| Multiple Linear Regression - Estimated Regression Equation |
| Assaults[t] = -46.195573681861 + 157.459475609288Pop[t] -2.24327138816698e-05BachDgr[t] + 0.553103839199705PoliceExp[t] + 5.52628914544458TotlPopul[t] + 7.69293391267485Unempl[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) | -46.195573681861 | 89.251115 | -0.5176 | 0.606782 | 0.303391 |
| Pop | 157.459475609288 | 61.207907 | 2.5725 | 0.012774 | 0.006387 |
| BachDgr | -2.24327138816698e-05 | 3.2e-05 | -0.6981 | 0.488031 | 0.244015 |
| PoliceExp | 0.553103839199705 | 0.226012 | 2.4472 | 0.017558 | 0.008779 |
| TotlPopul | 5.52628914544458 | 2.715911 | 2.0348 | 0.046617 | 0.023309 |
| Unempl | 7.69293391267485 | 8.574327 | 0.8972 | 0.37345 | 0.186725 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.545535887200971 |
| R-squared | 0.297609404224151 |
| Adjusted R-squared | 0.234895958172736 |
| F-TEST (value) | 4.7455437862585 |
| F-TEST (DF numerator) | 5 |
| F-TEST (DF denominator) | 56 |
| p-value | 0.001101536006332 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 145.629145880577 |
| Sum Squared Residuals | 1187639.49527476 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 521 | 290.898272661627 | 230.101727338373 |
| 2 | 367 | 511.529849979445 | -144.529849979445 |
| 3 | 443 | 380.716788855604 | 62.2832111443958 |
| 4 | 365 | 258.78198799166 | 106.21801200834 |
| 5 | 614 | 570.110000953506 | 43.8899990464941 |
| 6 | 385 | 327.957026865997 | 57.0429731340025 |
| 7 | 286 | 372.017209322434 | -86.0172093224338 |
| 8 | 397 | 343.968749697143 | 53.0312503028574 |
| 9 | 764 | 433.846969277139 | 330.153030722861 |
| 10 | 427 | 332.152750762846 | 94.8472492371539 |
| 11 | 153 | 315.83722599876 | -162.83722599876 |
| 12 | 231 | 272.646879295815 | -41.6468792958152 |
| 13 | 524 | 375.047333643381 | 148.952666356619 |
| 14 | 328 | 282.328931842916 | 45.6710681570836 |
| 15 | 240 | 266.706365925442 | -26.7063659254419 |
| 16 | 286 | 290.70636278889 | -4.70636278888987 |
| 17 | 285 | 293.354698232941 | -8.35469823294114 |
| 18 | 569 | 322.136843017627 | 246.863156982373 |
| 19 | 96 | 280.166559156379 | -184.166559156379 |
| 20 | 498 | 380.65308159856 | 117.34691840144 |
| 21 | 481 | 386.976207845948 | 94.0237921540516 |
| 22 | 468 | 400.004397229603 | 67.9956027703967 |
| 23 | 177 | 300.25321696175 | -123.25321696175 |
| 24 | 198 | 265.553917707814 | -67.5539177078135 |
| 25 | 458 | 294.292956985276 | 163.707043014724 |
| 26 | 108 | 277.082143967086 | -169.082143967086 |
| 27 | 246 | 241.772649711035 | 4.22735028896492 |
| 28 | 291 | 390.808706116199 | -99.8087061161987 |
| 29 | 68 | 301.494974909967 | -233.494974909967 |
| 30 | 311 | 397.258770293324 | -86.258770293324 |
| 31 | 606 | 329.68137202678 | 276.31862797322 |
| 32 | 512 | 539.991863731741 | -27.9918637317414 |
| 33 | 426 | 319.637726225002 | 106.362273774998 |
| 34 | 47 | 225.329423151704 | -178.329423151704 |
| 35 | 265 | 357.070499285198 | -92.0704992851983 |
| 36 | 370 | 287.731952451686 | 82.2680475483139 |
| 37 | 312 | 332.136386407045 | -20.1363864070445 |
| 38 | 222 | 355.274336847771 | -133.274336847771 |
| 39 | 280 | 340.7321834182 | -60.7321834182005 |
| 40 | 759 | 301.805856244096 | 457.194143755904 |
| 41 | 114 | 230.233340199819 | -116.233340199819 |
| 42 | 419 | 310.819724265704 | 108.180275734296 |
| 43 | 435 | 385.537310488815 | 49.4626895111852 |
| 44 | 186 | 279.909531945652 | -93.9095319456517 |
| 45 | 87 | 265.832053863073 | -178.832053863073 |
| 46 | 188 | 333.231416361717 | -145.231416361717 |
| 47 | 303 | 330.555206340038 | -27.5552063400383 |
| 48 | 102 | 267.04561184019 | -165.04561184019 |
| 49 | 127 | 327.481235479122 | -200.481235479122 |
| 50 | 251 | 318.901139830532 | -67.9011398305322 |
| 51 | 205 | 191.298522565388 | 13.7014774346121 |
| 52 | 453 | 381.733175791832 | 71.2668242081684 |
| 53 | 320 | 153.189733004551 | 166.810266995449 |
| 54 | 405 | 403.026109037574 | 1.97389096242615 |
| 55 | 89 | 93.3316535512012 | -4.33165355120119 |
| 56 | 74 | 138.843545953035 | -64.843545953035 |
| 57 | 101 | 147.620756342396 | -46.6207563423958 |
| 58 | 321 | 201.696758780246 | 119.303241219754 |
| 59 | 315 | 431.745096960359 | -116.745096960359 |
| 60 | 229 | 410.796224232271 | -181.796224232271 |
| 61 | 302 | 361.231808805712 | -59.2318088057116 |
| 62 | 216 | 115.486614975437 | 100.513385024563 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 9 | 0.643184690244923 | 0.713630619510155 | 0.356815309755077 |
| 10 | 0.54028547699957 | 0.919429046000861 | 0.45971452300043 |
| 11 | 0.569846185180483 | 0.860307629639035 | 0.430153814819517 |
| 12 | 0.575015386984897 | 0.849969226030206 | 0.424984613015103 |
| 13 | 0.47465350372977 | 0.94930700745954 | 0.52534649627023 |
| 14 | 0.385712583770837 | 0.771425167541675 | 0.614287416229163 |
| 15 | 0.29616726203082 | 0.592334524061639 | 0.70383273796918 |
| 16 | 0.208991828464654 | 0.417983656929308 | 0.791008171535346 |
| 17 | 0.207708307096219 | 0.415416614192438 | 0.792291692903781 |
| 18 | 0.266381341564891 | 0.532762683129783 | 0.733618658435109 |
| 19 | 0.481036827045444 | 0.962073654090888 | 0.518963172954556 |
| 20 | 0.45017218378668 | 0.900344367573359 | 0.54982781621332 |
| 21 | 0.378188282578346 | 0.756376565156693 | 0.621811717421654 |
| 22 | 0.317006260280902 | 0.634012520561804 | 0.682993739719098 |
| 23 | 0.311315418389472 | 0.622630836778943 | 0.688684581610528 |
| 24 | 0.30227318329922 | 0.60454636659844 | 0.69772681670078 |
| 25 | 0.303780177089513 | 0.607560354179027 | 0.696219822910487 |
| 26 | 0.335243872663872 | 0.670487745327743 | 0.664756127336128 |
| 27 | 0.264899277153796 | 0.529798554307592 | 0.735100722846204 |
| 28 | 0.21501434270982 | 0.430028685419639 | 0.78498565729018 |
| 29 | 0.312797402746552 | 0.625594805493105 | 0.687202597253448 |
| 30 | 0.27030994707892 | 0.540619894157841 | 0.72969005292108 |
| 31 | 0.500878418905728 | 0.998243162188544 | 0.499121581094272 |
| 32 | 0.444436779437172 | 0.888873558874344 | 0.555563220562828 |
| 33 | 0.417007367353936 | 0.834014734707872 | 0.582992632646064 |
| 34 | 0.441626253791996 | 0.883252507583992 | 0.558373746208004 |
| 35 | 0.401655227594308 | 0.803310455188616 | 0.598344772405692 |
| 36 | 0.352979234571239 | 0.705958469142478 | 0.647020765428761 |
| 37 | 0.281100923118012 | 0.562201846236024 | 0.718899076881988 |
| 38 | 0.261450908243826 | 0.522901816487652 | 0.738549091756174 |
| 39 | 0.202881662890125 | 0.40576332578025 | 0.797118337109875 |
| 40 | 0.939008013204275 | 0.121983973591451 | 0.0609919867957254 |
| 41 | 0.917955942315167 | 0.164088115369666 | 0.0820440576848331 |
| 42 | 0.949726867460394 | 0.100546265079212 | 0.0502731325396062 |
| 43 | 0.978200936220508 | 0.043598127558984 | 0.021799063779492 |
| 44 | 0.962397750512247 | 0.0752044989755071 | 0.0376022494877535 |
| 45 | 0.954717627142418 | 0.0905647457151641 | 0.0452823728575821 |
| 46 | 0.927393503268339 | 0.145212993463322 | 0.0726064967316608 |
| 47 | 0.92456865835566 | 0.15086268328868 | 0.0754313416443401 |
| 48 | 0.97396096423128 | 0.0520780715374404 | 0.0260390357687202 |
| 49 | 0.988686703069653 | 0.0226265938606947 | 0.0113132969303474 |
| 50 | 0.971462017225669 | 0.0570759655486613 | 0.0285379827743307 |
| 51 | 0.956560697578179 | 0.086878604843642 | 0.043439302421821 |
| 52 | 0.913259050925208 | 0.173481898149583 | 0.0867409490747916 |
| 53 | 0.872573041729087 | 0.254853916541827 | 0.127426958270913 |
| 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 | 0.0444444444444444 | OK |
| 10% type I error level | 7 | 0.155555555555556 | NOK |
