.999895969177563 |
| 94 | 5.79847818495108e-05 | 0.000115969563699022 | 0.99994201521815 |
| 95 | 3.60260331000785e-05 | 7.2052066200157e-05 | 0.9999639739669 |
| 96 | 2.05244509134607e-05 | 4.10489018269213e-05 | 0.999979475549087 |
| 97 | 1.21374596176589e-05 | 2.42749192353177e-05 | 0.999987862540382 |
| 98 | 6.39875059926074e-06 | 1.27975011985215e-05 | 0.9999936012494 |
| 99 | 3.96762739965327e-06 | 7.93525479930653e-06 | 0.9999960323726 |
| 100 | 1.95272394987841e-05 | 3.90544789975682e-05 | 0.999980472760501 |
| 101 | 0.000443369841144371 | 0.000886739682288742 | 0.999556630158856 |
| 102 | 0.00388452684507149 | 0.00776905369014298 | 0.996115473154929 |
| 103 | 0.00689861482265923 | 0.0137972296453185 | 0.99310138517734 |
| 104 | 0.0096123553199752 | 0.0192247106399504 | 0.990387644680025 |
| 105 | 0.0159812305117118 | 0.0319624610234235 | 0.984018769488288 |
| 106 | 0.0272385396922044 | 0.0544770793844089 | 0.972761460307796 |
| 107 | 0.0266798282154098 | 0.0533596564308195 | 0.97332017178459 |
| 108 | 0.0149109908772664 | 0.0298219817545329 | 0.985089009122734 |
| 109 | 0.117366354918165 | 0.234732709836331 | 0.882633645081835 |
| 110 | 0.440823014489926 | 0.881646028979851 | 0.559176985510074 |
| 111 | 0.49950037807072 | 0.99900075614144 | 0.50049962192928 |
| 112 | 0.79010014064965 | 0.419799718700699 | 0.20989985935035 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 97 | 0.906542056074766 | NOK |
| 5% type I error level | 101 | 0.94392523364486 | NOK |
| 10% type I error level | 103 | 0.962616822429907 | NOK |
