Multiple Linear Regression - Estimated Regression Equation |
belonging[t] = + 33.7628490052607 + 0.576297541832057popularity[t] + 0.478113214787677hapiness[t] -1.43366386194624gender[t] -0.413115473681592doubsaboutactions[t] + 0.180267632695104parentalexpectations[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) | 33.7628490052607 | 6.588503 | 5.1245 | 1e-06 | 0 |
popularity | 0.576297541832057 | 0.195775 | 2.9437 | 0.003811 | 0.001906 |
hapiness | 0.478113214787677 | 0.261714 | 1.8269 | 0.069898 | 0.034949 |
gender | -1.43366386194624 | 1.23424 | -1.1616 | 0.247428 | 0.123714 |
doubsaboutactions | -0.413115473681592 | 0.223849 | -1.8455 | 0.067122 | 0.033561 |
parentalexpectations | 0.180267632695104 | 0.172462 | 1.0453 | 0.297743 | 0.148872 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.417432508416781 |
R-squared | 0.174249899083126 |
Adjusted R-squared | 0.144113034086160 |
F-TEST (value) | 5.78195174251427 |
F-TEST (DF numerator) | 5 |
F-TEST (DF denominator) | 137 |
p-value | 7.09848962427984e-05 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 6.80662163087911 |
Sum Squared Residuals | 6347.22342955535 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 42 | 44.0042598762073 | -2.00425987620725 |
2 | 51 | 46.8367687387696 | 4.16323126123041 |
3 | 42 | 45.0386012280569 | -3.03860122805688 |
4 | 46 | 45.3923196194003 | 0.607680380599712 |
5 | 41 | 38.4149149725497 | 2.58508502745032 |
6 | 49 | 41.7778084974571 | 7.22219150254293 |
7 | 47 | 45.1934317758985 | 1.80656822410153 |
8 | 33 | 44.0386878499175 | -11.0386878499175 |
9 | 47 | 46.1327837725338 | 0.867216227466201 |
10 | 42 | 38.2152537175015 | 3.78474628249851 |
11 | 32 | 44.3480183377868 | -12.3480183377868 |
12 | 53 | 50.1655430507007 | 2.83445694929927 |
13 | 41 | 40.27577216656 | 0.724227833440006 |
14 | 41 | 44.9498786437781 | -3.9498786437781 |
15 | 33 | 42.0796463288628 | -9.0796463288628 |
16 | 37 | 40.4644889486936 | -3.46448894869356 |
17 | 43 | 44.0521720527685 | -1.05217205276850 |
18 | 33 | 37.7220240244711 | -4.72202402447114 |
19 | 49 | 46.6712786128107 | 2.32872138718934 |
20 | 42 | 44.6787417450835 | -2.67874174508349 |
21 | 43 | 38.7576888909785 | 4.24231110902155 |
22 | 37 | 36.4056013010121 | 0.59439869898794 |
23 | 43 | 46.5573322358791 | -3.55733223587911 |
24 | 42 | 41.9547835291927 | 0.0452164708072546 |
25 | 43 | 40.0991880224438 | 2.90081197755616 |
26 | 46 | 47.4532289560783 | -1.45322895607832 |
27 | 33 | 47.088753357488 | -14.088753357488 |
28 | 42 | 45.2142008290221 | -3.21420082902206 |
29 | 40 | 41.8204287759848 | -1.82042877598483 |
30 | 44 | 41.5325431236559 | 2.46745687634411 |
31 | 42 | 47.1507153422558 | -5.1507153422558 |
32 | 52 | 42.8239196498810 | 9.17608035011904 |
33 | 44 | 42.4466075806803 | 1.55339241931970 |
34 | 45 | 44.0032753330561 | 0.996724666943933 |
35 | 46 | 41.5419768162453 | 4.45802318375466 |
36 | 36 | 41.0738754473343 | -5.07387544733434 |
37 | 45 | 46.3291524266226 | -1.32915242662256 |
38 | 49 | 46.2755876751802 | 2.72441232481981 |
39 | 43 | 43.1462177736761 | -0.146217773676077 |
40 | 43 | 44.6153762793691 | -1.61537627936906 |
41 | 37 | 40.6048050375166 | -3.6048050375166 |
42 | 32 | 34.3959486579680 | -2.39594865796796 |
43 | 45 | 44.6458639198794 | 0.354136080120617 |
44 | 45 | 45.976109817696 | -0.97610981769596 |
45 | 45 | 45.4175455726492 | -0.417545572649211 |
46 | 45 | 42.0572969164606 | 2.94270308353941 |
47 | 31 | 43.067735829719 | -12.0677358297190 |
48 | 33 | 42.83154347166 | -9.83154347166001 |
49 | 44 | 43.7740288537632 | 0.225971146236796 |
50 | 49 | 36.2125771639958 | 12.7874228360042 |
51 | 44 | 41.6957771079194 | 2.30422289208061 |
52 | 41 | 38.0885508362488 | 2.91144916375125 |
53 | 44 | 42.0894470431349 | 1.91055295686515 |
54 | 38 | 42.6157811952182 | -4.61578119521817 |
55 | 33 | 42.4650166598824 | -9.4650166598824 |
56 | 47 | 43.6521737602553 | 3.34782623974469 |
57 | 37 | 39.3905869405912 | -2.39058694059117 |
58 | 48 | 45.9220284993284 | 2.07797150067163 |
59 | 40 | 40.4713674091024 | -0.471367409102381 |
60 | 50 | 44.5440782311414 | 5.45592176885862 |
61 | 54 | 48.179740930135 | 5.82025906986496 |
62 | 43 | 47.5296596868481 | -4.52965968684812 |
63 | 54 | 42.5919306727397 | 11.4080693272602 |
64 | 44 | 44.4871387518542 | -0.487138751854244 |
65 | 47 | 41.4846309470944 | 5.51536905290556 |
66 | 33 | 42.920346022228 | -9.92034602222798 |
67 | 45 | 46.7182062462211 | -1.71820624622112 |
68 | 33 | 34.3969332011189 | -1.39693320111894 |
69 | 44 | 45.5840202417591 | -1.58402024175911 |
70 | 47 | 44.9072303150742 | 2.09276968492577 |
71 | 45 | 40.320391742162 | 4.679608257838 |
72 | 43 | 41.782476529187 | 1.21752347081298 |
73 | 43 | 38.1449121622487 | 4.85508783775133 |
74 | 33 | 44.4236756570102 | -11.4236756570102 |
75 | 46 | 43.8551276162629 | 2.14487238373706 |
76 | 47 | 43.8937556454775 | 3.10624435452245 |
77 | 47 | 42.603024690897 | 4.39697530910302 |
78 | 0 | 40.8443202073073 | -40.8443202073073 |
79 | 43 | 43.9339183209542 | -0.933918320954231 |
80 | 46 | 42.5846458224672 | 3.41535417753283 |
81 | 36 | 37.6845083783094 | -1.68450837830939 |
82 | 42 | 38.7801182696698 | 3.21988173033017 |
83 | 44 | 43.3244341931839 | 0.675565806816119 |
84 | 47 | 47.3470839963446 | -0.347083996344561 |
85 | 41 | 39.5343753863885 | 1.46562461361146 |
86 | 47 | 44.4894468096627 | 2.51055319033731 |
87 | 46 | 45.0783730159141 | 0.921626984085934 |
88 | 47 | 47.2318141047555 | -0.231814104755542 |
89 | 46 | 47.0663239787966 | -1.06632397879663 |
90 | 46 | 44.2541932817382 | 1.74580671826182 |
91 | 36 | 44.9833220743376 | -8.98332207433755 |
92 | 30 | 40.2635041789879 | -10.2635041789879 |
93 | 48 | 42.3118464376086 | 5.68815356239138 |
94 | 45 | 40.786087424135 | 4.21391257586502 |
95 | 49 | 45.565611162557 | 3.43438883744299 |
96 | 55 | 47.1119280975496 | 7.88807190245038 |
97 | 11 | 41.2106358874803 | -30.2106358874803 |
98 | 52 | 45.8976278737389 | 6.10237212626114 |
99 | 33 | 35.8460503522182 | -2.84605035221816 |
100 | 47 | 48.4024792961153 | -1.40247929611528 |
101 | 33 | 39.5825444075711 | -6.58254440757113 |
102 | 44 | 44.4244490685566 | -0.424449068556609 |
103 | 42 | 40.4258609194790 | 1.57413908052104 |
104 | 55 | 42.8519735532771 | 12.1480264467229 |
105 | 42 | 44.2853286544892 | -2.28532865448918 |
106 | 46 | 44.9994230957312 | 1.0005769042688 |
107 | 46 | 46.9155594434609 | -0.915559443460863 |
108 | 47 | 45.5699704335528 | 1.43002956644724 |
109 | 33 | 43.4866317181834 | -10.4866317181834 |
110 | 53 | 49.7252325374682 | 3.27476746253175 |
111 | 42 | 42.2572971430153 | -0.257297143015258 |
112 | 44 | 44.0353952489580 | -0.0353952489580468 |
113 | 55 | 44.9434007412378 | 10.0565992587622 |
114 | 40 | 35.4674449791323 | 4.53255502086767 |
115 | 46 | 45.3200370280216 | 0.67996297197837 |
116 | 53 | 45.8805423091942 | 7.11945769080578 |
117 | 44 | 45.870432834188 | -1.87043283418797 |
118 | 35 | 40.6678336923207 | -5.66783369232071 |
119 | 40 | 39.7329699714004 | 0.267030028599579 |
120 | 44 | 45.0966228796246 | -1.09662287962459 |
121 | 46 | 46.7482594466916 | -0.748259446691554 |
122 | 45 | 42.4945197572417 | 2.50548024275826 |
123 | 53 | 45.1926583643521 | 7.8073416356479 |
124 | 45 | 43.5121944823426 | 1.48780551765740 |
125 | 48 | 42.7836312950986 | 5.21636870490143 |
126 | 46 | 44.4753970014563 | 1.52460299854366 |
127 | 55 | 41.7597081789892 | 13.2402918210108 |
128 | 47 | 49.7343574693235 | -2.73435746932351 |
129 | 43 | 42.6559438706948 | 0.344056129305151 |
130 | 38 | 38.0828982613678 | -0.0828982613678303 |
131 | 40 | 40.2315434785775 | -0.231543478577502 |
132 | 47 | 42.2529378720195 | 4.74706212798049 |
133 | 47 | 42.1068413684137 | 4.89315863158632 |
134 | 42 | 40.7197661683714 | 1.28023383162857 |
135 | 53 | 42.5732128328035 | 10.4267871671965 |
136 | 43 | 44.0521720527685 | -1.05217205276850 |
137 | 44 | 44.8536655636319 | -0.853665563631855 |
138 | 42 | 43.2926230380161 | -1.29262303801609 |
139 | 51 | 44.5581280393477 | 6.44187196065227 |
140 | 54 | 42.9524659381300 | 11.0475340618700 |
141 | 41 | 42.0995565181411 | -1.09955651814110 |
142 | 51 | 42.8128256317237 | 8.18717436827628 |
143 | 51 | 44.4987828731226 | 6.50121712687743 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
9 | 0.625479598830677 | 0.749040802338646 | 0.374520401169323 |
10 | 0.48978863462332 | 0.97957726924664 | 0.51021136537668 |
11 | 0.474338660514287 | 0.948677321028573 | 0.525661339485713 |
12 | 0.369242547572502 | 0.738485095145003 | 0.630757452427498 |
13 | 0.28139104572854 | 0.56278209145708 | 0.71860895427146 |
14 | 0.192075279610892 | 0.384150559221784 | 0.807924720389108 |
15 | 0.171661427117480 | 0.343322854234961 | 0.82833857288252 |
16 | 0.125844022450331 | 0.251688044900662 | 0.874155977549669 |
17 | 0.144721649968746 | 0.289443299937492 | 0.855278350031254 |
18 | 0.0983061725848849 | 0.196612345169770 | 0.901693827415115 |
19 | 0.114338625660729 | 0.228677251321458 | 0.88566137433927 |
20 | 0.100355345061709 | 0.200710690123417 | 0.899644654938291 |
21 | 0.117473136842153 | 0.234946273684305 | 0.882526863157847 |
22 | 0.0814774426745284 | 0.162954885349057 | 0.918522557325472 |
23 | 0.0626062325093802 | 0.125212465018760 | 0.93739376749062 |
24 | 0.0461221575759448 | 0.0922443151518895 | 0.953877842424055 |
25 | 0.0364422938838964 | 0.0728845877677928 | 0.963557706116104 |
26 | 0.0242733352926843 | 0.0485466705853686 | 0.975726664707316 |
27 | 0.0600328475122006 | 0.120065695024401 | 0.9399671524878 |
28 | 0.0465530033764704 | 0.0931060067529408 | 0.95344699662353 |
29 | 0.0322644290169215 | 0.064528858033843 | 0.967735570983078 |
30 | 0.021885400922732 | 0.043770801845464 | 0.978114599077268 |
31 | 0.0171853466829018 | 0.0343706933658037 | 0.982814653317098 |
32 | 0.0192589611838021 | 0.0385179223676043 | 0.980741038816198 |
33 | 0.0128339538011562 | 0.0256679076023124 | 0.987166046198844 |
34 | 0.00848461382060335 | 0.0169692276412067 | 0.991515386179397 |
35 | 0.00730537334364158 | 0.0146107466872832 | 0.992694626656358 |
36 | 0.00491177241641232 | 0.00982354483282465 | 0.995088227583588 |
37 | 0.0032527911652132 | 0.0065055823304264 | 0.996747208834787 |
38 | 0.00236295507723269 | 0.00472591015446538 | 0.997637044922767 |
39 | 0.00152424228584383 | 0.00304848457168765 | 0.998475757714156 |
40 | 0.000946264288637114 | 0.00189252857727423 | 0.999053735711363 |
41 | 0.000595651408963467 | 0.00119130281792693 | 0.999404348591037 |
42 | 0.000347862533781218 | 0.000695725067562437 | 0.999652137466219 |
43 | 0.000243585395748413 | 0.000487170791496826 | 0.999756414604252 |
44 | 0.000139895356023047 | 0.000279790712046094 | 0.999860104643977 |
45 | 7.86207430430635e-05 | 0.000157241486086127 | 0.999921379256957 |
46 | 9.93624592464402e-05 | 0.000198724918492880 | 0.999900637540754 |
47 | 0.000177055510202218 | 0.000354111020404435 | 0.999822944489798 |
48 | 0.000566704699634688 | 0.00113340939926938 | 0.999433295300365 |
49 | 0.000397170271791237 | 0.000794340543582473 | 0.999602829728209 |
50 | 0.0044244395442087 | 0.0088488790884174 | 0.995575560455791 |
51 | 0.00321309209460319 | 0.00642618418920638 | 0.996786907905397 |
52 | 0.00230252549001735 | 0.00460505098003470 | 0.997697474509983 |
53 | 0.00152203883988141 | 0.00304407767976283 | 0.998477961160119 |
54 | 0.00120395913717537 | 0.00240791827435075 | 0.998796040862825 |
55 | 0.00204356865281831 | 0.00408713730563662 | 0.997956431347182 |
56 | 0.00163860073497579 | 0.00327720146995158 | 0.998361399265024 |
57 | 0.00110806384769146 | 0.00221612769538293 | 0.998891936152309 |
58 | 0.000917739650250278 | 0.00183547930050056 | 0.99908226034975 |
59 | 0.000599281338231905 | 0.00119856267646381 | 0.999400718661768 |
60 | 0.000497624690026418 | 0.000995249380052836 | 0.999502375309974 |
61 | 0.000533329253905136 | 0.00106665850781027 | 0.999466670746095 |
62 | 0.000400558965733979 | 0.000801117931467958 | 0.999599441034266 |
63 | 0.00188341861353910 | 0.00376683722707821 | 0.998116581386461 |
64 | 0.00124204751161695 | 0.0024840950232339 | 0.998757952488383 |
65 | 0.00107889834091087 | 0.00215779668182175 | 0.99892110165909 |
66 | 0.00186592272656233 | 0.00373184545312467 | 0.998134077273438 |
67 | 0.00126569957793323 | 0.00253139915586647 | 0.998734300422067 |
68 | 0.000855590040042557 | 0.00171118008008511 | 0.999144409959957 |
69 | 0.00056457342228636 | 0.00112914684457272 | 0.999435426577714 |
70 | 0.000398911826995469 | 0.000797823653990937 | 0.999601088173005 |
71 | 0.00030133700853065 | 0.0006026740170613 | 0.99969866299147 |
72 | 0.000190551569050373 | 0.000381103138100746 | 0.99980944843095 |
73 | 0.000155192316221530 | 0.000310384632443060 | 0.999844807683778 |
74 | 0.000339927224344043 | 0.000679854448688086 | 0.999660072775656 |
75 | 0.000237952979395825 | 0.000475905958791649 | 0.999762047020604 |
76 | 0.000164171763506551 | 0.000328343527013102 | 0.999835828236493 |
77 | 0.000147613137363427 | 0.000295226274726853 | 0.999852386862637 |
78 | 0.895765879239366 | 0.208468241521267 | 0.104234120760634 |
79 | 0.871536685851211 | 0.256926628297578 | 0.128463314148789 |
80 | 0.849033315550944 | 0.301933368898112 | 0.150966684449056 |
81 | 0.832311290034144 | 0.335377419931711 | 0.167688709965856 |
82 | 0.804666708916257 | 0.390666582167485 | 0.195333291083743 |
83 | 0.768370056234955 | 0.463259887530089 | 0.231629943765045 |
84 | 0.730195616494612 | 0.539608767010776 | 0.269804383505388 |
85 | 0.687106366796466 | 0.625787266407068 | 0.312893633203534 |
86 | 0.660107309729117 | 0.679785380541767 | 0.339892690270883 |
87 | 0.638865525486242 | 0.722268949027517 | 0.361134474513758 |
88 | 0.591136008230444 | 0.817727983539111 | 0.408863991769556 |
89 | 0.549962971564927 | 0.900074056870145 | 0.450037028435073 |
90 | 0.518301177254985 | 0.96339764549003 | 0.481698822745015 |
91 | 0.587563984971085 | 0.82487203005783 | 0.412436015028915 |
92 | 0.662472876937075 | 0.675054246125851 | 0.337527123062925 |
93 | 0.643619335086792 | 0.712761329826415 | 0.356380664913208 |
94 | 0.621559295856643 | 0.756881408286714 | 0.378440704143357 |
95 | 0.579326705380457 | 0.841346589239085 | 0.420673294619543 |
96 | 0.584887752033363 | 0.830224495933274 | 0.415112247966637 |
97 | 0.998529304112251 | 0.00294139177549745 | 0.00147069588774873 |
98 | 0.998021377107474 | 0.00395724578505237 | 0.00197862289252619 |
99 | 0.998517000651073 | 0.00296599869785316 | 0.00148299934892658 |
100 | 0.998283791478668 | 0.00343241704266308 | 0.00171620852133154 |
101 | 0.99885410165978 | 0.00229179668043973 | 0.00114589834021987 |
102 | 0.998129210647506 | 0.00374157870498806 | 0.00187078935249403 |
103 | 0.99726721218381 | 0.00546557563237986 | 0.00273278781618993 |
104 | 0.998413010877918 | 0.00317397824416377 | 0.00158698912208188 |
105 | 0.998393982653714 | 0.00321203469257201 | 0.00160601734628601 |
106 | 0.997364296080438 | 0.00527140783912368 | 0.00263570391956184 |
107 | 0.99616526112611 | 0.00766947774778048 | 0.00383473887389024 |
108 | 0.994058855097942 | 0.0118822898041155 | 0.00594114490205773 |
109 | 0.997546025614996 | 0.00490794877000809 | 0.00245397438500404 |
110 | 0.996153821946647 | 0.00769235610670508 | 0.00384617805335254 |
111 | 0.994132555303736 | 0.0117348893925270 | 0.00586744469626352 |
112 | 0.992105286486273 | 0.0157894270274544 | 0.0078947135137272 |
113 | 0.993234058281636 | 0.0135318834367274 | 0.00676594171836368 |
114 | 0.99076594005831 | 0.0184681198833785 | 0.00923405994168925 |
115 | 0.985298988740902 | 0.0294020225181955 | 0.0147010112590977 |
116 | 0.980537996974147 | 0.0389240060517069 | 0.0194620030258534 |
117 | 0.985886636101466 | 0.0282267277970688 | 0.0141133638985344 |
118 | 0.988752618193024 | 0.0224947636139524 | 0.0112473818069762 |
119 | 0.994915974257321 | 0.0101680514853573 | 0.00508402574267863 |
120 | 0.990966249035018 | 0.0180675019299635 | 0.00903375096498175 |
121 | 0.989187878645253 | 0.0216242427094938 | 0.0108121213547469 |
122 | 0.993758473418765 | 0.0124830531624707 | 0.00624152658123534 |
123 | 0.99378960246765 | 0.0124207950646997 | 0.00621039753234983 |
124 | 0.991870673756406 | 0.0162586524871871 | 0.00812932624359357 |
125 | 0.985117712902062 | 0.0297645741958761 | 0.0148822870979380 |
126 | 0.972965053553615 | 0.0540698928927708 | 0.0270349464463854 |
127 | 0.957188567054805 | 0.0856228658903897 | 0.0428114329451948 |
128 | 0.961471489415025 | 0.0770570211699497 | 0.0385285105849748 |
129 | 0.983176279830487 | 0.0336474403390265 | 0.0168237201695132 |
130 | 0.971796168726139 | 0.0564076625477226 | 0.0282038312738613 |
131 | 0.95039050098662 | 0.0992189980267622 | 0.0496094990133811 |
132 | 0.906213123271643 | 0.187573753456715 | 0.0937868767283573 |
133 | 0.846983848070659 | 0.306032303858682 | 0.153016151929341 |
134 | 0.728984590377958 | 0.542030819244083 | 0.271015409622042 |
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
Description | # significant tests | % significant tests | OK/NOK |
1% type I error level | 55 | 0.436507936507937 | NOK |
5% type I error level | 79 | 0.626984126984127 | NOK |
10% type I error level | 88 | 0.698412698412698 | NOK |