Multiple Linear Regression - Estimated Regression Equation |
robberies[t] = + 210.888888888889 -18.7888888888889M1[t] -29.5888888888889M2[t] -28.8888888888889M3[t] -44.7888888888889M4[t] -49.5888888888889M5[t] -46.8888888888889M6[t] + 6.21111111111114M7[t] + 26.6111111111111M8[t] + 7.81111111111112M9[t] + 12.8111111111111M10[t] -7.99999999999998M11[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) | 210.888888888889 | 43.986697 | 4.7944 | 5e-06 | 3e-06 |
M1 | -18.7888888888889 | 60.631478 | -0.3099 | 0.757256 | 0.378628 |
M2 | -29.5888888888889 | 60.631478 | -0.488 | 0.626549 | 0.313275 |
M3 | -28.8888888888889 | 60.631478 | -0.4765 | 0.634723 | 0.317361 |
M4 | -44.7888888888889 | 60.631478 | -0.7387 | 0.461718 | 0.230859 |
M5 | -49.5888888888889 | 60.631478 | -0.8179 | 0.415264 | 0.207632 |
M6 | -46.8888888888889 | 60.631478 | -0.7733 | 0.441041 | 0.22052 |
M7 | 6.21111111111114 | 60.631478 | 0.1024 | 0.918601 | 0.4593 |
M8 | 26.6111111111111 | 60.631478 | 0.4389 | 0.661628 | 0.330814 |
M9 | 7.81111111111112 | 60.631478 | 0.1288 | 0.897737 | 0.448868 |
M10 | 12.8111111111111 | 60.631478 | 0.2113 | 0.833063 | 0.416532 |
M11 | -7.99999999999998 | 62.206584 | -0.1286 | 0.897915 | 0.448957 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.194284851062141 |
R-squared | 0.0377466033522383 |
Adjusted R-squared | -0.0621098812055483 |
F-TEST (value) | 0.378008534141761 |
F-TEST (DF numerator) | 11 |
F-TEST (DF denominator) | 106 |
p-value | 0.962041750191452 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 131.960091800863 |
Sum Squared Residuals | 1845827.37777778 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 41 | 192.1 | -151.1 |
2 | 39 | 181.3 | -142.3 |
3 | 50 | 182 | -132 |
4 | 40 | 166.1 | -126.1 |
5 | 43 | 161.3 | -118.3 |
6 | 38 | 164 | -126 |
7 | 44 | 217.1 | -173.1 |
8 | 35 | 237.5 | -202.5 |
9 | 39 | 218.7 | -179.7 |
10 | 35 | 223.7 | -188.7 |
11 | 29 | 202.888888888889 | -173.888888888889 |
12 | 49 | 210.888888888889 | -161.888888888889 |
13 | 50 | 192.1 | -142.1 |
14 | 59 | 181.3 | -122.3 |
15 | 63 | 182 | -119 |
16 | 32 | 166.1 | -134.1 |
17 | 39 | 161.3 | -122.3 |
18 | 47 | 164 | -117 |
19 | 53 | 217.1 | -164.1 |
20 | 60 | 237.5 | -177.5 |
21 | 57 | 218.7 | -161.7 |
22 | 52 | 223.7 | -171.7 |
23 | 70 | 202.888888888889 | -132.888888888889 |
24 | 90 | 210.888888888889 | -120.888888888889 |
25 | 74 | 192.1 | -118.1 |
26 | 62 | 181.3 | -119.3 |
27 | 55 | 182 | -127 |
28 | 84 | 166.1 | -82.1 |
29 | 94 | 161.3 | -67.3 |
30 | 70 | 164 | -94 |
31 | 108 | 217.1 | -109.1 |
32 | 139 | 237.5 | -98.5 |
33 | 120 | 218.7 | -98.7 |
34 | 97 | 223.7 | -126.7 |
35 | 126 | 202.888888888889 | -76.8888888888889 |
36 | 149 | 210.888888888889 | -61.8888888888889 |
37 | 158 | 192.1 | -34.1 |
38 | 124 | 181.3 | -57.3 |
39 | 140 | 182 | -42 |
40 | 109 | 166.1 | -57.1 |
41 | 114 | 161.3 | -47.3 |
42 | 77 | 164 | -87 |
43 | 120 | 217.1 | -97.1 |
44 | 133 | 237.5 | -104.5 |
45 | 110 | 218.7 | -108.7 |
46 | 92 | 223.7 | -131.7 |
47 | 97 | 202.888888888889 | -105.888888888889 |
48 | 78 | 210.888888888889 | -132.888888888889 |
49 | 99 | 192.1 | -93.1 |
50 | 107 | 181.3 | -74.3 |
51 | 112 | 182 | -70 |
52 | 90 | 166.1 | -76.1 |
53 | 98 | 161.3 | -63.3 |
54 | 125 | 164 | -39 |
55 | 155 | 217.1 | -62.1 |
56 | 190 | 237.5 | -47.5 |
57 | 236 | 218.7 | 17.3 |
58 | 189 | 223.7 | -34.7 |
59 | 174 | 202.888888888889 | -28.8888888888889 |
60 | 178 | 210.888888888889 | -32.8888888888889 |
61 | 136 | 192.1 | -56.1 |
62 | 161 | 181.3 | -20.3 |
63 | 171 | 182 | -11 |
64 | 149 | 166.1 | -17.1 |
65 | 184 | 161.3 | 22.7 |
66 | 155 | 164 | -8.99999999999997 |
67 | 276 | 217.1 | 58.9 |
68 | 224 | 237.5 | -13.5 |
69 | 213 | 218.7 | -5.69999999999997 |
70 | 279 | 223.7 | 55.3 |
71 | 268 | 202.888888888889 | 65.1111111111111 |
72 | 287 | 210.888888888889 | 76.1111111111111 |
73 | 238 | 192.1 | 45.9000000000001 |
74 | 213 | 181.3 | 31.7 |
75 | 257 | 182 | 75 |
76 | 293 | 166.1 | 126.9 |
77 | 212 | 161.3 | 50.7 |
78 | 246 | 164 | 82 |
79 | 353 | 217.1 | 135.9 |
80 | 339 | 237.5 | 101.5 |
81 | 308 | 218.7 | 89.3 |
82 | 247 | 223.7 | 23.3 |
83 | 257 | 202.888888888889 | 54.1111111111111 |
84 | 322 | 210.888888888889 | 111.111111111111 |
85 | 298 | 192.1 | 105.9 |
86 | 273 | 181.3 | 91.7 |
87 | 312 | 182 | 130 |
88 | 249 | 166.1 | 82.9 |
89 | 286 | 161.3 | 124.7 |
90 | 279 | 164 | 115 |
91 | 309 | 217.1 | 91.9 |
92 | 401 | 237.5 | 163.5 |
93 | 309 | 218.7 | 90.3 |
94 | 328 | 223.7 | 104.3 |
95 | 353 | 202.888888888889 | 150.111111111111 |
96 | 354 | 210.888888888889 | 143.111111111111 |
97 | 327 | 192.1 | 134.9 |
98 | 324 | 181.3 | 142.7 |
99 | 285 | 182 | 103 |
100 | 243 | 166.1 | 76.9 |
101 | 241 | 161.3 | 79.7 |
102 | 287 | 164 | 123 |
103 | 355 | 217.1 | 137.9 |
104 | 460 | 237.5 | 222.5 |
105 | 364 | 218.7 | 145.3 |
106 | 487 | 223.7 | 263.3 |
107 | 452 | 202.888888888889 | 249.111111111111 |
108 | 391 | 210.888888888889 | 180.111111111111 |
109 | 500 | 192.1 | 307.9 |
110 | 451 | 181.3 | 269.7 |
111 | 375 | 182 | 193 |
112 | 372 | 166.1 | 205.9 |
113 | 302 | 161.3 | 140.7 |
114 | 316 | 164 | 152 |
115 | 398 | 217.1 | 180.9 |
116 | 394 | 237.5 | 156.5 |
117 | 431 | 218.7 | 212.3 |
118 | 431 | 223.7 | 207.3 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
15 | 0.000784263213970067 | 0.00156852642794013 | 0.99921573678603 |
16 | 6.53353176146948e-05 | 0.00013067063522939 | 0.999934664682385 |
17 | 4.5509154699391e-06 | 9.10183093987821e-06 | 0.99999544908453 |
18 | 3.85022377068844e-07 | 7.70044754137687e-07 | 0.999999614977623 |
19 | 3.44410631033663e-08 | 6.88821262067325e-08 | 0.999999965558937 |
20 | 1.89297073594603e-08 | 3.78594147189207e-08 | 0.999999981070293 |
21 | 3.70064447015035e-09 | 7.40128894030069e-09 | 0.999999996299356 |
22 | 6.89152264609263e-10 | 1.37830452921853e-09 | 0.999999999310848 |
23 | 1.47520065357976e-09 | 2.95040130715952e-09 | 0.999999998524799 |
24 | 1.47174506919379e-09 | 2.94349013838757e-09 | 0.999999998528255 |
25 | 6.41623338409731e-10 | 1.28324667681946e-09 | 0.999999999358377 |
26 | 1.19704287345512e-10 | 2.39408574691025e-10 | 0.999999999880296 |
27 | 1.81202349854204e-11 | 3.62404699708409e-11 | 0.99999999998188 |
28 | 4.55960604230892e-11 | 9.11921208461784e-11 | 0.999999999954404 |
29 | 1.00731705747779e-10 | 2.01463411495559e-10 | 0.999999999899268 |
30 | 3.52405365226052e-11 | 7.04810730452104e-11 | 0.999999999964759 |
31 | 9.43129824366731e-11 | 1.88625964873346e-10 | 0.999999999905687 |
32 | 1.65075609471195e-09 | 3.30151218942389e-09 | 0.999999998349244 |
33 | 3.4730845445164e-09 | 6.9461690890328e-09 | 0.999999996526915 |
34 | 3.29541070269235e-09 | 6.5908214053847e-09 | 0.999999996704589 |
35 | 6.30684896324202e-09 | 1.2613697926484e-08 | 0.999999993693151 |
36 | 1.10563964735157e-08 | 2.21127929470313e-08 | 0.999999988943604 |
37 | 5.34101377117397e-08 | 1.06820275423479e-07 | 0.999999946589862 |
38 | 6.14526206202255e-08 | 1.22905241240451e-07 | 0.999999938547379 |
39 | 9.61738084162731e-08 | 1.92347616832546e-07 | 0.999999903826192 |
40 | 7.32935179346717e-08 | 1.46587035869343e-07 | 0.999999926706482 |
41 | 5.16699696493706e-08 | 1.03339939298741e-07 | 0.99999994833003 |
42 | 2.80993183337567e-08 | 5.61986366675134e-08 | 0.999999971900682 |
43 | 2.60015600883378e-08 | 5.20031201766756e-08 | 0.99999997399844 |
44 | 2.88208867027904e-08 | 5.76417734055809e-08 | 0.999999971179113 |
45 | 2.51600365448025e-08 | 5.03200730896049e-08 | 0.999999974839964 |
46 | 2.74631657295003e-08 | 5.49263314590006e-08 | 0.999999972536834 |
47 | 2.32011872696053e-08 | 4.64023745392106e-08 | 0.999999976798813 |
48 | 2.50230948777581e-08 | 5.00461897555162e-08 | 0.999999974976905 |
49 | 2.34634138241249e-08 | 4.69268276482497e-08 | 0.999999976536586 |
50 | 2.35366752730606e-08 | 4.70733505461211e-08 | 0.999999976463325 |
51 | 2.2784653953727e-08 | 4.55693079074539e-08 | 0.999999977215346 |
52 | 2.09232469582804e-08 | 4.18464939165607e-08 | 0.999999979076753 |
53 | 1.67772238092416e-08 | 3.35544476184831e-08 | 0.999999983222776 |
54 | 2.64238416558992e-08 | 5.28476833117984e-08 | 0.999999973576158 |
55 | 7.95314108648735e-08 | 1.59062821729747e-07 | 0.999999920468589 |
56 | 4.32713415008382e-07 | 8.65426830016764e-07 | 0.999999567286585 |
57 | 6.41017814743909e-06 | 1.28203562948782e-05 | 0.999993589821853 |
58 | 3.37942490724089e-05 | 6.75884981448177e-05 | 0.999966205750928 |
59 | 8.35784239031365e-05 | 0.000167156847806273 | 0.999916421576097 |
60 | 0.000185381833318745 | 0.00037076366663749 | 0.999814618166681 |
61 | 0.000471323311888708 | 0.000942646623777415 | 0.999528676688111 |
62 | 0.000996955773881464 | 0.00199391154776293 | 0.999003044226119 |
63 | 0.00186541292820782 | 0.00373082585641563 | 0.998134587071792 |
64 | 0.00325895285385107 | 0.00651790570770213 | 0.996741047146149 |
65 | 0.00486756797289739 | 0.00973513594579479 | 0.995132432027103 |
66 | 0.00774165873812172 | 0.0154833174762434 | 0.992258341261878 |
67 | 0.0255115428842266 | 0.0510230857684533 | 0.974488457115773 |
68 | 0.0639411495359028 | 0.127882299071806 | 0.936058850464097 |
69 | 0.105078885738556 | 0.210157771477112 | 0.894921114261444 |
70 | 0.206438062139145 | 0.41287612427829 | 0.793561937860855 |
71 | 0.296208827143944 | 0.592417654287888 | 0.703791172856056 |
72 | 0.385886728162308 | 0.771773456324615 | 0.614113271837692 |
73 | 0.51628699104817 | 0.967426017903659 | 0.48371300895183 |
74 | 0.624199743004046 | 0.751600513991909 | 0.375800256995954 |
75 | 0.672580251161486 | 0.654839497677027 | 0.327419748838514 |
76 | 0.73294939220475 | 0.534101215590501 | 0.26705060779525 |
77 | 0.734043875058083 | 0.531912249883833 | 0.265956124941917 |
78 | 0.74921058848569 | 0.50157882302862 | 0.25078941151431 |
79 | 0.793012810589696 | 0.413974378820607 | 0.206987189410304 |
80 | 0.83803064920206 | 0.323938701595879 | 0.16196935079794 |
81 | 0.848980557461994 | 0.302038885076012 | 0.151019442538006 |
82 | 0.923446389696569 | 0.153107220606862 | 0.0765536103034311 |
83 | 0.955116587024296 | 0.0897668259514083 | 0.0448834129757042 |
84 | 0.954898476944296 | 0.0902030461114089 | 0.0451015230557044 |
85 | 0.970591530252453 | 0.0588169394950945 | 0.0294084697475473 |
86 | 0.980170348436559 | 0.0396593031268811 | 0.0198296515634405 |
87 | 0.976225459219595 | 0.0475490815608102 | 0.0237745407804051 |
88 | 0.971619262185365 | 0.0567614756292691 | 0.0283807378146346 |
89 | 0.963130482942812 | 0.0737390341143755 | 0.0368695170571878 |
90 | 0.95201623374066 | 0.0959675325186797 | 0.0479837662593399 |
91 | 0.945015764426325 | 0.10996847114735 | 0.0549842355736748 |
92 | 0.936328077956994 | 0.127343844086013 | 0.0636719220430064 |
93 | 0.934010611622646 | 0.131978776754708 | 0.065989388377354 |
94 | 0.957166907627129 | 0.0856661847457421 | 0.042833092372871 |
95 | 0.957346310449465 | 0.0853073791010692 | 0.0426536895505346 |
96 | 0.937977970549926 | 0.124044058900147 | 0.0620220294500735 |
97 | 0.97394442529174 | 0.05211114941652 | 0.02605557470826 |
98 | 0.982768969641225 | 0.0344620607175494 | 0.0172310303587747 |
99 | 0.980117315331704 | 0.0397653693365914 | 0.0198826846682957 |
100 | 0.991568890292388 | 0.0168622194152245 | 0.00843110970761225 |
101 | 0.985570576326513 | 0.0288588473469748 | 0.0144294236734874 |
102 | 0.962640521860536 | 0.074718956278929 | 0.0373594781394645 |
103 | 0.916161650153269 | 0.167676699693462 | 0.0838383498467312 |
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
Description | # significant tests | % significant tests | OK/NOK |
1% type I error level | 51 | 0.573033707865168 | NOK |
5% type I error level | 58 | 0.651685393258427 | NOK |
10% type I error level | 69 | 0.775280898876405 | NOK |