Multiple Linear Regression - Estimated Regression Equation

Happiness[t] = + 14.2913833810387 + 0.0447596128803711Learning[t] + 0.0438619025707971Connected[t] -0.359814744565595Depression[t] + 0.0312054961791069`Belonging `[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)	14.2913833810387	2.293571	6.2311	0	0
Learning	0.0447596128803711	0.071294	0.6278	0.531036	0.265518
Connected	0.0438619025707971	0.046731	0.9386	0.349379	0.17469
Depression	-0.359814744565595	0.051739	-6.9545	0	0
`Belonging `	0.0312054961791069	0.014905	2.0937	0.037898	0.018949

Multiple Linear Regression - Regression Statistics
Multiple R	0.568382414414984
R-squared	0.323058569016207
Adjusted R-squared	0.305811653577129
F-TEST (value)	18.731382440957
F-TEST (DF numerator)	4
F-TEST (DF denominator)	157
p-value	1.31583632878574e-12
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	1.94765583064057
Sum Squared Residuals	595.558027836631

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	14	14.0077107165917	-0.00771071659171896
2	18	15.4438618685673	2.55613813143268
3	11	13.4798294267923	-2.47982942679234
4	12	14.0954878631519	-2.09548786315195
5	16	11.2248307225056	4.77516927749443
6	18	14.5246767056446	3.47532329435543
7	14	10.5903971430764	3.40960285692364
8	14	14.9925597657583	-0.992559765758324
9	15	15.2081057255105	-0.208105725510501
10	15	14.2796939996231	0.720306000376903
11	17	15.5413762373084	1.45862376269163
12	19	15.3931445168203	3.60685548317971
13	10	13.3678365603311	-3.36783656033111
14	16	13.3658417571391	2.63415824286089
15	18	15.6164703067676	2.38352969323239
16	14	13.1388708109796	0.861129189020408
17	14	13.8448118563076	0.155188143692402
18	17	15.6414494098762	1.35855059012378
19	14	15.2066749229533	-1.20667492295331
20	16	13.5122396722465	2.48776032775355
21	18	15.951977605252	2.04802239474801
22	11	13.4518234830802	-2.45182348308023
23	14	14.2197500849114	-0.219750084911419
24	12	13.3405289443557	-1.34052894435573
25	17	15.4886214814477	1.51137851855231
26	9	16.1087417986458	-7.10874179864584
27	16	15.0002211990639	0.999778800936138
28	14	13.166178426955	0.833821573045031
29	15	13.8516022500129	1.1483977499871
30	11	13.8224992134184	-2.82249921341837
31	16	15.5806035471771	0.419396452822876
32	13	12.3006457302025	0.69935426979753
33	17	15.158351139544	1.84164886045602
34	15	15.1621413633551	-0.162141363355123
35	14	14.0409376866721	-0.0409376866721208
36	16	15.3453538256586	0.654646174341414
37	9	10.7806260523673	-1.78062605236731
38	15	14.394859747842	0.605140252158011
39	17	15.0530026256339	1.94699737436612
40	13	15.0977355678049	-2.09773556780491
41	15	15.7013015984076	-0.701301598407636
42	16	13.7123284382856	2.28767156171437
43	16	15.6599067734834	0.340093226516626
44	12	13.038463928737	-1.03846392873697
45	12	14.779987305191	-2.77998730519097
46	11	13.8510115786688	-2.85101157866876
47	15	15.3747948096057	-0.374794809605728
48	15	14.792670382292	0.207329617708007
49	17	13.4985512284433	3.50144877155673
50	13	14.9672202822656	-1.96722028226561
51	16	15.0597663486298	0.940233651370159
52	14	13.3749606637112	0.625039336288817
53	11	11.7213604749716	-0.721360474971631
54	12	13.396176213718	-1.39617621371798
55	12	14.1057848482897	-2.10578484828969
56	15	14.5947491313083	0.405250868691679
57	16	14.3497664252868	1.65023357471315
58	15	15.1319679045875	-0.131967904587511
59	12	15.2655217447826	-3.26552174478256
60	12	13.329867341156	-1.32986734115604
61	8	10.6019522189078	-2.60195221890778
62	13	14.759335755819	-1.75933575581897
63	11	14.5838881455358	-3.58388814553578
64	14	12.8630163184538	1.13698368154622
65	15	13.5063469888507	1.49365301114928
66	10	15.1259408940899	-5.12594089408986
67	11	12.61879699564	-1.61879699563996
68	12	14.3731377762969	-2.3731377762969
69	15	13.8274675157952	1.17253248420481
70	15	13.6584765895425	1.34152341045747
71	14	13.8189083721801	0.181091627819924
72	16	12.5656125662464	3.4343874337536
73	15	14.4384146114474	0.561585388552646
74	15	15.318840501278	-0.318840501278045
75	13	15.1621413633551	-2.16214136335512
76	12	12.4228705478483	-0.422870547848288
77	17	14.1372206354288	2.86277936457117
78	13	12.5351704532749	0.464829546725053
79	15	13.8266231469043	1.17337685309571
80	13	15.0771916748255	-2.0771916748255
81	15	14.9622519798888	0.0377480201112086
82	16	14.1474834734828	1.85251652651718
83	15	15.5199613047287	-0.519961304728721
84	16	14.5458922556514	1.45410774434863
85	15	14.2953772466183	0.704622753381721
86	14	14.1802114983994	-0.180211498399387
87	15	14.2475907931344	0.752409206865584
88	14	14.2903822735321	-0.290382273532127
89	13	12.5674079868655	0.432592013134452
90	7	10.6786807111749	-3.67868071117491
91	17	13.7886272570199	3.21137274298012
92	13	12.9192009177415	0.080799082258501
93	15	14.267935303541	0.732064696459019
94	14	13.5279879747126	0.472012025287438
95	13	15.0435457717092	-2.04354577170919
96	16	15.2566288914927	0.74337110850732
97	12	13.0265709055529	-1.02657090555293
98	14	15.0187702888513	-1.01877028885128
99	17	15.2001105825302	1.79988941746981
100	15	15.0950691075855	-0.0950691075855265
101	17	15.4477597487711	1.55224025122895
102	12	13.1513928902694	-1.15139289026936
103	16	15.1002943716317	0.899705628368287
104	11	14.4679590141092	-3.46795901410923
105	15	13.1631782570608	1.83682174293919
106	9	11.9132280447483	-2.91322804474832
107	16	15.1327046170858	0.867295382914173
108	15	13.2644295081943	1.73557049180566
109	10	12.8744413048611	-2.87444130486113
110	10	9.51445950081201	0.485540499187991
111	15	13.8448385270169	1.15516147298307
112	11	13.2792417155893	-2.27924171558928
113	13	15.2439991558103	-2.24399915581033
114	14	12.0654269170711	1.93457308292888
115	18	14.5052299055476	3.49477009445242
116	16	15.8054720337521	0.194527966247934
117	14	13.0131511159536	0.98684888404641
118	14	13.9161157019557	0.0838842980443069
119	14	15.2355476685878	-1.2355476685878
120	14	14.0855629724506	-0.085562972450571
121	12	12.6085767585076	-0.608576758507623
122	14	13.7014674525131	0.29853254748691
123	15	15.3593376158927	-0.359337615892732
124	15	16.1235273353314	-1.12352733533144
125	15	14.7302593899338	0.269740610066221
126	13	14.8745281747472	-1.8745281747472
127	17	16.6033684741002	0.396631525899836
128	17	15.693279784718	1.30672021528201
129	19	14.9799033593666	4.02009664063336
130	15	13.932869371124	1.06713062887604
131	13	14.6687461078851	-1.66874610788514
132	9	10.8303806383338	-1.83038063833383
133	15	15.5666890500918	-0.566689050091752
134	15	12.6439061881726	2.35609381182735
135	15	14.5323381389501	0.467661861049893
136	16	13.8878027192782	2.11219728072184
137	11	9.51074928912887	1.48925071087113
138	14	13.3826220970167	0.61737790298328
139	11	12.0276570804689	-1.02765708046889
140	15	14.4028548908223	0.597145109177703
141	13	13.8445815653476	-0.844581565347564
142	15	14.4980674174059	0.501932582594083
143	16	13.8624899064948	2.13751009350522
144	14	14.7340496137449	-0.734049613744924
145	15	14.4523024378234	0.547697562176612
146	16	15.3127825823932	0.687217417606787
147	16	14.5544780699758	1.44552193002418
148	11	13.6470249324258	-2.64702493242585
149	12	14.7935680926016	-2.79356809260157
150	9	11.8499460127899	-2.84994601278987
151	16	14.7404220479696	1.2595779520304
152	13	13.153361022752	-0.153361022752021
153	16	15.4760994021579	0.523900597842076
154	12	14.471722567211	-2.47172256721104
155	9	11.7698836409538	-2.76988364095381
156	13	12.1437855944683	0.85621440553171
157	13	12.9192009177415	0.080799082258501
158	14	13.392612043189	0.607387956810975
159	19	14.9799033593666	4.02009664063336
160	13	15.8817708524863	-2.88177085248631
161	12	12.3766758947329	-0.376675894732876
162	13	12.7607063591994	0.239293640800571

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
8	0.365085965013503	0.730171930027007	0.634914034986497
9	0.212165227334682	0.424330454669365	0.787834772665318
10	0.154483058414701	0.308966116829401	0.845516941585299
11	0.101480530701343	0.202961061402686	0.898519469298657
12	0.868448496822769	0.263103006354461	0.13155150317723
13	0.981928548574682	0.0361429028506365	0.0180714514253182
14	0.975913240303621	0.0481735193927583	0.0240867596963792
15	0.977585877918614	0.0448282441627715	0.0224141220813857
16	0.966115331162468	0.0677693376750643	0.0338846688375321
17	0.95398353350074	0.0920329329985191	0.0460164664992595
18	0.933753972649678	0.132492054700644	0.0662460273503222
19	0.923199947749031	0.153600104501937	0.0768000522509687
20	0.932046395556798	0.135907208886404	0.0679536044432022
21	0.93427523005931	0.131449539881381	0.0657247699406904
22	0.952328331792302	0.0953433364153952	0.0476716682076976
23	0.935037872545583	0.129924254908833	0.0649621274544166
24	0.932836888825488	0.134326222349025	0.0671631111745123
25	0.912507315818068	0.174985368363864	0.0874926841819321
26	0.998796052184957	0.00240789563008682	0.00120394781504341
27	0.998160046149248	0.00367990770150392	0.00183995385075196
28	0.997173897574627	0.00565220485074675	0.00282610242537338
29	0.995808016801514	0.00838396639697242	0.00419198319848621
30	0.997894749662696	0.00421050067460742	0.00210525033730371
31	0.996755108882282	0.006489782235435	0.0032448911177175
32	0.995206189478203	0.00958762104359303	0.00479381052179652
33	0.99434982615347	0.0113003476930598	0.0056501738465299
34	0.991814235634451	0.0163715287310986	0.0081857643655493
35	0.988642456439984	0.0227150871200315	0.0113575435600158
36	0.984043150067617	0.0319136998647659	0.015956849932383
37	0.988088437046738	0.0238231259065244	0.0119115629532622
38	0.983472017681802	0.0330559646363954	0.0165279823181977
39	0.982279395707794	0.0354412085844117	0.0177206042922059
40	0.982883109426618	0.0342337811467641	0.017116890573382
41	0.977422002559946	0.0451559948801084	0.0225779974400542
42	0.976713196874128	0.0465736062517444	0.0232868031258722
43	0.969458416212909	0.061083167574182	0.030541583787091
44	0.963179921823712	0.0736401563525763	0.0368200781762881
45	0.971841145442528	0.056317709114944	0.028158854557472
46	0.978797847212486	0.0424043055750278	0.0212021527875139
47	0.971798914424073	0.0564021711518546	0.0282010855759273
48	0.962779281976481	0.0744414360470379	0.0372207180235189
49	0.975804176044429	0.0483916479111422	0.0241958239555711
50	0.975394799401203	0.0492104011975948	0.0246052005987974
51	0.968819928610942	0.0623601427781162	0.0311800713890581
52	0.959837186359743	0.0803256272805148	0.0401628136402574
53	0.951548508977013	0.096902982045974	0.048451491022987
54	0.946629243207726	0.106741513584548	0.0533707567922742
55	0.946502331260171	0.106995337479659	0.0534976687398294
56	0.932598228801481	0.134803542397037	0.0674017711985187
57	0.926307751184755	0.14738449763049	0.0736922488152451
58	0.908392121064069	0.183215757871861	0.0916078789359307
59	0.937418492577977	0.125163014844047	0.0625815074220233
60	0.93194716108252	0.136105677834961	0.0680528389174803
61	0.943807929156831	0.112384141686339	0.0561920708431694
62	0.942069718398924	0.115860563202153	0.0579302816010765
63	0.969005979976875	0.0619880400462504	0.0309940200231252
64	0.963296980002356	0.0734060399952874	0.0367030199976437
65	0.958995108087246	0.0820097838255088	0.0410048919127544
66	0.992349955543713	0.0153000889125748	0.00765004445628738
67	0.991666853332622	0.0166662933347553	0.00833314666737765
68	0.9928973915258	0.0142052169483993	0.00710260847419963
69	0.991271974551817	0.0174560508963664	0.00872802544818321
70	0.989664527637525	0.0206709447249508	0.0103354723624754
71	0.986143170251468	0.0277136594970647	0.0138568297485323
72	0.992518705167069	0.0149625896658618	0.00748129483293091
73	0.990062527958804	0.0198749440823924	0.00993747204119622
74	0.986682665644648	0.0266346687107047	0.0133173343553524
75	0.987558792266753	0.0248824154664933	0.0124412077332466
76	0.983587247466518	0.0328255050669631	0.0164127525334815
77	0.988308101485422	0.0233837970291565	0.0116918985145782
78	0.98470868823197	0.0305826235360607	0.0152913117680304
79	0.981618761294174	0.0367624774116511	0.0183812387058255
80	0.983052408108696	0.0338951837826073	0.0169475918913036
81	0.977562927640392	0.0448741447192155	0.0224370723596077
82	0.977007959399962	0.0459840812000753	0.0229920406000377
83	0.970657593428403	0.0586848131431944	0.0293424065715972
84	0.967021926197111	0.0659561476057781	0.032978073802889
85	0.958873926575218	0.0822521468495639	0.0411260734247819
86	0.947615180903252	0.104769638193496	0.0523848190967481
87	0.936005333873353	0.127989332253295	0.0639946661266473
88	0.920386294239275	0.15922741152145	0.0796137057607249
89	0.90441402205598	0.191171955888041	0.0955859779440204
90	0.943379342977465	0.11324131404507	0.0566206570225348
91	0.962991554169248	0.0740168916615043	0.0370084458307522
92	0.952808599614923	0.0943828007701538	0.0471914003850769
93	0.942113946776157	0.115772106447687	0.0578860532238433
94	0.928105826956804	0.143788346086391	0.0718941730431957
95	0.931314125165656	0.137371749668689	0.0686858748343443
96	0.91680971853118	0.166380562937639	0.0831902814688197
97	0.901821852579457	0.196356294841087	0.0981781474205434
98	0.886173681291055	0.22765263741789	0.113826318708945
99	0.882456149315932	0.235087701368136	0.117543850684068
100	0.857264045417043	0.285471909165914	0.142735954582957
101	0.847590532425213	0.304818935149573	0.152409467574787
102	0.826711064231326	0.346577871537349	0.173288935768674
103	0.803334246164391	0.393331507671217	0.196665753835609
104	0.868055288437522	0.263889423124956	0.131944711562478
105	0.86888595401171	0.26222809197658	0.13111404598829
106	0.897737112482749	0.204525775034501	0.102262887517251
107	0.879625103546276	0.240749792907449	0.120374896453724
108	0.879668158956763	0.240663682086474	0.120331841043237
109	0.902944692631237	0.194110614737527	0.0970553073687633
110	0.882484703733832	0.235030592532336	0.117515296266168
111	0.867775811148956	0.264448377702088	0.132224188851044
112	0.874650982345228	0.250698035309544	0.125349017654772
113	0.885967613286583	0.228064773426834	0.114032386713417
114	0.89349591025629	0.21300817948742	0.10650408974371
115	0.94042506364563	0.11914987270874	0.0595749363543698
116	0.922919951894706	0.154160096210588	0.077080048105294
117	0.912996900460334	0.174006199079332	0.087003099539666
118	0.889679933405166	0.220640133189668	0.110320066594834
119	0.875640465191109	0.248719069617783	0.124359534808891
120	0.845265759757547	0.309468480484905	0.154734240242453
121	0.811014392756635	0.37797121448673	0.188985607243365
122	0.771414921429846	0.457170157140308	0.228585078570154
123	0.731776053124521	0.536447893750957	0.268223946875479
124	0.703466296617045	0.593067406765909	0.296533703382955
125	0.652566799985642	0.694866400028716	0.347433200014358
126	0.673719886009833	0.652560227980333	0.326280113990167
127	0.621055397719649	0.757889204560703	0.378944602280351
128	0.615841752610348	0.768316494779304	0.384158247389652
129	0.755724243257247	0.488551513485507	0.244275756742753
130	0.724618344748268	0.550763310503464	0.275381655251732
131	0.717955224930101	0.564089550139799	0.282044775069899
132	0.73246342566222	0.535073148675559	0.26753657433778
133	0.67844430947587	0.64311138104826	0.32155569052413
134	0.671382957565726	0.657234084868549	0.328617042434274
135	0.619664831344933	0.760670337310134	0.380335168655067
136	0.615597156306574	0.768805687386852	0.384402843693426
137	0.631006435107961	0.737987129784078	0.368993564892039
138	0.591442459995049	0.817115080009902	0.408557540004951
139	0.524131195703973	0.951737608592054	0.475868804296027
140	0.465681752978022	0.931363505956044	0.534318247021978
141	0.425435102613815	0.850870205227631	0.574564897386185
142	0.37295257645862	0.745905152917241	0.62704742354138
143	0.369572145088925	0.73914429017785	0.630427854911075
144	0.308152437564444	0.616304875128888	0.691847562435556
145	0.245599959878672	0.491199919757345	0.754400040121328
146	0.184158905113172	0.368317810226344	0.815841094886828
147	0.19659792116426	0.393195842328521	0.80340207883574
148	0.268284913669905	0.53656982733981	0.731715086330095
149	0.272308222438452	0.544616444876903	0.727691777561548
150	0.266020765054446	0.532041530108892	0.733979234945554
151	0.200621688255076	0.401243376510152	0.799378311744924
152	0.242306884278805	0.48461376855761	0.757693115721195
153	0.150331427919978	0.300662855839955	0.849668572080022
154	0.103690929063558	0.207381858127116	0.896309070936442

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	7	0.0476190476190476	NOK
5% type I error level	40	0.272108843537415	NOK
10% type I error level	59	0.401360544217687	NOK