Multiple Linear Regression - Estimated Regression Equation |
Depression[t] = + 7.49200704176759 + 0.0408955674052273CriticParents[t] -0.0669085142751476ExpecParents[t] + 0.586756102445572FutureWorrying[t] + 0.202166740732203SleepDepri[t] + 0.35634657786847ChangesLastYear[t] -0.121340486208485FreqSmoking[t] + 0.264713129723179FreqHighAlc[t] + 0.292590037590936FreqBeerOrWine[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) | 7.49200704176759 | 1.445238 | 5.1839 | 1e-06 | 0 |
CriticParents | 0.0408955674052273 | 0.115754 | 0.3533 | 0.724412 | 0.362206 |
ExpecParents | -0.0669085142751476 | 0.086583 | -0.7728 | 0.441 | 0.2205 |
FutureWorrying | 0.586756102445572 | 0.168257 | 3.4873 | 0.000658 | 0.000329 |
SleepDepri | 0.202166740732203 | 0.141208 | 1.4317 | 0.154525 | 0.077263 |
ChangesLastYear | 0.35634657786847 | 0.134922 | 2.6411 | 0.00923 | 0.004615 |
FreqSmoking | -0.121340486208485 | 0.273487 | -0.4437 | 0.65798 | 0.32899 |
FreqHighAlc | 0.264713129723179 | 0.314605 | 0.8414 | 0.401593 | 0.200796 |
FreqBeerOrWine | 0.292590037590936 | 0.278532 | 1.0505 | 0.295364 | 0.147682 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.453459545887258 |
R-squared | 0.205625559756278 |
Adjusted R-squared | 0.158897651506647 |
F-TEST (value) | 4.40048714908833 |
F-TEST (DF numerator) | 8 |
F-TEST (DF denominator) | 136 |
p-value | 9.38949108088005e-05 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 2.89966249185119 |
Sum Squared Residuals | 1143.49378906421 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 12 | 12.0805628449277 | -0.0805628449276666 |
2 | 11 | 11.9235069029631 | -0.923506902963089 |
3 | 14 | 15.4094415553154 | -1.40944155531539 |
4 | 12 | 11.8717505874073 | 0.128249412592660 |
5 | 21 | 16.1618309539449 | 4.8381690460551 |
6 | 12 | 13.4046617162138 | -1.40466171621376 |
7 | 22 | 15.2081173527299 | 6.7918826472701 |
8 | 11 | 13.294824974175 | -2.29482497417500 |
9 | 10 | 12.3079978875984 | -2.30799788759839 |
10 | 13 | 12.9732583214999 | 0.0267416785001346 |
11 | 10 | 13.7575717009992 | -3.75757170099921 |
12 | 8 | 12.2979245276434 | -4.29792452764335 |
13 | 15 | 14.4334547170335 | 0.566545282966519 |
14 | 10 | 12.2059971291089 | -2.20599712910895 |
15 | 14 | 12.8443840645661 | 1.15561593543394 |
16 | 14 | 10.3953785832469 | 3.6046214167531 |
17 | 11 | 12.9877181789441 | -1.98771817894410 |
18 | 10 | 12.9894302733557 | -2.98943027335566 |
19 | 13 | 14.5340560419106 | -1.53405604191056 |
20 | 7 | 10.8530854073948 | -3.85308540739482 |
21 | 12 | 13.9630218499075 | -1.96302184990746 |
22 | 14 | 12.9522890770089 | 1.04771092299107 |
23 | 11 | 12.3766356140442 | -1.37663561404422 |
24 | 9 | 11.4521237868814 | -2.45212378688137 |
25 | 11 | 12.1626005016107 | -1.16260050161066 |
26 | 15 | 13.5686730374838 | 1.43132696251624 |
27 | 13 | 13.1981328501974 | -0.198132850197392 |
28 | 9 | 9.75538643577493 | -0.755386435774928 |
29 | 15 | 10.1914291408358 | 4.80857085916418 |
30 | 10 | 12.7560557753254 | -2.75605577532537 |
31 | 11 | 10.9237436646135 | 0.0762563353865289 |
32 | 13 | 11.5712805745575 | 1.42871942544252 |
33 | 8 | 10.6086037247257 | -2.60860372472569 |
34 | 20 | 13.8397031042181 | 6.16029689578191 |
35 | 12 | 13.1994426294348 | -1.19944262943476 |
36 | 10 | 10.4759398798182 | -0.475939879818229 |
37 | 10 | 12.3306278138505 | -2.33062781385050 |
38 | 9 | 12.7449262774030 | -3.74492627740305 |
39 | 14 | 14.8647940804501 | -0.86479408045014 |
40 | 8 | 11.0725370447259 | -3.07253704472590 |
41 | 14 | 12.0841375820163 | 1.91586241798366 |
42 | 11 | 12.567986413666 | -1.56798641366600 |
43 | 13 | 11.3638646923948 | 1.63613530760518 |
44 | 11 | 12.1122347878330 | -1.11223478783297 |
45 | 11 | 11.9822838799943 | -0.98228387999426 |
46 | 10 | 12.1329437878707 | -2.13294378787075 |
47 | 14 | 10.5942401650745 | 3.40575983492549 |
48 | 18 | 13.7919802888337 | 4.20801971116633 |
49 | 14 | 12.5897259261661 | 1.41027407383393 |
50 | 11 | 13.1558663500304 | -2.15586635003041 |
51 | 12 | 11.2391194193309 | 0.760880580669071 |
52 | 13 | 13.1832502296621 | -0.183250229662084 |
53 | 9 | 13.9792753460670 | -4.97927534606705 |
54 | 10 | 12.3104228182865 | -2.31042281828649 |
55 | 15 | 13.6370164586804 | 1.36298354131957 |
56 | 20 | 14.1001976074003 | 5.89980239259967 |
57 | 12 | 11.7034382372401 | 0.296561762759900 |
58 | 12 | 12.1199054413807 | -0.119905441380711 |
59 | 14 | 11.2514782680112 | 2.74852173198882 |
60 | 13 | 14.9218163051899 | -1.92181630518988 |
61 | 11 | 14.2759504044091 | -3.27595040440913 |
62 | 17 | 13.3148035357248 | 3.68519646427524 |
63 | 12 | 12.1222701077126 | -0.122270107712629 |
64 | 13 | 12.8439185606381 | 0.156081439361885 |
65 | 14 | 13.8406243973194 | 0.159375602680603 |
66 | 13 | 10.6938870864331 | 2.30611291356686 |
67 | 15 | 13.9834842709352 | 1.0165157290648 |
68 | 13 | 11.8926064789396 | 1.10739352106036 |
69 | 10 | 13.6050017195018 | -3.60500171950182 |
70 | 11 | 11.2954337208940 | -0.295433720893954 |
71 | 13 | 12.8333059768669 | 0.166694023133087 |
72 | 17 | 14.1334685636616 | 2.86653143633839 |
73 | 13 | 12.9456518202285 | 0.0543481797715108 |
74 | 9 | 11.8461956050346 | -2.84619560503464 |
75 | 11 | 12.3572945704317 | -1.35729457043169 |
76 | 10 | 10.0936373227236 | -0.0936373227235615 |
77 | 9 | 10.1996736606694 | -1.19967366066936 |
78 | 12 | 11.4549756820502 | 0.545024317949755 |
79 | 12 | 12.4198409594227 | -0.419840959422669 |
80 | 13 | 12.2797551037535 | 0.720244896246507 |
81 | 13 | 12.3625035198552 | 0.637496480144759 |
82 | 22 | 14.6489865961670 | 7.35101340383298 |
83 | 13 | 11.9956888503439 | 1.00431114965606 |
84 | 15 | 13.6658398757758 | 1.33416012422415 |
85 | 13 | 14.1858042120834 | -1.18580421208342 |
86 | 15 | 11.6401309115437 | 3.35986908845631 |
87 | 10 | 11.6114389131177 | -1.61143891311767 |
88 | 11 | 10.7890994809401 | 0.210900519059895 |
89 | 16 | 14.1353082071647 | 1.86469179283533 |
90 | 11 | 11.8993022808498 | -0.899302280849812 |
91 | 11 | 12.2999647274325 | -1.29996472743248 |
92 | 10 | 12.5555985598113 | -2.55559855981128 |
93 | 10 | 14.5203082518953 | -4.52030825189527 |
94 | 16 | 14.0418752920142 | 1.9581247079858 |
95 | 12 | 13.3111487926171 | -1.31114879261707 |
96 | 11 | 13.6768538243424 | -2.67685382434239 |
97 | 16 | 14.3149648204109 | 1.68503517958910 |
98 | 19 | 14.861638711274 | 4.13836128872598 |
99 | 11 | 14.8795757571412 | -3.87957575714115 |
100 | 15 | 12.521063908045 | 2.47893609195499 |
101 | 24 | 16.3214780755001 | 7.67852192449986 |
102 | 14 | 11.5119024489110 | 2.48809755108905 |
103 | 15 | 13.4467301542144 | 1.5532698457856 |
104 | 11 | 14.7404744662841 | -3.74047446628405 |
105 | 15 | 13.2298164507161 | 1.77018354928388 |
106 | 12 | 12.7913012044466 | -0.791301204446649 |
107 | 10 | 10.6950402700760 | -0.695040270075978 |
108 | 14 | 13.6430495931279 | 0.356950406872131 |
109 | 9 | 12.7424535712216 | -3.74245357122163 |
110 | 15 | 10.4692068230364 | 4.53079317696355 |
111 | 15 | 9.68420656641496 | 5.31579343358504 |
112 | 14 | 12.8453686162963 | 1.15463138370367 |
113 | 11 | 14.0815179803778 | -3.0815179803778 |
114 | 8 | 14.2146627734475 | -6.21466277344749 |
115 | 11 | 14.1080885041867 | -3.10808850418670 |
116 | 8 | 11.6187647066161 | -3.61876470661612 |
117 | 10 | 11.2876993236633 | -1.28769932366329 |
118 | 11 | 13.4296441481942 | -2.42964414819416 |
119 | 13 | 13.9924275035589 | -0.992427503558935 |
120 | 11 | 13.6864081234133 | -2.6864081234133 |
121 | 20 | 12.6859973663376 | 7.31400263366237 |
122 | 10 | 12.0897220832703 | -2.08972208327026 |
123 | 12 | 10.7450502790942 | 1.25494972090576 |
124 | 14 | 12.4057624221899 | 1.59423757781014 |
125 | 23 | 13.7439933852377 | 9.25600661476226 |
126 | 14 | 12.6418698839366 | 1.35813011606345 |
127 | 16 | 15.0988549553836 | 0.901145044616358 |
128 | 11 | 13.2935633971562 | -2.29356339715624 |
129 | 12 | 13.9791757181162 | -1.97917571811624 |
130 | 10 | 13.5188769807189 | -3.51887698071890 |
131 | 14 | 13.7236415136882 | 0.276358486311758 |
132 | 12 | 9.64600343102413 | 2.35399656897587 |
133 | 12 | 13.4775159069585 | -1.47751590695849 |
134 | 11 | 10.0239195735866 | 0.97608042641338 |
135 | 12 | 12.2535525196977 | -0.253552519697721 |
136 | 13 | 15.6147192027332 | -2.61471920273317 |
137 | 17 | 16.2518729175104 | 0.748127082489616 |
138 | 11 | 12.1626005016107 | -1.16260050161066 |
139 | 12 | 13.5154478216585 | -1.51544782165847 |
140 | 19 | 14.9582927796672 | 4.04170722033279 |
141 | 15 | 13.6658398757758 | 1.33416012422415 |
142 | 14 | 13.3077033417826 | 0.692296658217409 |
143 | 11 | 13.4296441481942 | -2.42964414819416 |
144 | 9 | 10.4591886130326 | -1.45918861303263 |
145 | 18 | 11.6539904487848 | 6.34600955121516 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
12 | 0.192625916249130 | 0.385251832498259 | 0.80737408375087 |
13 | 0.299178553490283 | 0.598357106980566 | 0.700821446509717 |
14 | 0.455826015851385 | 0.91165203170277 | 0.544173984148615 |
15 | 0.400852228842388 | 0.801704457684777 | 0.599147771157612 |
16 | 0.553425921034396 | 0.893148157931209 | 0.446574078965604 |
17 | 0.469288556542059 | 0.938577113084117 | 0.530711443457941 |
18 | 0.383439008529484 | 0.766878017058968 | 0.616560991470516 |
19 | 0.4899877617262 | 0.9799755234524 | 0.5100122382738 |
20 | 0.419335969986465 | 0.83867193997293 | 0.580664030013535 |
21 | 0.352317848399479 | 0.704635696798958 | 0.647682151600521 |
22 | 0.398227228468739 | 0.796454456937478 | 0.601772771531261 |
23 | 0.444379302368579 | 0.888758604737159 | 0.555620697631421 |
24 | 0.372311506143255 | 0.74462301228651 | 0.627688493856745 |
25 | 0.315646327630738 | 0.631292655261475 | 0.684353672369262 |
26 | 0.274395939183484 | 0.548791878366967 | 0.725604060816516 |
27 | 0.224567112903166 | 0.449134225806332 | 0.775432887096834 |
28 | 0.189364914144113 | 0.378729828288226 | 0.810635085855887 |
29 | 0.247970962540508 | 0.495941925081016 | 0.752029037459492 |
30 | 0.207940257680449 | 0.415880515360899 | 0.79205974231955 |
31 | 0.170976250671609 | 0.341952501343218 | 0.829023749328391 |
32 | 0.134191744151734 | 0.268383488303468 | 0.865808255848266 |
33 | 0.129331584603051 | 0.258663169206103 | 0.870668415396949 |
34 | 0.146633033695004 | 0.293266067390009 | 0.853366966304996 |
35 | 0.149075587878985 | 0.298151175757969 | 0.850924412121015 |
36 | 0.154133783813512 | 0.308267567627025 | 0.845866216186488 |
37 | 0.194418374656501 | 0.388836749313002 | 0.805581625343499 |
38 | 0.246768149425659 | 0.493536298851319 | 0.753231850574341 |
39 | 0.270391572681662 | 0.540783145363325 | 0.729608427318338 |
40 | 0.263992609285095 | 0.527985218570191 | 0.736007390714905 |
41 | 0.275657559902065 | 0.551315119804131 | 0.724342440097935 |
42 | 0.244713460056936 | 0.489426920113873 | 0.755286539943063 |
43 | 0.243974473846869 | 0.487948947693739 | 0.75602552615313 |
44 | 0.208068438071616 | 0.416136876143232 | 0.791931561928384 |
45 | 0.173129524740868 | 0.346259049481737 | 0.826870475259132 |
46 | 0.151648813618584 | 0.303297627237167 | 0.848351186381416 |
47 | 0.158384637576189 | 0.316769275152377 | 0.841615362423811 |
48 | 0.259057983066465 | 0.51811596613293 | 0.740942016933535 |
49 | 0.242975783342214 | 0.485951566684428 | 0.757024216657786 |
50 | 0.214840901206893 | 0.429681802413787 | 0.785159098793107 |
51 | 0.181694415122013 | 0.363388830244026 | 0.818305584877987 |
52 | 0.148298621153626 | 0.296597242307251 | 0.851701378846374 |
53 | 0.212102965186804 | 0.424205930373608 | 0.787897034813196 |
54 | 0.204643313695715 | 0.40928662739143 | 0.795356686304285 |
55 | 0.187205652683021 | 0.374411305366043 | 0.812794347316979 |
56 | 0.279810922584899 | 0.559621845169799 | 0.7201890774151 |
57 | 0.241402248401640 | 0.482804496803280 | 0.75859775159836 |
58 | 0.209239621770775 | 0.418479243541549 | 0.790760378229225 |
59 | 0.195127117735141 | 0.390254235470281 | 0.80487288226486 |
60 | 0.208596030124509 | 0.417192060249017 | 0.791403969875491 |
61 | 0.259587648450418 | 0.519175296900837 | 0.740412351549582 |
62 | 0.297408185294235 | 0.59481637058847 | 0.702591814705765 |
63 | 0.255341430577098 | 0.510682861154195 | 0.744658569422902 |
64 | 0.216811313463058 | 0.433622626926116 | 0.783188686536942 |
65 | 0.18277089627203 | 0.36554179254406 | 0.81722910372797 |
66 | 0.170406673849962 | 0.340813347699924 | 0.829593326150038 |
67 | 0.146233525047382 | 0.292467050094764 | 0.853766474952618 |
68 | 0.122440494408183 | 0.244880988816366 | 0.877559505591817 |
69 | 0.131407143055225 | 0.262814286110451 | 0.868592856944775 |
70 | 0.106506882616367 | 0.213013765232734 | 0.893493117383633 |
71 | 0.0852151160175108 | 0.170430232035022 | 0.914784883982489 |
72 | 0.091578288854766 | 0.183156577709532 | 0.908421711145234 |
73 | 0.0726656465614145 | 0.145331293122829 | 0.927334353438586 |
74 | 0.0729803783849186 | 0.145960756769837 | 0.927019621615081 |
75 | 0.0602030234768755 | 0.120406046953751 | 0.939796976523125 |
76 | 0.0482657480817911 | 0.0965314961635822 | 0.95173425191821 |
77 | 0.0419288928221853 | 0.0838577856443705 | 0.958071107177815 |
78 | 0.0323428614940421 | 0.0646857229880843 | 0.967657138505958 |
79 | 0.0245612606367160 | 0.0491225212734321 | 0.975438739363284 |
80 | 0.0187288099665433 | 0.0374576199330867 | 0.981271190033457 |
81 | 0.0145848119417764 | 0.0291696238835528 | 0.985415188058224 |
82 | 0.0772304576769332 | 0.154460915353866 | 0.922769542323067 |
83 | 0.0617937855269883 | 0.123587571053977 | 0.938206214473012 |
84 | 0.0495823656109909 | 0.0991647312219817 | 0.95041763438901 |
85 | 0.0395100603219933 | 0.0790201206439866 | 0.960489939678007 |
86 | 0.04045340023924 | 0.08090680047848 | 0.95954659976076 |
87 | 0.0338060264302043 | 0.0676120528604086 | 0.966193973569796 |
88 | 0.0252906708935400 | 0.0505813417870801 | 0.97470932910646 |
89 | 0.0218443626254198 | 0.0436887252508397 | 0.97815563737458 |
90 | 0.0171102176003264 | 0.0342204352006528 | 0.982889782399674 |
91 | 0.0140076239375292 | 0.0280152478750584 | 0.98599237606247 |
92 | 0.0135403407510975 | 0.0270806815021949 | 0.986459659248903 |
93 | 0.0194307227263764 | 0.0388614454527527 | 0.980569277273624 |
94 | 0.0156493628519552 | 0.0312987257039105 | 0.984350637148045 |
95 | 0.0122548017796604 | 0.0245096035593208 | 0.98774519822034 |
96 | 0.0127884572841935 | 0.0255769145683871 | 0.987211542715806 |
97 | 0.0113122322928564 | 0.0226244645857128 | 0.988687767707144 |
98 | 0.0178957000494474 | 0.0357914000988949 | 0.982104299950552 |
99 | 0.020217840215409 | 0.040435680430818 | 0.97978215978459 |
100 | 0.0166235193367434 | 0.0332470386734867 | 0.983376480663257 |
101 | 0.0826466351110462 | 0.165293270222092 | 0.917353364888954 |
102 | 0.0756485408084938 | 0.151297081616988 | 0.924351459191506 |
103 | 0.062039208968117 | 0.124078417936234 | 0.937960791031883 |
104 | 0.0622281130500313 | 0.124456226100063 | 0.937771886949969 |
105 | 0.0508474192411014 | 0.101694838482203 | 0.949152580758899 |
106 | 0.039148867812884 | 0.078297735625768 | 0.960851132187116 |
107 | 0.0333396281963746 | 0.0666792563927491 | 0.966660371803626 |
108 | 0.0240155174551972 | 0.0480310349103945 | 0.975984482544803 |
109 | 0.0223247641607205 | 0.0446495283214409 | 0.97767523583928 |
110 | 0.0323414694254969 | 0.0646829388509938 | 0.967658530574503 |
111 | 0.0432307964816776 | 0.0864615929633552 | 0.956769203518322 |
112 | 0.0323370129829684 | 0.0646740259659367 | 0.967662987017032 |
113 | 0.0316426459996855 | 0.063285291999371 | 0.968357354000315 |
114 | 0.0582824833704015 | 0.116564966740803 | 0.941717516629599 |
115 | 0.0600374629431044 | 0.120074925886209 | 0.939962537056896 |
116 | 0.0950809153277885 | 0.190161830655577 | 0.904919084672211 |
117 | 0.0732660571948747 | 0.146532114389749 | 0.926733942805125 |
118 | 0.0608945966588741 | 0.121789193317748 | 0.939105403341126 |
119 | 0.0442052588804292 | 0.0884105177608583 | 0.95579474111957 |
120 | 0.0532328954116544 | 0.106465790823309 | 0.946767104588346 |
121 | 0.217780961705628 | 0.435561923411257 | 0.782219038294372 |
122 | 0.244419201412835 | 0.488838402825671 | 0.755580798587165 |
123 | 0.189846551377590 | 0.379693102755179 | 0.81015344862241 |
124 | 0.166034303938112 | 0.332068607876225 | 0.833965696061888 |
125 | 0.581131900378031 | 0.837736199243938 | 0.418868099621969 |
126 | 0.865921123766255 | 0.26815775246749 | 0.134078876233745 |
127 | 0.8580350864207 | 0.283929827158601 | 0.141964913579301 |
128 | 0.795145551723492 | 0.409708896553017 | 0.204854448276508 |
129 | 0.732768894656602 | 0.534462210686795 | 0.267231105343398 |
130 | 0.71097626261815 | 0.578047474763699 | 0.289023737381849 |
131 | 0.706498922170355 | 0.587002155659291 | 0.293501077829645 |
132 | 0.613284437896728 | 0.773431124206545 | 0.386715562103272 |
133 | 0.779367601863615 | 0.441264796272769 | 0.220632398136385 |
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 | 17 | 0.139344262295082 | NOK |
10% type I error level | 32 | 0.262295081967213 | NOK |