Multiple Linear Regression - Estimated Regression Equation |
Year[t] = + 1967.10365283744 -0.125902148332274Month[t] + 0.0210291378753831robberies[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) | 1967.10365283744 | 0.22656 | 8682.4754 | 0 | 0 |
Month | -0.125902148332274 | 0.026629 | -4.728 | 6e-06 | 3e-06 |
robberies | 0.0210291378753831 | 0.000714 | 29.4572 | 0 | 0 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.939769286485165 |
R-squared | 0.883166311820837 |
Adjusted R-squared | 0.881134421591634 |
F-TEST (value) | 434.652570856312 |
F-TEST (DF numerator) | 2 |
F-TEST (DF denominator) | 115 |
p-value | 0 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 0.981805734481531 |
Sum Squared Residuals | 110.853387529994 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 1966 | 1967.839945342 | -1.83994534200346 |
2 | 1966 | 1967.67198491792 | -1.67198491791526 |
3 | 1966 | 1967.77740328621 | -1.7774032862122 |
4 | 1966 | 1967.44120975913 | -1.44120975912609 |
5 | 1966 | 1967.37839502442 | -1.37839502441997 |
6 | 1966 | 1967.14734718671 | -1.14734718671078 |
7 | 1966 | 1967.14761986563 | -1.1476198656308 |
8 | 1966 | 1966.83245547642 | -0.832455476420079 |
9 | 1966 | 1966.79066987959 | -0.790669879589338 |
10 | 1966 | 1966.58065117976 | -0.580651179755531 |
11 | 1966 | 1966.32857420417 | -0.32857420417096 |
12 | 1966 | 1966.62325481335 | -0.623254813346346 |
13 | 1967 | 1968.02920758288 | -1.02920758287674 |
14 | 1967 | 1968.09256767542 | -1.09256767542292 |
15 | 1967 | 1968.05078207859 | -1.05078207859217 |
16 | 1967 | 1967.27297665612 | -0.272976656123026 |
17 | 1967 | 1967.29427847292 | -0.294278472918433 |
18 | 1967 | 1967.33660942759 | -0.336609427589224 |
19 | 1967 | 1967.33688210651 | -0.336882106509248 |
20 | 1967 | 1967.3581839233 | -0.358183923304655 |
21 | 1967 | 1967.16919436135 | -0.169194361346232 |
22 | 1967 | 1966.93814652364 | 0.0618534763629574 |
23 | 1967 | 1967.19076885706 | -0.190768857061664 |
24 | 1967 | 1967.48544946624 | -0.485449466237051 |
25 | 1968 | 1968.53390689189 | -0.533906891885936 |
26 | 1968 | 1968.15565508905 | -0.155655089049065 |
27 | 1968 | 1967.88254897559 | 0.11745102441089 |
28 | 1968 | 1968.36649182564 | -0.366491825642944 |
29 | 1968 | 1968.45088105606 | -0.450881056064501 |
30 | 1968 | 1967.82027959872 | 0.179720401276966 |
31 | 1968 | 1968.49348468966 | -0.493484689655316 |
32 | 1968 | 1969.01948581546 | -1.01948581545992 |
33 | 1968 | 1968.4940300475 | -0.494030047495364 |
34 | 1968 | 1967.88445772803 | 0.11554227197072 |
35 | 1968 | 1968.36840057808 | -0.368400578083114 |
36 | 1968 | 1968.72616860088 | -0.726168600884651 |
37 | 1969 | 1970.30035447342 | -1.30035447341811 |
38 | 1969 | 1969.45946163732 | -0.459461637322815 |
39 | 1969 | 1969.670025695 | -0.67002569499667 |
40 | 1969 | 1968.89222027253 | 0.107779727472479 |
41 | 1969 | 1968.87146381357 | 0.128536186427838 |
42 | 1969 | 1967.96748356385 | 1.03251643614928 |
43 | 1969 | 1968.74583434416 | 0.254165655840088 |
44 | 1969 | 1968.89331098821 | 0.106689011792382 |
45 | 1969 | 1968.28373866874 | 0.716261331258466 |
46 | 1969 | 1967.77931203865 | 1.22068796134764 |
47 | 1969 | 1967.7585555797 | 1.24144442030299 |
48 | 1969 | 1967.23309981173 | 1.76690018826755 |
49 | 1970 | 1969.05963533877 | 0.940364661229488 |
50 | 1970 | 1969.10196629344 | 0.898033706558697 |
51 | 1970 | 1969.08120983449 | 0.918790165514056 |
52 | 1970 | 1968.4926666529 | 1.50733334710476 |
53 | 1970 | 1968.53499760757 | 1.46500239243397 |
54 | 1970 | 1968.97688218187 | 1.0231178181309 |
55 | 1970 | 1969.4818541698 | 0.518145830201681 |
56 | 1970 | 1970.0919718471 | -0.0919718471044521 |
57 | 1970 | 1970.93341004104 | -0.933410041039798 |
58 | 1970 | 1969.81913841256 | 0.180861587435479 |
59 | 1970 | 1969.3777991961 | 0.622200803898499 |
60 | 1970 | 1969.33601359927 | 0.663986400729241 |
61 | 1971 | 1969.83771344016 | 1.16228655984031 |
62 | 1971 | 1970.23753973871 | 0.762460261288012 |
63 | 1971 | 1970.32192896913 | 0.678071030866456 |
64 | 1971 | 1969.73338578754 | 1.26661421245716 |
65 | 1971 | 1970.34350346485 | 0.656496535151024 |
66 | 1971 | 1969.60775631813 | 1.39224368186941 |
67 | 1971 | 1972.02637985272 | -1.02637985271967 |
68 | 1971 | 1970.80696253487 | 0.193037465132524 |
69 | 1971 | 1970.44973986991 | 0.550260130094012 |
70 | 1971 | 1971.71176082135 | -0.711760821348996 |
71 | 1971 | 1971.35453815639 | -0.354538156387508 |
72 | 1971 | 1971.62818962769 | -0.628189627687512 |
73 | 1972 | 1971.98268550345 | 0.0173144965512435 |
74 | 1972 | 1971.33105490823 | 0.668945091768093 |
75 | 1972 | 1972.13043482642 | -0.130434826416487 |
76 | 1972 | 1972.7615816416 | -0.761581641598003 |
77 | 1972 | 1970.93231932536 | 1.0676806746403 |
78 | 1972 | 1971.52140786479 | 0.478592135209549 |
79 | 1972 | 1973.64562346912 | -1.64562346912416 |
80 | 1972 | 1973.22531339054 | -1.22531339053653 |
81 | 1972 | 1972.44750796807 | -0.447507968067379 |
82 | 1972 | 1971.03882840934 | 0.961171590663262 |
83 | 1972 | 1971.12321763976 | 0.876782360241705 |
84 | 1972 | 1972.36420945333 | -0.364209453325919 |
85 | 1973 | 1973.24443377597 | -0.24443377597174 |
86 | 1973 | 1972.59280318075 | 0.40719681924511 |
87 | 1973 | 1973.28703740956 | -0.287037409562555 |
88 | 1973 | 1971.83629957508 | 1.16370042491885 |
89 | 1973 | 1972.48847552814 | 0.511524471861953 |
90 | 1973 | 1972.21536941468 | 0.784630585321908 |
91 | 1973 | 1972.72034140261 | 0.27965859739269 |
92 | 1973 | 1974.52911993881 | -1.52911993881028 |
93 | 1973 | 1972.46853710594 | 0.531462894057238 |
94 | 1973 | 1972.74218857724 | 0.257811422757234 |
95 | 1973 | 1973.14201487579 | -0.142014875795068 |
96 | 1973 | 1973.03714186534 | -0.0371418653381769 |
97 | 1974 | 1973.85427877436 | 0.145721225642151 |
98 | 1974 | 1973.6652892124 | 0.334710787600574 |
99 | 1974 | 1972.71925068693 | 1.28074931307279 |
100 | 1974 | 1971.71012474783 | 2.28987525217115 |
101 | 1974 | 1971.54216432375 | 2.45783567625419 |
102 | 1974 | 1972.38360251768 | 1.61639748231884 |
103 | 1974 | 1973.68768174487 | 0.31231825512507 |
104 | 1974 | 1975.76983907346 | -1.76983907345788 |
105 | 1974 | 1973.62513968909 | 0.37486031091117 |
106 | 1974 | 1976.08582149943 | -2.08582149942867 |
107 | 1974 | 1975.22389952546 | -1.22389952545799 |
108 | 1974 | 1973.81521996673 | 0.18478003327265 |
109 | 1975 | 1977.4923196268 | -2.49231962679912 |
110 | 1975 | 1976.33598972257 | -1.33598972257307 |
111 | 1975 | 1974.61187309571 | 0.388126904288312 |
112 | 1975 | 1974.42288353375 | 0.577116466246735 |
113 | 1975 | 1972.82494173414 | 2.17505826585582 |
114 | 1975 | 1972.99344751607 | 2.00655248393273 |
115 | 1975 | 1974.59193467352 | 0.408065326483598 |
116 | 1975 | 1974.38191597368 | 0.618084026317404 |
117 | 1975 | 1975.03409192674 | -0.0340919267394948 |
118 | 1975 | 1974.90818977841 | 0.0918102215927801 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
6 | 3.64720047330966e-39 | 7.29440094661932e-39 | 1 |
7 | 3.58906407244503e-56 | 7.17812814489006e-56 | 1 |
8 | 3.52826565266546e-63 | 7.05653130533092e-63 | 1 |
9 | 8.90797518222781e-78 | 1.78159503644556e-77 | 1 |
10 | 6.98523522154154e-91 | 1.39704704430831e-90 | 1 |
11 | 2.71577648095989e-108 | 5.43155296191977e-108 | 1 |
12 | 2.92123671309534e-112 | 5.84247342619067e-112 | 1 |
13 | 8.32683578043886e-05 | 0.000166536715608777 | 0.999916731642196 |
14 | 8.82483957169387e-05 | 0.000176496791433877 | 0.999911751604283 |
15 | 3.70938237516678e-05 | 7.41876475033356e-05 | 0.999962906176248 |
16 | 0.000760275173300972 | 0.00152055034660194 | 0.999239724826699 |
17 | 0.00146758397273992 | 0.00293516794547985 | 0.99853241602726 |
18 | 0.00166149588809393 | 0.00332299177618787 | 0.998338504111906 |
19 | 0.0013530096388692 | 0.00270601927773839 | 0.998646990361131 |
20 | 0.000792730336110778 | 0.00158546067222156 | 0.999207269663889 |
21 | 0.000465732512954506 | 0.000931465025909013 | 0.999534267487046 |
22 | 0.000307515046277329 | 0.000615030092554658 | 0.999692484953723 |
23 | 0.000152428422200795 | 0.00030485684440159 | 0.999847571577799 |
24 | 0.000129680684479849 | 0.000259361368959698 | 0.99987031931552 |
25 | 0.000174366292944986 | 0.000348732585889971 | 0.999825633707055 |
26 | 0.000364648958121679 | 0.000729297916243357 | 0.999635351041878 |
27 | 0.000977586489015544 | 0.00195517297803109 | 0.999022413510984 |
28 | 0.000622099215836095 | 0.00124419843167219 | 0.999377900784164 |
29 | 0.00040202324944778 | 0.00080404649889556 | 0.999597976750552 |
30 | 0.000429445110836269 | 0.000858890221672538 | 0.999570554889164 |
31 | 0.000368090780268503 | 0.000736181560537006 | 0.999631909219732 |
32 | 0.000974742235504515 | 0.00194948447100903 | 0.999025257764495 |
33 | 0.000712957675578748 | 0.0014259153511575 | 0.999287042324421 |
34 | 0.000533931650037082 | 0.00106786330007416 | 0.999466068349963 |
35 | 0.000388366174830142 | 0.000776732349660284 | 0.99961163382517 |
36 | 0.000485602051864326 | 0.000971204103728651 | 0.999514397948136 |
37 | 0.000713042075710933 | 0.00142608415142187 | 0.999286957924289 |
38 | 0.000777985405887616 | 0.00155597081177523 | 0.999222014594112 |
39 | 0.000797648708913308 | 0.00159529741782662 | 0.999202351291087 |
40 | 0.00129239493184212 | 0.00258478986368424 | 0.998707605068158 |
41 | 0.00172124434683561 | 0.00344248869367122 | 0.998278755653164 |
42 | 0.0103080084689011 | 0.0206160169378023 | 0.989691991531099 |
43 | 0.0106705210595978 | 0.0213410421191956 | 0.989329478940402 |
44 | 0.00943802500967994 | 0.0188760500193599 | 0.99056197499032 |
45 | 0.0122163675342902 | 0.0244327350685805 | 0.98778363246571 |
46 | 0.025853995356068 | 0.051707990712136 | 0.974146004643932 |
47 | 0.0389814866830316 | 0.0779629733660632 | 0.961018513316968 |
48 | 0.0859672053153787 | 0.171934410630757 | 0.914032794684621 |
49 | 0.157498596975399 | 0.314997193950798 | 0.842501403024601 |
50 | 0.206781042039587 | 0.413562084079174 | 0.793218957960413 |
51 | 0.237810457182079 | 0.475620914364157 | 0.762189542817921 |
52 | 0.343180235600433 | 0.686360471200867 | 0.656819764399566 |
53 | 0.413269898406894 | 0.826539796813788 | 0.586730101593106 |
54 | 0.398642471604279 | 0.797284943208559 | 0.601357528395721 |
55 | 0.357196673238069 | 0.714393346476139 | 0.642803326761931 |
56 | 0.360453106443524 | 0.720906212887048 | 0.639546893556476 |
57 | 0.503659489817096 | 0.992681020365809 | 0.496340510182904 |
58 | 0.471846074316465 | 0.943692148632931 | 0.528153925683535 |
59 | 0.42787855069622 | 0.855757101392439 | 0.57212144930378 |
60 | 0.382967009604083 | 0.765934019208166 | 0.617032990395917 |
61 | 0.404552098346148 | 0.809104196692295 | 0.595447901653852 |
62 | 0.383991430569318 | 0.767982861138636 | 0.616008569430682 |
63 | 0.356572524103421 | 0.713145048206843 | 0.643427475896579 |
64 | 0.351621797862077 | 0.703243595724153 | 0.648378202137924 |
65 | 0.317214682648936 | 0.634429365297873 | 0.682785317351064 |
66 | 0.307710409643668 | 0.615420819287337 | 0.692289590356332 |
67 | 0.469708533119391 | 0.939417066238782 | 0.530291466880609 |
68 | 0.445758400212267 | 0.891516800424534 | 0.554241599787733 |
69 | 0.406394109849869 | 0.812788219699737 | 0.593605890150131 |
70 | 0.484455093476463 | 0.968910186952927 | 0.515544906523536 |
71 | 0.50955009705618 | 0.98089980588764 | 0.49044990294382 |
72 | 0.573121504905698 | 0.853756990188605 | 0.426878495094302 |
73 | 0.568495733502644 | 0.863008532994713 | 0.431504266497356 |
74 | 0.549561924698182 | 0.900876150603637 | 0.450438075301818 |
75 | 0.564575357926874 | 0.870849284146252 | 0.435424642073126 |
76 | 0.646118009840885 | 0.70776398031823 | 0.353881990159115 |
77 | 0.637684266936316 | 0.724631466127369 | 0.362315733063684 |
78 | 0.62662815167608 | 0.746743696647839 | 0.37337184832392 |
79 | 0.805583905287761 | 0.388832189424479 | 0.194416094712239 |
80 | 0.884648784536184 | 0.230702430927632 | 0.115351215463816 |
81 | 0.905169898530793 | 0.189660202938414 | 0.0948301014692068 |
82 | 0.90039804576344 | 0.19920390847312 | 0.0996019542365602 |
83 | 0.895883059993201 | 0.208233880013598 | 0.104116940006799 |
84 | 0.921504530882704 | 0.156990938234592 | 0.0784954691172958 |
85 | 0.931218004151679 | 0.137563991696643 | 0.0687819958483215 |
86 | 0.934424812086069 | 0.131150375827862 | 0.0655751879139308 |
87 | 0.950061098778198 | 0.0998778024436039 | 0.049938901221802 |
88 | 0.952602924284181 | 0.0947941514316371 | 0.0473970757158186 |
89 | 0.956457666294576 | 0.0870846674108478 | 0.0435423337054239 |
90 | 0.958383969860512 | 0.0832320602789765 | 0.0416160301394882 |
91 | 0.962422253728479 | 0.0751554925430425 | 0.0375777462715212 |
92 | 0.985206911642197 | 0.0295861767156066 | 0.0147930883578033 |
93 | 0.985859939278352 | 0.0282801214432963 | 0.0141400607216482 |
94 | 0.98758821598567 | 0.0248235680286605 | 0.0124117840143303 |
95 | 0.991497609888609 | 0.0170047802227821 | 0.00850239011139106 |
96 | 0.995984554163509 | 0.00803089167298203 | 0.00401544583649102 |
97 | 0.995644070001626 | 0.0087118599967477 | 0.00435592999837385 |
98 | 0.995662039037945 | 0.00867592192411039 | 0.00433796096205519 |
99 | 0.995657040891901 | 0.0086859182161981 | 0.00434295910809905 |
100 | 0.996288079043263 | 0.00742384191347337 | 0.00371192095673669 |
101 | 0.997321682523783 | 0.00535663495243385 | 0.00267831747621692 |
102 | 0.998399982278576 | 0.00320003544284892 | 0.00160001772142446 |
103 | 0.999034142996767 | 0.00193171400646674 | 0.00096585700323337 |
104 | 0.999100768557726 | 0.00179846288454713 | 0.000899231442273564 |
105 | 0.999416247549957 | 0.00116750490008573 | 0.000583752450042867 |
106 | 0.99930175895634 | 0.00139648208731905 | 0.000698241043659525 |
107 | 0.999502777722284 | 0.000994444555431747 | 0.000497222277715874 |
108 | 1 | 1.14804331201647e-95 | 5.74021656008233e-96 |
109 | 1 | 1.77637738632269e-78 | 8.88188693161344e-79 |
110 | 1 | 3.24024151081195e-64 | 1.62012075540597e-64 |
111 | 1 | 1.38622839575486e-59 | 6.9311419787743e-60 |
112 | 1 | 4.68236943622658e-38 | 2.34118471811329e-38 |
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
Description | # significant tests | % significant tests | OK/NOK |
1% type I error level | 53 | 0.495327102803738 | NOK |
5% type I error level | 61 | 0.570093457943925 | NOK |
10% type I error level | 68 | 0.635514018691589 | NOK |