Multiple Linear Regression - Estimated Regression Equation

Belonging[t] = + 56.1224985935191 + 1.31579631412692Happiness[t] -0.670539009034875Age[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)	56.1224985935191	6.345014	8.8451	0	0
Happiness	1.31579631412692	0.347687	3.7844	0.000218	0.000109
Age	-0.670539009034875	0.700296	-0.9575	0.339764	0.169882

Multiple Linear Regression - Regression Statistics
Multiple R	0.294702194149267
R-squared	0.0868493832363925
Adjusted R-squared	0.0753632119563472
F-TEST (value)	7.56121261984606
F-TEST (DF numerator)	2
F-TEST (DF denominator)	159
p-value	0.000729662680479581
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	10.3113450175692
Sum Squared Residuals	16905.4899353446

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	53	69.849873928052	-16.849873928052
2	86	76.4541372026293	9.5458627973707
3	66	67.2435630037409	-1.24356300374086
4	67	68.5593593178678	-1.55935931786778
5	76	71.8109275472708	4.18907245272917
6	78	75.7835981935944	2.21640180640558
7	53	71.1909519461216	-18.1909519461216
8	80	70.5204129370867	9.47958706291326
9	74	72.5067482602485	1.49325173975146
10	76	73.1772872692834	2.82271273071659
11	79	74.4678018794675	4.5321981205325
12	54	77.7699335167562	-23.7699335167562
13	67	65.9277666896139	1.07223331038606
14	54	73.1520055653406	-19.1520055653406
15	87	75.1130591845595	11.8869408154405
16	58	70.5204129370867	-12.5204129370867
17	75	69.8498739280519	5.15012607194813
18	88	74.4678018794675	13.5321981205325
19	64	69.179334919017	-5.17933491901699
20	57	72.4814665563057	-15.4814665563057
21	66	76.4541372026293	-10.4541372026293
22	68	67.2435630037409	0.75643699625914
23	54	69.8498739280519	-15.8498739280519
24	56	67.218281299798	-11.218281299798
25	86	75.1383408885024	10.8616591114976
26	80	65.2825093845219	14.7174906154781
27	76	70.4698495292011	5.53015047079892
28	69	70.5204129370867	-1.52041293708674
29	78	72.5067482602485	5.49325173975146
30	67	67.2435630037409	-0.24356300374086
31	80	73.8225445743755	6.17745542562454
32	54	69.8751556319947	-15.8751556319947
33	71	74.4678018794675	-3.4678018794675
34	84	72.5067482602485	11.4932517397515
35	74	71.1909519461216	2.80904805387838
36	71	73.8225445743755	-2.82254457437546
37	63	64.611970375487	-1.61197037548702
38	71	72.5067482602485	-1.50674826024854
39	76	75.1383408885024	0.861659111497621
40	69	69.8751556319947	-0.875155631994699
41	74	72.5067482602485	1.49325173975146
42	75	72.4814665563057	2.51853344369429
43	54	73.8225445743755	-19.8225445743755
44	52	67.8888203088329	-15.8888203088329
45	69	67.218281299798	1.78171870020197
46	68	65.9024849856711	2.09751501432889
47	65	72.5067482602485	-7.50674826024854
48	75	72.5067482602485	2.49325173975146
49	74	75.8088798975373	-1.80887989753725
50	75	69.8751556319947	5.1248443680053
51	72	74.4930835834103	-2.49308358341033
52	67	71.1909519461216	-4.19095194612162
53	63	67.2435630037409	-4.24356300374086
54	62	67.218281299798	-5.21828129979803
55	63	68.5593593178678	-5.55935931786778
56	76	72.5067482602485	3.49325173975146
57	74	73.1520055653406	0.847994434659416
58	67	73.1772872692834	-6.17728726928341
59	73	67.8888203088329	5.1111796911671
60	70	67.8888203088329	2.1111796911671
61	53	63.2961740613601	-10.2961740613601
62	77	68.5340776139249	8.46592238607505
63	77	66.573023994706	10.426976005294
64	52	69.179334919017	-17.179334919017
65	54	71.1656702421788	-17.1656702421788
66	80	65.9277666896139	14.0722333103861
67	66	66.573023994706	-0.573023994705984
68	73	67.8888203088329	5.1111796911671
69	63	72.5067482602485	-9.50674826024854
70	69	72.5067482602485	-3.50674826024854
71	67	71.1909519461216	-4.19095194612162
72	54	73.8225445743755	-19.8225445743755
73	81	73.1772872692834	7.82271273071659
74	69	71.8362092512137	-2.83620925121366
75	84	69.2046166229598	14.7953833770402
76	80	67.8888203088329	12.1111796911671
77	70	74.4678018794675	-4.4678018794675
78	69	68.5340776139249	0.465922386075051
79	77	72.5067482602485	4.49325173975146
80	54	68.5340776139249	-14.5340776139249
81	79	71.8362092512137	7.16379074878634
82	30	73.8225445743755	-43.8225445743755
83	71	72.5067482602485	-1.50674826024854
84	73	74.4930835834103	-1.49308358341033
85	72	70.4951312331439	1.50486876685609
86	77	69.179334919017	7.82066508098301
87	75	72.5067482602485	2.49325173975146
88	69	71.1909519461216	-2.19095194612162
89	54	69.2046166229598	-15.2046166229598
90	70	62.6509167562681	7.34908324373195
91	73	75.1383408885024	-2.13834088850238
92	54	69.8751556319947	-15.8751556319947
93	77	72.5067482602485	4.49325173975146
94	82	71.1909519461216	10.8090480538784
95	80	69.2046166229598	10.7953833770402
96	80	73.1520055653406	6.84799443465942
97	69	68.5593593178678	0.44064068213222
98	78	70.5204129370867	7.47958706291326
99	81	75.1383408885024	5.86165911149762
100	76	71.1656702421788	4.83432975782121
101	76	75.1383408885024	0.861659111497621
102	73	67.8888203088329	5.1111796911671
103	85	73.1520055653406	11.8479944346594
104	66	66.573023994706	-0.573023994705984
105	79	73.1772872692834	5.82271273071659
106	68	64.611970375487	3.38802962451298
107	76	73.8225445743755	2.17745542562454
108	71	71.1656702421788	-0.165670242178789
109	54	65.2572276805791	-11.2572276805791
110	46	63.2456106534744	-17.2456106534744
111	82	71.8362092512137	10.1637907487863
112	74	66.573023994706	7.42697600529402
113	88	69.8751556319947	18.1248443680053
114	38	70.5204129370867	-32.5204129370867
115	76	76.4541372026293	-0.454137202629298
116	86	71.8109275472708	14.1890724527292
117	54	69.8498739280519	-15.8498739280519
118	70	71.1909519461216	-1.19095194612162
119	69	69.8498739280519	-0.849873928051869
120	90	70.5204129370867	19.4795870629133
121	54	67.8888203088329	-13.8888203088329
122	76	68.5087959099821	7.49120409001788
123	89	71.1656702421788	17.8343297578212
124	76	71.8362092512137	4.16379074878634
125	73	72.5067482602485	0.493251739751461
126	79	69.8751556319947	9.1248443680053
127	90	74.4678018794675	15.5321981205325
128	74	74.4678018794675	-0.467801879467504
129	81	76.4288554986865	4.57114450131353
130	72	72.5067482602485	-0.506748260248539
131	71	69.8751556319947	1.1248443680053
132	66	64.611970375487	1.38802962451298
133	77	71.8362092512137	5.16379074878634
134	65	73.1772872692834	-8.17728726928341
135	74	72.5067482602485	1.49325173975146
136	82	72.4814665563057	9.51853344369429
137	54	67.2435630037409	-13.2435630037409
138	63	69.8498739280519	-6.84987392805187
139	54	65.9024849856711	-11.9024849856711
140	64	71.8362092512137	-7.83620925121366
141	69	69.8751556319947	-0.875155631994699
142	54	70.4951312331439	-16.4951312331439
143	84	73.8225445743755	10.1774554256245
144	86	71.1909519461216	14.8090480538784
145	77	72.5067482602485	4.49325173975146
146	89	73.1520055653406	15.8479944346594
147	76	74.4930835834103	1.50691641658967
148	60	67.2435630037409	-7.24356300374086
149	75	68.5593593178678	6.44064068213222
150	73	63.2708923574173	9.72910764258273
151	85	73.1520055653406	11.8479944346594
152	79	68.5340776139249	10.4659223860751
153	71	70.4698495292011	0.530150470798918
154	72	67.8888203088329	4.1111796911671
155	69	62.6003533483824	6.39964665161761
156	78	70.5456946410296	7.45430535897042
157	54	69.8751556319947	-15.8751556319947
158	69	70.5204129370867	-1.52041293708674
159	81	76.4288554986865	4.57114450131353
160	84	68.5340776139249	15.4659223860751
161	84	67.8888203088329	16.1111796911671
162	69	69.2046166229598	-0.204616622959824

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
6	0.463889847094619	0.927779694189238	0.536110152905381
7	0.694461309841551	0.611077380316898	0.305538690158449
8	0.731314931849527	0.537370136300947	0.268685068150473
9	0.620741403243298	0.758517193513405	0.379258596756702
10	0.506643065316439	0.986713869367122	0.493356934683561
11	0.399710617156733	0.799421234313467	0.600289382843267
12	0.817412389388014	0.365175221223972	0.182587610611986
13	0.753000373811774	0.493999252376452	0.246999626188226
14	0.82864228915763	0.34271542168474	0.17135771084237
15	0.856116567042364	0.287766865915273	0.143883432957636
16	0.850935018101219	0.298129963797562	0.149064981898781
17	0.81613172775177	0.367736544496459	0.18386827224823
18	0.851726616727225	0.296546766545551	0.148273383272775
19	0.818515280034114	0.362969439931771	0.181484719965886
20	0.849962351087502	0.300075297824996	0.150037648912498
21	0.831997081941975	0.336005836116051	0.168002918058025
22	0.790436357202879	0.419127285594242	0.209563642797121
23	0.817274855052783	0.365450289894435	0.182725144947217
24	0.797127580394875	0.40574483921025	0.202872419605125
25	0.810980480211417	0.378039039577166	0.189019519788583
26	0.85117382941685	0.297652341166299	0.14882617058315
27	0.851740394430989	0.296519211138023	0.148259605569011
28	0.813912999874401	0.372174000251198	0.186087000125599
29	0.78706821591062	0.42586356817876	0.21293178408938
30	0.741266541182062	0.517466917635876	0.258733458817938
31	0.712733880104056	0.574532239791888	0.287266119895944
32	0.75979281587614	0.480414368247721	0.24020718412386
33	0.71549728021995	0.5690054395601	0.28450271978005
34	0.731167275411377	0.537665449177247	0.268832724588623
35	0.688073036176987	0.623853927646026	0.311926963823013
36	0.639997625272379	0.720004749455241	0.360002374727621
37	0.587473005252633	0.825053989494733	0.412526994747367
38	0.533970615799012	0.932058768401977	0.466029384200988
39	0.480544251595717	0.961088503191433	0.519455748404283
40	0.427070493142264	0.854140986284527	0.572929506857736
41	0.377050931246405	0.754101862492811	0.622949068753595
42	0.335589278178175	0.671178556356349	0.664410721821825
43	0.461735446302795	0.923470892605589	0.538264553697205
44	0.511506438005268	0.976987123989465	0.488493561994732
45	0.467678278653978	0.935356557307957	0.532321721346022
46	0.424458909232404	0.848917818464808	0.575541090767596
47	0.395245867110214	0.790491734220429	0.604754132889786
48	0.353146060935474	0.706292121870948	0.646853939064526
49	0.308343792934361	0.616687585868722	0.691656207065639
50	0.280407979894339	0.560815959788677	0.719592020105661
51	0.241498750841105	0.48299750168221	0.758501249158895
52	0.208513397646856	0.417026795293712	0.791486602353144
53	0.178344140588921	0.356688281177842	0.821655859411079
54	0.152420518052425	0.304841036104849	0.847579481947575
55	0.13071511001213	0.261430220024259	0.86928488998787
56	0.111095654203558	0.222191308407116	0.888904345796442
57	0.0906966470101215	0.181393294020243	0.909303352989879
58	0.0779425718560584	0.155885143712117	0.922057428143942
59	0.0680355867602016	0.136071173520403	0.931964413239798
60	0.0550303202860417	0.110060640572083	0.944969679713958
61	0.0531408457077773	0.106281691415555	0.946859154292223
62	0.052332657205263	0.104665314410526	0.947667342794737
63	0.0560522583046463	0.112104516609293	0.943947741695354
64	0.0808144482155246	0.161628896431049	0.919185551784475
65	0.111776006480478	0.223552012960956	0.888223993519522
66	0.137597202347985	0.275194404695971	0.862402797652015
67	0.113657853838224	0.227315707676447	0.886342146161776
68	0.0993582769680768	0.198716553936154	0.900641723031923
69	0.0953621449524742	0.190724289904948	0.904637855047526
70	0.0788889574611769	0.157777914922354	0.921111042538823
71	0.0653605313061793	0.130721062612359	0.934639468693821
72	0.114070167056264	0.228140334112529	0.885929832943736
73	0.106695204122913	0.213390408245826	0.893304795877087
74	0.0885775631888958	0.177155126377792	0.911422436811104
75	0.114991503773132	0.229983007546264	0.885008496226868
76	0.126364587570911	0.252729175141821	0.873635412429089
77	0.108690426824478	0.217380853648956	0.891309573175522
78	0.0893111621180485	0.178622324236097	0.910688837881952
79	0.0760861486587889	0.152172297317578	0.923913851341211
80	0.0922188430223747	0.184437686044749	0.907781156977625
81	0.0846203915504345	0.169240783100869	0.915379608449566
82	0.737725237707246	0.524549524585508	0.262274762292754
83	0.703360832822989	0.593278334354022	0.296639167177011
84	0.669119389948778	0.661761220102444	0.330880610051222
85	0.631020334627628	0.737959330744744	0.368979665372372
86	0.614893367194639	0.770213265610721	0.385106632805361
87	0.575073895992519	0.849852208014962	0.424926104007481
88	0.535209444532463	0.929581110935074	0.464790555467537
89	0.59714465410649	0.805710691787019	0.40285534589351
90	0.580944276277607	0.838111447444786	0.419055723722393
91	0.549262080617304	0.901475838765392	0.450737919382696
92	0.625996948832781	0.748006102334438	0.374003051167219
93	0.590318793757231	0.819362412485538	0.409681206242769
94	0.590046468553228	0.819907062893543	0.409953531446772
95	0.592769730205298	0.814460539589405	0.407230269794702
96	0.565366100439733	0.869267799120533	0.434633899560267
97	0.519446766747323	0.961106466505355	0.480553233252677
98	0.494481964423414	0.988963928846827	0.505518035576586
99	0.461234683000365	0.92246936600073	0.538765316999635
100	0.423979106375336	0.847958212750672	0.576020893624664
101	0.385296736128278	0.770593472256555	0.614703263871722
102	0.351181448754446	0.702362897508893	0.648818551245554
103	0.354092383651917	0.708184767303834	0.645907616348083
104	0.311204584395442	0.622409168790885	0.688795415604558
105	0.278783708294874	0.557567416589747	0.721216291705126
106	0.247290280343353	0.494580560686707	0.752709719656647
107	0.213618804367894	0.427237608735789	0.786381195632106
108	0.182121470671122	0.364242941342244	0.817878529328878
109	0.183395129773237	0.366790259546475	0.816604870226763
110	0.238235010128503	0.476470020257005	0.761764989871497
111	0.228985726789289	0.457971453578579	0.77101427321071
112	0.209960029074916	0.419920058149832	0.790039970925084
113	0.281005428954988	0.562010857909975	0.718994571045012
114	0.746109270950982	0.507781458098036	0.253890729049018
115	0.712677480040646	0.574645039918707	0.287322519959354
116	0.728639369814309	0.542721260371382	0.271360630185691
117	0.81561298734732	0.368774025305361	0.18438701265268
118	0.782603917418038	0.434792165163925	0.217396082581962
119	0.748362600196626	0.503274799606747	0.251637399803374
120	0.829204295188472	0.341591409623055	0.170795704811528
121	0.872513653051549	0.254972693896901	0.127486346948451
122	0.850210051407515	0.29957989718497	0.149789948592485
123	0.891314075496225	0.21737184900755	0.108685924503775
124	0.864569314679524	0.270861370640952	0.135430685320476
125	0.833225016009117	0.333549967981765	0.166774983990883
126	0.81859669931784	0.362806601364319	0.18140330068216
127	0.843611063184952	0.312777873630095	0.156388936815048
128	0.810564331953751	0.378871336092498	0.189435668046249
129	0.770194525745916	0.459610948508169	0.229805474254084
130	0.726033009163727	0.547933981672547	0.273966990836273
131	0.674001670650679	0.651996658698642	0.325998329349321
132	0.618474190219186	0.763051619561627	0.381525809780814
133	0.564558914966641	0.870882170066718	0.435441085033359
134	0.568799324647414	0.862401350705172	0.431200675352586
135	0.508311478067587	0.983377043864826	0.491688521932413
136	0.47307800370504	0.946156007410081	0.52692199629496
137	0.550331705431774	0.899336589136451	0.449668294568226
138	0.534723285418508	0.930553429162983	0.465276714581492
139	0.60531068348513	0.789378633029739	0.39468931651487
140	0.624966594838524	0.750066810322952	0.375033405161476
141	0.576117291859695	0.84776541628061	0.423882708140305
142	0.817267510121216	0.365464979757568	0.182732489878784
143	0.780662400502012	0.438675198995977	0.219337599497988
144	0.798430211843984	0.403139576312032	0.201569788156016
145	0.736305819558278	0.527388360883445	0.263694180441722
146	0.772692410486095	0.454615179027811	0.227307589513905
147	0.700291122403063	0.599417755193875	0.299708877596937
148	0.729814631817653	0.540370736364695	0.270185368182347
149	0.649173163116248	0.701653673767504	0.350826836883752
150	0.564273892564993	0.871452214870013	0.435726107435007
151	0.543915306928705	0.912169386142589	0.456084693071295
152	0.470978609821113	0.941957219642226	0.529021390178887
153	0.415187843648371	0.830375687296742	0.584812156351629
154	0.29809529432391	0.596190588647819	0.70190470567609
155	0.237701690768523	0.475403381537045	0.762298309231477
156	0.712191096815126	0.575617806369748	0.287808903184874

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	0	0	OK
10% type I error level	0	0	OK