Multiple Linear Regression - Estimated Regression Equation

Happiness[t] = + 14.6633477594121 + 0.062586920850308Learning[t] + 0.0501534777877726Connected[t] -0.34600999963173Depression[t] + 0.024722046127967`Belonging `[t] -1.05075722573654M1[t] -0.724924910489709M2[t] + 0.00389266642390334M3[t] -1.17093606188741M4[t] -0.0626785758889235M5[t] -1.21148726676641M6[t] + 0.0958045316136582M7[t] -0.93618993019189M8[t] + 0.302874051916047M9[t] -0.975158158591014M10[t] -1.12689558410354M11[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)	14.6633477594121	2.380334	6.1602	0	0
Learning	0.062586920850308	0.072798	0.8597	0.391344	0.195672
Connected	0.0501534777877726	0.048297	1.0384	0.300781	0.15039
Depression	-0.34600999963173	0.054574	-6.3402	0	0
`Belonging `	0.024722046127967	0.015359	1.6096	0.109637	0.054818
M1	-1.05075722573654	0.752902	-1.3956	0.164951	0.082476
M2	-0.724924910489709	0.750422	-0.966	0.33563	0.167815
M3	0.00389266642390334	0.766342	0.0051	0.995954	0.497977
M4	-1.17093606188741	0.752593	-1.5559	0.121905	0.060952
M5	-0.0626785758889235	0.753656	-0.0832	0.933833	0.466917
M6	-1.21148726676641	0.752536	-1.6099	0.109586	0.054793
M7	0.0958045316136582	0.761292	0.1258	0.900028	0.450014
M8	-0.93618993019189	0.768661	-1.2179	0.225208	0.112604
M9	0.302874051916047	0.765696	0.3956	0.693012	0.346506
M10	-0.975158158591014	0.764683	-1.2752	0.204248	0.102124
M11	-1.12689558410354	0.765763	-1.4716	0.143281	0.071641

Multiple Linear Regression - Regression Statistics
Multiple R	0.615372287306375
R-squared	0.37868305198468
Adjusted R-squared	0.314849118969408
F-TEST (value)	5.93231584044929
F-TEST (DF numerator)	15
F-TEST (DF denominator)	146
p-value	1.64585656214911e-09
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	1.93493627345523
Sum Squared Residuals	546.620843820589

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	14	13.6406615432297	0.35933845677026
2	18	15.2157851873066	2.78421481269345
3	11	14.1485113052266	-3.1485113052266
4	12	13.4902304166933	-1.49023041669326
5	16	11.7947698336709	4.20523016632911
6	18	13.7970617886724	4.20293821132763
7	14	11.6023378737889	2.3976621262111
8	14	14.5428335810474	-0.542833581047397
9	15	16.0172953207445	-1.0172953207445
10	15	13.8634176022363	1.13658239776374
11	17	14.9366167126409	2.0633832873591
12	19	16.0371741872332	2.96282581276681
13	10	12.9860405193137	-2.98604051931366
14	16	13.3866497123164	2.61335028768358
15	18	16.0770008641035	1.92299913589647
16	14	12.6258654800659	1.37413451993413
17	14	14.3550116613909	-0.355011661390885
18	17	14.9788611288992	2.02113887110075
19	14	15.963813455927	-1.96381345592699
20	16	13.2444864861155	2.75551351388454
21	18	16.7821088811655	1.21789111883452
22	11	13.0812972877045	-2.08129728770447
23	14	13.864459800517	0.135540199483034
24	12	14.0607117594865	-2.06071175948652
25	17	14.95253979291	2.04746020708997
26	9	15.9223667862281	-6.92236678622806
27	16	15.5469218695772	0.453078130422824
28	14	12.6019514656295	1.39804853437045
29	15	14.3413042872618	0.658695712738224
30	11	13.1915427246955	-2.19154272469554
31	16	16.1163876087531	-0.116387608753087
32	13	11.977185276128	1.022814723872
33	17	15.9932826601484	1.00671733985163
34	15	14.6653404580104	0.33465954198955
35	14	13.4491887302542	0.550811269745827
36	16	15.6935527726048	0.306447227395235
37	9	10.3301995114513	-1.33019951145134
38	15	14.2233102206914	0.776689779308616
39	17	15.5418575246945	1.4581424753055
40	13	14.4948953402141	-1.49489534021405
41	15	16.1730800120596	-1.17308001205965
42	16	13.0433090940875	2.95669090591245
43	16	16.4836333578236	-0.483633357823623
44	12	12.8001528475066	-0.800152847506597
45	12	15.6479820460485	-3.64798204604848
46	11	13.4152935498113	-2.4152935498113
47	15	14.8113442247805	0.18865577521952
48	15	15.3052598028117	-0.30525980281168
49	17	13.0587878866339	3.94121211336612
50	13	14.7685153604105	-1.76851536041053
51	16	15.5934297735459	0.406570226454052
52	14	12.7857769743673	1.21422302563274
53	11	12.2859324356263	-1.28593243562635
54	12	12.8470963361246	-0.847096336124594
55	12	14.6787247780001	-2.67872477800011
56	15	14.1858089094168	0.81419109058319
57	16	15.2548995969132	0.745100403086756
58	15	14.6863182841596	0.313681715840392
59	12	14.675544037235	-2.67554403723502
60	12	13.9605034500708	-1.96050345007078
61	8	10.2583063696601	-2.25830636966006
62	13	14.5971232947353	-1.59712329473535
63	11	15.1253269604979	-4.12532696049787
64	14	12.36479280466	1.63520719534001
65	15	14.1441386576101	0.855861342389929
66	10	14.4428635639613	-4.44286356396127
67	11	13.4407271173975	-2.4407271173975
68	12	14.0109161099197	-2.01091610991973
69	15	14.7326094061044	0.267390593895626
70	15	13.3066332449835	1.69336675501647
71	14	13.2264006351083	0.773599364891738
72	16	13.2391629591716	2.7608370408284
73	15	13.9487290949182	1.05127090508182
74	15	15.2165407666757	-0.216540766675686
75	13	15.6443912830254	-2.64439128302537
76	12	11.9159486829375	0.0840513170624827
77	17	14.6901518290209	2.30984817097914
78	13	11.9821206601252	1.01787933987483
79	15	14.3825471967783	0.617452803221667
80	13	14.8051277351973	-1.80512773519734
81	15	15.7696089600899	-0.769608960089903
82	16	14.0771680834965	1.92283191650349
83	15	14.9343899098856	0.0656100901144201
84	16	15.1104196220751	0.889580377924894
85	15	13.7841729612717	1.21582703872826
86	14	14.0003459061648	-0.000345906164753977
87	15	14.8053129380607	0.194687061939322
88	14	13.702568385375	0.297431614624954
89	13	13.2013512694077	-0.201351269407748
90	7	10.1640523094564	-3.16405230945641
91	17	14.3715325247795	2.62846747522052
92	13	12.7415011804695	0.258498819530502
93	15	15.1284518241461	-0.128451824146054
94	14	13.0689624908017	0.931037509198256
95	13	14.322196696128	-1.32219669612799
96	16	15.7923778210285	0.207622178971542
97	12	12.6393211341501	-0.639321134150086
98	14	14.8173949071317	-0.817394907131726
99	17	15.7206855780048	1.27931442199522
100	15	14.3923153880459	0.607684611954114
101	17	15.9266675824716	1.07333241752838
102	12	12.5774792776321	-0.577479277632088
103	16	15.7656698336881	0.234330166311864
104	11	14.0964179796803	-3.09641797968031
105	15	14.0395589619313	0.960441038068746
106	9	11.6148678270849	-2.61486782708485
107	16	14.5790274954756	1.42097250452442
108	15	13.9401363632937	1.05986363670635
109	10	12.5643469640745	-2.56434696407454
110	10	9.67903957472524	0.320960425274757
111	15	14.3563032807232	0.643696719276847
112	11	12.6878416615441	-1.68784166154415
113	13	15.6389881904992	-2.63898819049917
114	14	11.6196895112952	2.38031048870481
115	18	15.0926295295217	2.90737047047826
116	16	15.3753970533612	0.624602946638829
117	14	13.9883539662949	0.0116460337050773
118	14	13.5020379712548	0.497962028745164
119	14	14.5968780995032	-0.596878099503177
120	14	14.6054048059934	-0.605404805993436
121	12	12.2261257681603	-0.226125768160297
122	14	13.5293069048295	0.470693095170488
123	15	15.7808546622654	-0.780854662265368
124	15	15.4602766179488	-0.460276617948825
125	15	15.1931371346668	-0.193137134666822
126	13	14.1549406858319	-1.1549406858319
127	17	17.1108458919667	-0.110845891966667
128	17	15.3672199234897	1.63278007651033
129	19	15.7564661314955	3.24353386850447
130	15	13.4764616995979	1.52353830040207
131	13	14.0919094772588	-1.0919094772588
132	9	11.404969397784	-2.40496939778401
133	15	15.0636179343275	-0.0636179343275189
134	15	12.4603928032378	2.53960719676218
135	15	15.0764474137767	-0.0764474137766686
136	16	13.2191945871371	2.78080541286292
137	11	10.1953570320152	0.804642967984787
138	14	12.8092314614023	1.19076853859775
139	11	12.7510432508148	-1.75104325081483
140	15	14.0096735582368	0.990326441763225
141	13	14.5753761768005	-1.57537617680049
142	15	14.1693821182276	0.830617881772375
143	16	13.2123722016013	2.78762779839867
144	14	15.2059057189249	-1.20590571892489
145	15	13.9202166349741	1.07978336502589
146	16	14.9645832783764	1.03541672162362
147	16	15.125471800495	0.874528199505028
148	11	13.096759641404	-2.09675964140401
149	12	15.2550146699853	-3.25501466998529
150	9	11.2513815606104	-2.25138156061043
151	16	15.2401075807606	0.7598924192394
152	13	12.8432793594312	0.156720640568767
153	16	16.3140060681174	-0.314006068117399
154	12	14.0728193826309	-2.07281938263089
155	9	11.2996719796117	-2.29967197961173
156	13	12.6444213395219	0.355578660478068
157	13	12.6269338849248	0.373066115075153
158	14	13.2186452971706	0.781354702829409
159	19	15.4574847460034	3.54251525399661
160	13	15.1615825539775	-2.16158255397751
161	12	12.8050954043137	-0.805095404313654
162	13	12.140369897206	0.859630102794021

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
19	0.180147499154489	0.360294998308978	0.819852500845511
20	0.80279721729211	0.39440556541578	0.19720278270789
21	0.946669315850119	0.106661368299761	0.0533306841498807
22	0.925931544348368	0.148136911303264	0.074068455651632
23	0.891759842520861	0.216480314958278	0.108240157479139
24	0.971564959888719	0.0568700802225624	0.0284350401112812
25	0.986679514728041	0.0266409705439179	0.013320485271959
26	0.99993924078078	0.000121518438440136	6.0759219220068e-05
27	0.999877232439087	0.000245535121826962	0.000122767560913481
28	0.999782280721037	0.000435438557924972	0.000217719278962486
29	0.999587224602146	0.000825550795707098	0.000412775397853549
30	0.999922749864582	0.000154500270836134	7.72501354180669e-05
31	0.999847963752329	0.000304072495342516	0.000152036247671258
32	0.999733493073183	0.000533013853634185	0.000266506926817092
33	0.999528685692742	0.000942628614515314	0.000471314307257657
34	0.999206268520025	0.0015874629599508	0.000793731479975401
35	0.998824589222918	0.0023508215541642	0.0011754107770821
36	0.998142439259899	0.00371512148020202	0.00185756074010101
37	0.99744557613318	0.00510884773364097	0.00255442386682048
38	0.996389675764382	0.00722064847123538	0.00361032423561769
39	0.995847486324899	0.00830502735020121	0.0041525136751006
40	0.994746593127149	0.0105068137457014	0.00525340687285069
41	0.992927042462866	0.0141459150742681	0.00707295753713405
42	0.993070445859408	0.0138591082811846	0.0069295541405923
43	0.990280965718728	0.0194380685625433	0.00971903428127163
44	0.98812164470543	0.0237567105891405	0.0118783552945703
45	0.995154081661626	0.00969183667674895	0.00484591833837448
46	0.995095722354166	0.00980855529166706	0.00490427764583353
47	0.992725098822043	0.0145498023559141	0.00727490117795706
48	0.990277386372578	0.019445227254843	0.0097226136274215
49	0.996010531657547	0.00797893668490585	0.00398946834245293
50	0.995444220108967	0.00911155978206669	0.00455577989103335
51	0.993445393759767	0.0131092124804654	0.00655460624023268
52	0.991449311402772	0.0171013771944562	0.0085506885972281
53	0.989970012619296	0.0200599747614075	0.0100299873807038
54	0.98824706950245	0.0235058609951006	0.0117529304975503
55	0.98995761940365	0.0200847611926994	0.0100423805963497
56	0.986532861761677	0.0269342764766456	0.0134671382383228
57	0.981684254873876	0.0366314902522475	0.0183157451261238
58	0.976989769458948	0.0460204610821047	0.0230102305410523
59	0.983363458407461	0.0332730831850782	0.0166365415925391
60	0.986433649942432	0.0271327001151363	0.0135663500575681
61	0.987378794536646	0.0252424109267075	0.0126212054633537
62	0.985897562826258	0.0282048743474832	0.0141024371737416
63	0.995388162146155	0.00922367570768936	0.00461183785384468
64	0.994812783962712	0.0103744320745758	0.00518721603728791
65	0.993052450024165	0.0138950999516691	0.00694754997583457
66	0.998834472433906	0.00233105513218707	0.00116552756609353
67	0.999137375306797	0.00172524938640549	0.000862624693202747
68	0.999199767983665	0.00160046403267027	0.000800232016335137
69	0.998796796668248	0.00240640666350451	0.00120320333175226
70	0.99866216056658	0.00267567886683979	0.00133783943341989
71	0.998120878045375	0.00375824390925054	0.00187912195462527
72	0.99862599476375	0.0027480104725008	0.0013740052362504
73	0.998174297889177	0.00365140422164577	0.00182570211082288
74	0.997548358574575	0.00490328285085019	0.0024516414254251
75	0.998443519849841	0.00311296030031769	0.00155648015015884
76	0.997830889292415	0.00433822141516936	0.00216911070758468
77	0.998273719523062	0.00345256095387662	0.00172628047693831
78	0.997760622873456	0.00447875425308768	0.00223937712654384
79	0.996902887182688	0.00619422563462316	0.00309711281731158
80	0.996959416541948	0.00608116691610323	0.00304058345805161
81	0.996017149321297	0.00796570135740603	0.00398285067870302
82	0.995472555675669	0.00905488864866276	0.00452744432433138
83	0.993503964369867	0.0129920712602662	0.00649603563013309
84	0.991442140720452	0.0171157185590954	0.00855785927954771
85	0.98966369225935	0.0206726154812995	0.0103363077406498
86	0.986147485621899	0.0277050287562025	0.0138525143781013
87	0.98211328189293	0.0357734362141393	0.0178867181070696
88	0.976416227346291	0.0471675453074177	0.0235837726537089
89	0.969796925265965	0.0604061494680709	0.0302030747340354
90	0.980654864657082	0.0386902706858361	0.019345135342918
91	0.984410445596624	0.0311791088067528	0.0155895544033764
92	0.978757328905076	0.0424853421898472	0.0212426710949236
93	0.971824803970692	0.056350392058615	0.0281751960293075
94	0.965745572719382	0.0685088545612357	0.0342544272806178
95	0.960251074304555	0.0794978513908909	0.0397489256954454
96	0.948295518861177	0.103408962277646	0.0517044811388228
97	0.934101081234571	0.131797837530857	0.0658989187654285
98	0.929173085156527	0.141653829686945	0.0708269148434726
99	0.915507884490417	0.168984231019165	0.0844921155095827
100	0.899630400277237	0.200739199445526	0.100369599722763
101	0.893217752234976	0.213564495530048	0.106782247765024
102	0.870259960217489	0.259480079565021	0.129740039782511
103	0.841571800722315	0.31685639855537	0.158428199277685
104	0.90537114238227	0.18925771523546	0.0946288576177299
105	0.884109852335829	0.231780295328342	0.115890147664171
106	0.895160028463767	0.209679943072465	0.104839971536233
107	0.886239145772133	0.227521708455734	0.113760854227867
108	0.890608538782965	0.21878292243407	0.109391461217035
109	0.907531169368706	0.184937661262588	0.0924688306312939
110	0.883652464193199	0.232695071613602	0.116347535806801
111	0.857004682337797	0.285990635324406	0.142995317662203
112	0.847008350816519	0.305983298366963	0.152991649183481
113	0.853332632871919	0.293334734256163	0.146667367128081
114	0.899361432248031	0.201277135503938	0.100638567751969
115	0.935560176655384	0.128879646689233	0.0644398233446164
116	0.92284403657076	0.154311926858479	0.0771559634292396
117	0.898246741891823	0.203506516216354	0.101753258108177
118	0.868057238657562	0.263885522684875	0.131942761342438
119	0.833357081328817	0.333285837342367	0.166642918671183
120	0.7975853146028	0.4048293707944	0.2024146853972
121	0.74993610915939	0.500127781681221	0.25006389084061
122	0.725296573234415	0.54940685353117	0.274703426765585
123	0.709431790589272	0.581136418821456	0.290568209410728
124	0.654974238634274	0.690051522731452	0.345025761365726
125	0.623703059976675	0.752593880046649	0.376296940023325
126	0.604951407030637	0.790097185938726	0.395048592969363
127	0.535646786445117	0.928706427109766	0.464353213554883
128	0.532163670982796	0.935672658034408	0.467836329017204
129	0.628619448703267	0.742761102593467	0.371380551296733
130	0.590948549295025	0.81810290140995	0.409051450704975
131	0.52438076165464	0.95123847669072	0.47561923834536
132	0.529522055622193	0.940955888755615	0.470477944377807
133	0.449119912872687	0.898239825745373	0.550880087127313
134	0.383764236292879	0.767528472585759	0.616235763707121
135	0.318638676326513	0.637277352653027	0.681361323673487
136	0.468979457132666	0.937958914265332	0.531020542867334
137	0.612817906967112	0.774364186065777	0.387182093032888
138	0.561338118437131	0.877323763125738	0.438661881562869
139	0.488347393961583	0.976694787923165	0.511652606038417
140	0.42171084650682	0.843421693013639	0.57828915349318
141	0.742058487986422	0.515883024027155	0.257941512013578
142	0.613434169267491	0.773131661465018	0.386565830732509
143	0.683392697850592	0.633214604298816	0.316607302149408

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	36	0.288	NOK
5% type I error level	67	0.536	NOK
10% type I error level	72	0.576	NOK