| Multiple Linear Regression - Estimated Regression Equation |
| robberies[t] = + 168.006060941351 + 4.40856645828339month[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) | 168.006060941351 | 24.998678 | 6.7206 | 0 | 0 |
| month | 4.40856645828339 | 3.43906 | 1.2819 | 0.20243 | 0.101215 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.118188165015181 |
| R-squared | 0.0139684423496558 |
| Adjusted R-squared | 0.00546817030094593 |
| F-TEST (value) | 1.64329356397197 |
| F-TEST (DF numerator) | 1 |
| F-TEST (DF denominator) | 116 |
| p-value | 0.202430372384786 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 127.693040460136 |
| Sum Squared Residuals | 1891439.45950664 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 41 | 172.414627399635 | -131.414627399635 |
| 2 | 39 | 176.823193857918 | -137.823193857918 |
| 3 | 50 | 181.231760316202 | -131.231760316202 |
| 4 | 40 | 185.640326774485 | -145.640326774485 |
| 5 | 43 | 190.048893232768 | -147.048893232768 |
| 6 | 38 | 194.457459691052 | -156.457459691052 |
| 7 | 44 | 198.866026149335 | -154.866026149335 |
| 8 | 35 | 203.274592607619 | -168.274592607619 |
| 9 | 39 | 207.683159065902 | -168.683159065902 |
| 10 | 35 | 212.091725524185 | -177.091725524185 |
| 11 | 29 | 216.500291982469 | -187.500291982469 |
| 12 | 49 | 220.908858440752 | -171.908858440752 |
| 13 | 50 | 172.414627399635 | -122.414627399635 |
| 14 | 59 | 176.823193857918 | -117.823193857918 |
| 15 | 63 | 181.231760316202 | -118.231760316202 |
| 16 | 32 | 185.640326774485 | -153.640326774485 |
| 17 | 39 | 190.048893232768 | -151.048893232768 |
| 18 | 47 | 194.457459691052 | -147.457459691052 |
| 19 | 53 | 198.866026149335 | -145.866026149335 |
| 20 | 60 | 203.274592607619 | -143.274592607619 |
| 21 | 57 | 207.683159065902 | -150.683159065902 |
| 22 | 52 | 212.091725524185 | -160.091725524185 |
| 23 | 70 | 216.500291982469 | -146.500291982469 |
| 24 | 90 | 220.908858440752 | -130.908858440752 |
| 25 | 74 | 172.414627399635 | -98.4146273996349 |
| 26 | 62 | 176.823193857918 | -114.823193857918 |
| 27 | 55 | 181.231760316202 | -126.231760316202 |
| 28 | 84 | 185.640326774485 | -101.640326774485 |
| 29 | 94 | 190.048893232768 | -96.0488932327684 |
| 30 | 70 | 194.457459691052 | -124.457459691052 |
| 31 | 108 | 198.866026149335 | -90.8660261493352 |
| 32 | 139 | 203.274592607619 | -64.2745926076186 |
| 33 | 120 | 207.683159065902 | -87.683159065902 |
| 34 | 97 | 212.091725524185 | -115.091725524185 |
| 35 | 126 | 216.500291982469 | -90.5002919824688 |
| 36 | 149 | 220.908858440752 | -71.9088584407522 |
| 37 | 158 | 172.414627399635 | -14.4146273996348 |
| 38 | 124 | 176.823193857918 | -52.8231938579182 |
| 39 | 140 | 181.231760316202 | -41.2317603162016 |
| 40 | 109 | 185.640326774485 | -76.640326774485 |
| 41 | 114 | 190.048893232768 | -76.0488932327684 |
| 42 | 77 | 194.457459691052 | -117.457459691052 |
| 43 | 120 | 198.866026149335 | -78.8660261493352 |
| 44 | 133 | 203.274592607619 | -70.2745926076186 |
| 45 | 110 | 207.683159065902 | -97.683159065902 |
| 46 | 92 | 212.091725524185 | -120.091725524185 |
| 47 | 97 | 216.500291982469 | -119.500291982469 |
| 48 | 78 | 220.908858440752 | -142.908858440752 |
| 49 | 99 | 172.414627399635 | -73.4146273996349 |
| 50 | 107 | 176.823193857918 | -69.8231938579182 |
| 51 | 112 | 181.231760316202 | -69.2317603162016 |
| 52 | 90 | 185.640326774485 | -95.640326774485 |
| 53 | 98 | 190.048893232768 | -92.0488932327684 |
| 54 | 125 | 194.457459691052 | -69.4574596910518 |
| 55 | 155 | 198.866026149335 | -43.8660261493352 |
| 56 | 190 | 203.274592607619 | -13.2745926076186 |
| 57 | 236 | 207.683159065902 | 28.316840934098 |
| 58 | 189 | 212.091725524185 | -23.0917255241854 |
| 59 | 174 | 216.500291982469 | -42.5002919824688 |
| 60 | 178 | 220.908858440752 | -42.9088584407522 |
| 61 | 136 | 172.414627399635 | -36.4146273996349 |
| 62 | 161 | 176.823193857918 | -15.8231938579182 |
| 63 | 171 | 181.231760316202 | -10.2317603162016 |
| 64 | 149 | 185.640326774485 | -36.640326774485 |
| 65 | 184 | 190.048893232768 | -6.04889323276842 |
| 66 | 155 | 194.457459691052 | -39.4574596910518 |
| 67 | 276 | 198.866026149335 | 77.1339738506648 |
| 68 | 224 | 203.274592607619 | 20.7254073923814 |
| 69 | 213 | 207.683159065902 | 5.31684093409802 |
| 70 | 279 | 212.091725524185 | 66.9082744758146 |
| 71 | 268 | 216.500291982469 | 51.4997080175312 |
| 72 | 287 | 220.908858440752 | 66.0911415592478 |
| 73 | 238 | 172.414627399635 | 65.5853726003651 |
| 74 | 213 | 176.823193857918 | 36.1768061420818 |
| 75 | 257 | 181.231760316202 | 75.7682396837984 |
| 76 | 293 | 185.640326774485 | 107.359673225515 |
| 77 | 212 | 190.048893232768 | 21.9511067672316 |
| 78 | 246 | 194.457459691052 | 51.5425403089482 |
| 79 | 353 | 198.866026149335 | 154.133973850665 |
| 80 | 339 | 203.274592607619 | 135.725407392381 |
| 81 | 308 | 207.683159065902 | 100.316840934098 |
| 82 | 247 | 212.091725524185 | 34.9082744758146 |
| 83 | 257 | 216.500291982469 | 40.4997080175312 |
| 84 | 322 | 220.908858440752 | 101.091141559248 |
| 85 | 298 | 172.414627399635 | 125.585372600365 |
| 86 | 273 | 176.823193857918 | 96.1768061420818 |
| 87 | 312 | 181.231760316202 | 130.768239683798 |
| 88 | 249 | 185.640326774485 | 63.359673225515 |
| 89 | 286 | 190.048893232768 | 95.9511067672316 |
| 90 | 279 | 194.457459691052 | 84.5425403089482 |
| 91 | 309 | 198.866026149335 | 110.133973850665 |
| 92 | 401 | 203.274592607619 | 197.725407392381 |
| 93 | 309 | 207.683159065902 | 101.316840934098 |
| 94 | 328 | 212.091725524185 | 115.908274475815 |
| 95 | 353 | 216.500291982469 | 136.499708017531 |
| 96 | 354 | 220.908858440752 | 133.091141559248 |
| 97 | 327 | 172.414627399635 | 154.585372600365 |
| 98 | 324 | 176.823193857918 | 147.176806142082 |
| 99 | 285 | 181.231760316202 | 103.768239683798 |
| 100 | 243 | 185.640326774485 | 57.359673225515 |
| 101 | 241 | 190.048893232768 | 50.9511067672316 |
| 102 | 287 | 194.457459691052 | 92.5425403089482 |
| 103 | 355 | 198.866026149335 | 156.133973850665 |
| 104 | 460 | 203.274592607619 | 256.725407392381 |
| 105 | 364 | 207.683159065902 | 156.316840934098 |
| 106 | 487 | 212.091725524185 | 274.908274475815 |
| 107 | 452 | 216.500291982469 | 235.499708017531 |
| 108 | 391 | 220.908858440752 | 170.091141559248 |
| 109 | 500 | 172.414627399635 | 327.585372600365 |
| 110 | 451 | 176.823193857918 | 274.176806142082 |
| 111 | 375 | 181.231760316202 | 193.768239683798 |
| 112 | 372 | 185.640326774485 | 186.359673225515 |
| 113 | 302 | 190.048893232768 | 111.951106767232 |
| 114 | 316 | 194.457459691052 | 121.542540308948 |
| 115 | 398 | 198.866026149335 | 199.133973850665 |
| 116 | 394 | 203.274592607619 | 190.725407392381 |
| 117 | 431 | 207.683159065902 | 223.316840934098 |
| 118 | 431 | 212.091725524185 | 218.908274475815 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 5 | 8.45539593221504e-05 | 0.000169107918644301 | 0.999915446040678 |
| 6 | 4.24121253274766e-06 | 8.48242506549533e-06 | 0.999995758787467 |
| 7 | 1.67386859719996e-07 | 3.34773719439993e-07 | 0.99999983261314 |
| 8 | 1.19214232751847e-08 | 2.38428465503694e-08 | 0.999999988078577 |
| 9 | 4.17329680698925e-10 | 8.34659361397851e-10 | 0.99999999958267 |
| 10 | 1.71053846230112e-11 | 3.42107692460223e-11 | 0.999999999982895 |
| 11 | 1.69383631115823e-12 | 3.38767262231647e-12 | 0.999999999998306 |
| 12 | 2.27822806320118e-12 | 4.55645612640236e-12 | 0.999999999997722 |
| 13 | 2.0148205727685e-13 | 4.029641145537e-13 | 0.999999999999798 |
| 14 | 1.14983932106603e-13 | 2.29967864213206e-13 | 0.999999999999885 |
| 15 | 8.97960447887053e-14 | 1.79592089577411e-13 | 0.99999999999991 |
| 16 | 2.25497010812917e-14 | 4.50994021625835e-14 | 0.999999999999977 |
| 17 | 2.03999646311921e-15 | 4.07999292623843e-15 | 0.999999999999998 |
| 18 | 1.90310746853972e-16 | 3.80621493707944e-16 | 1 |
| 19 | 3.84100565931148e-17 | 7.68201131862297e-17 | 1 |
| 20 | 2.72224668675239e-17 | 5.44449337350478e-17 | 1 |
| 21 | 8.62014676603365e-18 | 1.72402935320673e-17 | 1 |
| 22 | 1.38793902107419e-18 | 2.77587804214838e-18 | 1 |
| 23 | 2.95763580539019e-18 | 5.91527161078038e-18 | 1 |
| 24 | 7.513041170866e-17 | 1.5026082341732e-16 | 1 |
| 25 | 8.26403640809659e-17 | 1.65280728161932e-16 | 1 |
| 26 | 2.01526703515772e-17 | 4.03053407031545e-17 | 1 |
| 27 | 3.63707694197307e-18 | 7.27415388394614e-18 | 1 |
| 28 | 7.16477821748374e-18 | 1.43295564349675e-17 | 1 |
| 29 | 3.20296818592055e-17 | 6.40593637184109e-17 | 1 |
| 30 | 1.11941527636032e-17 | 2.23883055272064e-17 | 1 |
| 31 | 1.44282452466779e-16 | 2.88564904933558e-16 | 1 |
| 32 | 2.40443718408348e-14 | 4.80887436816697e-14 | 0.999999999999976 |
| 33 | 8.79075188467245e-14 | 1.75815037693449e-13 | 0.999999999999912 |
| 34 | 6.18247155010763e-14 | 1.23649431002153e-13 | 0.999999999999938 |
| 35 | 1.50110506825246e-13 | 3.00221013650492e-13 | 0.99999999999985 |
| 36 | 7.96791748503508e-13 | 1.59358349700702e-12 | 0.999999999999203 |
| 37 | 2.56196515603515e-11 | 5.1239303120703e-11 | 0.99999999997438 |
| 38 | 3.7676700439398e-11 | 7.5353400878796e-11 | 0.999999999962323 |
| 39 | 8.1551176154712e-11 | 1.63102352309424e-10 | 0.999999999918449 |
| 40 | 6.03984797113182e-11 | 1.20796959422636e-10 | 0.999999999939602 |
| 41 | 4.96988457322806e-11 | 9.93976914645612e-11 | 0.999999999950301 |
| 42 | 3.18519579501876e-11 | 6.37039159003752e-11 | 0.999999999968148 |
| 43 | 3.18135887889753e-11 | 6.36271775779506e-11 | 0.999999999968186 |
| 44 | 4.32886845867008e-11 | 8.65773691734016e-11 | 0.999999999956711 |
| 45 | 3.79299088879944e-11 | 7.58598177759888e-11 | 0.99999999996207 |
| 46 | 3.38225374496622e-11 | 6.76450748993245e-11 | 0.999999999966177 |
| 47 | 3.56219119580888e-11 | 7.12438239161775e-11 | 0.999999999964378 |
| 48 | 5.92063963202442e-11 | 1.18412792640488e-10 | 0.999999999940794 |
| 49 | 4.78221854966784e-11 | 9.56443709933568e-11 | 0.999999999952178 |
| 50 | 4.61484351867862e-11 | 9.22968703735724e-11 | 0.999999999953852 |
| 51 | 5.23081964969037e-11 | 1.04616392993807e-10 | 0.999999999947692 |
| 52 | 6.49500421919825e-11 | 1.29900084383965e-10 | 0.99999999993505 |
| 53 | 9.6177502562422e-11 | 1.92355005124844e-10 | 0.999999999903822 |
| 54 | 1.98809240107658e-10 | 3.97618480215316e-10 | 0.999999999801191 |
| 55 | 8.28599314555244e-10 | 1.65719862911049e-09 | 0.999999999171401 |
| 56 | 9.40568161487846e-09 | 1.88113632297569e-08 | 0.999999990594318 |
| 57 | 3.52639534083599e-07 | 7.05279068167199e-07 | 0.999999647360466 |
| 58 | 1.35537289788226e-06 | 2.71074579576453e-06 | 0.999998644627102 |
| 59 | 3.89773387505815e-06 | 7.79546775011629e-06 | 0.999996102266125 |
| 60 | 1.23289535446879e-05 | 2.46579070893757e-05 | 0.999987671046455 |
| 61 | 2.17098966590061e-05 | 4.34197933180121e-05 | 0.999978290103341 |
| 62 | 4.62865424686942e-05 | 9.25730849373883e-05 | 0.999953713457531 |
| 63 | 0.000106057210289663 | 0.000212114420579325 | 0.99989394278971 |
| 64 | 0.000245173457092706 | 0.000490346914185412 | 0.999754826542907 |
| 65 | 0.00062887253043182 | 0.00125774506086364 | 0.999371127469568 |
| 66 | 0.00170178532320322 | 0.00340357064640644 | 0.998298214676797 |
| 67 | 0.00913802761138006 | 0.0182760552227601 | 0.99086197238862 |
| 68 | 0.0198267287024636 | 0.0396534574049271 | 0.980173271297536 |
| 69 | 0.0390578994969623 | 0.0781157989939246 | 0.960942100503038 |
| 70 | 0.083678583099708 | 0.167357166199416 | 0.916321416900292 |
| 71 | 0.138893363127689 | 0.277786726255378 | 0.861106636872311 |
| 72 | 0.211352127008932 | 0.422704254017865 | 0.788647872991068 |
| 73 | 0.275823393509129 | 0.551646787018259 | 0.724176606490871 |
| 74 | 0.339580352986481 | 0.679160705972963 | 0.660419647013519 |
| 75 | 0.409630242835338 | 0.819260485670677 | 0.590369757164662 |
| 76 | 0.492831930235858 | 0.985663860471716 | 0.507168069764142 |
| 77 | 0.577140209421536 | 0.845719581156928 | 0.422859790578464 |
| 78 | 0.642047037821589 | 0.715905924356822 | 0.357952962178411 |
| 79 | 0.740384079800054 | 0.519231840399892 | 0.259615920199946 |
| 80 | 0.792180337671263 | 0.415639324657473 | 0.207819662328737 |
| 81 | 0.815800702289395 | 0.36839859542121 | 0.184199297710605 |
| 82 | 0.857401435155039 | 0.285197129689923 | 0.142598564844961 |
| 83 | 0.896822734503057 | 0.206354530993885 | 0.103177265496943 |
| 84 | 0.911924129452332 | 0.176151741095336 | 0.0880758705476681 |
| 85 | 0.917524868257576 | 0.164950263484848 | 0.0824751317424242 |
| 86 | 0.919907112922786 | 0.160185774154428 | 0.0800928870772141 |
| 87 | 0.921140608346456 | 0.157718783307089 | 0.0788593916535444 |
| 88 | 0.933459700398899 | 0.133080599202202 | 0.0665402996011012 |
| 89 | 0.936787875462147 | 0.126424249075707 | 0.0632121245378533 |
| 90 | 0.943617713620952 | 0.112764572758096 | 0.0563822863790481 |
| 91 | 0.944659624499194 | 0.110680751001612 | 0.0553403755008058 |
| 92 | 0.951356644017748 | 0.0972867119645036 | 0.0486433559822518 |
| 93 | 0.952081796662528 | 0.0958364066749449 | 0.0479182033374725 |
| 94 | 0.950538549512163 | 0.0989229009756741 | 0.049461450487837 |
| 95 | 0.946190223232288 | 0.107619553535425 | 0.0538097767677125 |
| 96 | 0.943076332773983 | 0.113847334452033 | 0.0569236672260167 |
| 97 | 0.932039153940501 | 0.135921692118998 | 0.0679608460594992 |
| 98 | 0.91726818099249 | 0.165463638015019 | 0.0827318190075096 |
| 99 | 0.911063681388507 | 0.177872637222986 | 0.088936318611493 |
| 100 | 0.942115847307423 | 0.115768305385153 | 0.0578841526925765 |
| 101 | 0.977394519666191 | 0.0452109606676178 | 0.0226054803338089 |
| 102 | 0.98774284985798 | 0.0245143002840396 | 0.0122571501420198 |
| 103 | 0.985049874238929 | 0.029900251522142 | 0.014950125761071 |
| 104 | 0.9845164443091 | 0.0309671113818003 | 0.0154835556909001 |
| 105 | 0.978406943018312 | 0.0431861139633753 | 0.0215930569816876 |
| 106 | 0.983454448730557 | 0.0330911025388853 | 0.0165455512694426 |
| 107 | 0.980801879976661 | 0.0383962400466785 | 0.0191981200233392 |
| 108 | 0.964318118003582 | 0.0713637639928366 | 0.0356818819964183 |
| 109 | 0.984710495916364 | 0.0305790081672712 | 0.0152895040836356 |
| 110 | 0.995560844044602 | 0.00887831191079666 | 0.00443915595539833 |
| 111 | 0.994187416042289 | 0.0116251679154229 | 0.00581258395771143 |
| 112 | 0.997903549139634 | 0.00419290172073251 | 0.00209645086036625 |
| 113 | 0.988478892314352 | 0.023042215371295 | 0.0115211076856475 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 64 | 0.587155963302752 | NOK |
| 5% type I error level | 76 | 0.697247706422018 | NOK |
| 10% type I error level | 81 | 0.743119266055046 | NOK |
