Multiple Linear Regression - Estimated Regression Equation

I1[t] = + 5.36134261525376 + 0.366963117541319I2[t] + 0.255826668828208I3[t] + 0.264181871301092E1[t] -0.119732604002764E2[t] + 0.0260781950766237E3[t] -0.207942418540606A[t] + 0.0449203061958693Happiness[t] + 0.116248276524842`Depression\r`[t] -0.00354742887974725t + 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)	5.36134261525376	2.884834	1.8585	0.065038	0.032519
I2	0.366963117541319	0.063539	5.7754	0	0
I3	0.255826668828208	0.050628	5.053	1e-06	1e-06
E1	0.264181871301092	0.075272	3.5097	0.00059	0.000295
E2	-0.119732604002764	0.059044	-2.0279	0.044322	0.022161
E3	0.0260781950766237	0.061678	0.4228	0.673028	0.336514
A	-0.207942418540606	0.084223	-2.469	0.014658	0.007329
Happiness	0.0449203061958693	0.101712	0.4416	0.659374	0.329687
`Depression\r`	0.116248276524842	0.075645	1.5368	0.126428	0.063214
t	-0.00354742887974725	0.00431	-0.823	0.411812	0.205906

Multiple Linear Regression - Regression Statistics
Multiple R	0.747502040838054
R-squared	0.558759301057056
Adjusted R-squared	0.532633207040697
F-TEST (value)	21.3870202222803
F-TEST (DF numerator)	9
F-TEST (DF denominator)	152
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	2.50012463601008
Sum Squared Residuals	950.094725728849

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	26	24.2690018896524	1.73099811034757
2	20	21.1450590944267	-1.14505909442669
3	19	21.9802025271728	-2.9802025271728
4	19	18.3539608554854	0.646039144514599
5	20	19.3296175729825	0.670382427017548
6	25	24.3668095135607	0.633190486439267
7	25	20.6747383898775	4.32526161012252
8	22	20.1174870900675	1.88251290993248
9	26	22.2681150794534	3.73188492054655
10	22	20.6529087389486	1.34709126105141
11	17	19.9984061937854	-2.99840619378543
12	22	22.7370523941991	-0.737052394199061
13	19	21.0588518278945	-2.05885182789453
14	24	22.9178958429478	1.08210415705222
15	26	26.7915124353041	-0.791512435304066
16	21	19.2051221698112	1.7948778301888
17	13	16.4002088533209	-3.40020885332089
18	26	27.3151780292841	-1.31517802928415
19	20	22.3963503527224	-2.39635035272236
20	22	18.9673795111304	3.03262048886957
21	14	17.730065367142	-3.73006536714204
22	21	20.5114268377785	0.488573162221478
23	7	13.9966443491655	-6.99664434916552
24	23	21.795625579326	1.20437442067399
25	17	19.0458880791825	-2.04588807918252
26	25	22.611720500707	2.38827949929296
27	25	23.1551117682481	1.84488823175194
28	19	16.4145426301547	2.5854573698453
29	20	16.7961644183871	3.20383558161288
30	23	21.3723574191564	1.62764258084364
31	22	23.8926453164331	-1.89264531643311
32	22	22.1745364011991	-0.174536401199143
33	21	17.9677681752719	3.03223182472807
34	15	17.6974205392187	-2.69742053921874
35	20	16.0152657239586	3.9847342760414
36	22	21.3397250418337	0.660274958166284
37	18	17.1349678530951	0.865032146904864
38	20	20.8381982868572	-0.83819828685722
39	28	27.4808492798154	0.519150720184633
40	22	23.8341995561028	-1.83419955610283
41	18	21.3484946856089	-3.34849468560889
42	23	20.8641421655914	2.13585783440858
43	20	21.2712217143381	-1.27122171433811
44	25	24.7318740122966	0.26812598770337
45	26	21.9606316418186	4.03936835818137
46	15	14.336757818874	0.663242181126034
47	17	17.4516335038606	-0.451633503860646
48	23	15.1677081529403	7.83229184705966
49	21	22.4332992853811	-1.43329928538114
50	13	16.011179152682	-3.01117915268204
51	18	19.9742670958358	-1.97426709583584
52	19	19.3390921286354	-0.339092128635403
53	22	22.3743867302045	-0.374386730204476
54	16	17.5206356351669	-1.52063563516694
55	24	22.9146115881717	1.08538841182833
56	18	19.9345460368046	-1.93454603680459
57	20	21.6045495135626	-1.60454951356262
58	24	20.3946678425397	3.60533215746029
59	14	17.9317140995585	-3.93171409955845
60	22	20.5212332556349	1.47876674436514
61	24	18.6536785036671	5.34632149633294
62	18	18.4303024611745	-0.430302461174513
63	21	24.4255915394658	-3.42559153946582
64	23	21.9274554036	1.07254459640001
65	17	18.7217875345678	-1.72178753456777
66	22	22.3255886670647	-0.325588667064662
67	24	25.3859684080114	-1.38596840801145
68	21	22.8153956207646	-1.81539562076456
69	22	22.1657491004181	-0.165749100418053
70	16	17.2591365955959	-1.25913659559592
71	21	25.2040750483629	-4.20407504836292
72	23	24.3026035080371	-1.30260350803709
73	22	19.514580837657	2.48541916234302
74	24	22.4251543817276	1.57484561827238
75	24	24.5231020645492	-0.523102064549158
76	16	18.2195067513847	-2.21950675138466
77	16	17.7183545310396	-1.71835453103964
78	21	23.4186320732371	-2.41863207323708
79	26	26.1136424108203	-0.113642410820307
80	15	16.8845466166244	-1.88454661662438
81	25	23.1918060496506	1.80819395034943
82	18	17.821582750884	0.178417249116008
83	23	20.4842866240701	2.51571337592986
84	20	21.2986252955417	-1.29862529554169
85	17	20.759164817462	-3.75916481746202
86	25	24.9945169676929	0.00548303230711119
87	24	22.5692480826879	1.43075191731214
88	17	14.5780131532651	2.42198684673489
89	19	18.843389149632	0.156610850368008
90	20	20.9938787430608	-0.993878743060797
91	15	16.6899000460098	-1.68990004600984
92	27	24.8793828869335	2.12061711306654
93	22	19.5903831635319	2.40961683646811
94	23	23.0564845548718	-0.0564845548718204
95	16	20.3370367015813	-4.33703670158129
96	19	20.8500418708961	-1.85004187089614
97	25	20.7277929477306	4.27220705226938
98	19	19.4077980909133	-0.407798090913332
99	19	19.2715240881752	-0.271524088175187
100	26	25.0330914982788	0.966908501721158
101	21	18.6022642209701	2.39773577902987
102	20	20.1403109728158	-0.140310972815796
103	24	19.948686641961	4.051313358039
104	22	23.5911941270117	-1.59119412701169
105	20	21.5323057410323	-1.53230574103232
106	18	19.6194068875338	-1.61940688753378
107	18	16.7617482425631	1.23825175743687
108	24	21.5665173696736	2.43348263032636
109	24	21.3609328654182	2.63906713458181
110	22	24.5765498925719	-2.57654989257191
111	23	19.9313834264428	3.06861657355719
112	22	20.0065433410742	1.99345665892583
113	20	17.9761545342716	2.02384546572842
114	18	19.9276994656743	-1.92769946567429
115	25	24.6903501894972	0.309649810502811
116	18	18.2151056173744	-0.215105617374351
117	16	17.7075368275458	-1.70753682754581
118	20	19.9553036827894	0.0446963172105687
119	19	18.2093886324	0.790611367599982
120	15	15.9107424131907	-0.910742413190707
121	19	19.1772833759981	-0.177283375998138
122	19	22.1307041984445	-3.13070419844447
123	16	17.3869555697449	-1.38695556974488
124	17	17.5508407935518	-0.55084079355182
125	28	23.3126216377138	4.68737836228616
126	23	22.7911618856223	0.208838114377692
127	25	23.3778749361019	1.62212506389814
128	20	18.6295101307485	1.3704898692515
129	17	20.203267669844	-3.20326766984402
130	23	22.794248620264	0.205751379735988
131	16	19.8416758309848	-3.84167583098482
132	23	24.011392612818	-1.01139261281798
133	11	15.8899711870925	-4.88997118709253
134	18	20.4538793133825	-2.4538793133825
135	24	23.0832868278044	0.91671317219564
136	23	19.008388612753	3.99161138724698
137	21	21.7399751739539	-0.739975173953852
138	16	19.5615700326193	-3.56157003261928
139	24	25.0043549044312	-1.00435490443115
140	23	21.5055480254134	1.49445197458658
141	18	15.6863953759695	2.31360462403053
142	20	20.6862125586204	-0.686212558620399
143	9	18.683415311195	-9.68341531119505
144	24	20.3055951242867	3.69440487571327
145	25	24.7368399253391	0.263160074660941
146	20	18.21765473132	1.78234526867998
147	21	18.9742539558637	2.02574604413625
148	25	22.7410754262094	2.25892457379063
149	22	22.1379069994252	-0.137906999425155
150	21	21.3494891256899	-0.349489125689907
151	21	20.1570070029282	0.842992997071792
152	22	20.3908060900486	1.60919390995139
153	27	23.1418694706609	3.85813052933912
154	24	21.3822064363008	2.61779356369924
155	24	24.2416429607606	-0.241642960760583
156	21	20.4601222308716	0.5398777691284
157	18	20.7329806098738	-2.73298060987381
158	16	16.1333970191681	-0.133397019168116
159	22	19.3034375292024	2.69656247079763
160	20	19.6012175964445	0.398782403555531
161	18	19.4108723768202	-1.41087237682017
162	20	21.1905386266962	-1.19053862669619

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
13	0.949968682086013	0.100062635827973	0.0500313179139865
14	0.902382251249203	0.195235497501594	0.0976177487507972
15	0.833961970180114	0.332076059639773	0.166038029819886
16	0.787718880154491	0.424562239691017	0.212281119845509
17	0.715528033359739	0.568943933280522	0.284471966640261
18	0.636329443717261	0.727341112565477	0.363670556282739
19	0.566638361213805	0.866723277572389	0.433361638786195
20	0.559603573460695	0.88079285307861	0.440396426539305
21	0.496563333057085	0.993126666114169	0.503436666942915
22	0.421124088010425	0.84224817602085	0.578875911989575
23	0.505528745682949	0.988942508634101	0.494471254317051
24	0.482011316000125	0.96402263200025	0.517988683999875
25	0.411693529854217	0.823387059708435	0.588306470145783
26	0.488894079569246	0.977788159138493	0.511105920430754
27	0.430006781376613	0.860013562753226	0.569993218623387
28	0.585294837332489	0.829410325335023	0.414705162667511
29	0.598449988500033	0.803100022999935	0.401550011499968
30	0.538458703187147	0.923082593625707	0.461541296812853
31	0.536464467558681	0.927071064882638	0.463535532441319
32	0.519560574496019	0.960878851007963	0.480439425503981
33	0.499936394837702	0.999872789675405	0.500063605162298
34	0.572101377623636	0.855797244752727	0.427898622376364
35	0.713183848484573	0.573632303030854	0.286816151515427
36	0.662827219154309	0.674345561691383	0.337172780845691
37	0.615579807393832	0.768840385212336	0.384420192606168
38	0.562148068916967	0.875703862166066	0.437851931083033
39	0.505762022302144	0.988475955395712	0.494237977697856
40	0.481351392100526	0.962702784201051	0.518648607899474
41	0.486126499114738	0.972252998229476	0.513873500885262
42	0.454779829056897	0.909559658113795	0.545220170943103
43	0.406470647181246	0.812941294362492	0.593529352818754
44	0.375866964235689	0.751733928471378	0.624133035764311
45	0.435843281578875	0.87168656315775	0.564156718421125
46	0.383962687240296	0.767925374480592	0.616037312759704
47	0.339075138258244	0.678150276516488	0.660924861741756
48	0.756347032343295	0.487305935313409	0.243652967656705
49	0.751436180111088	0.497127639777824	0.248563819888912
50	0.779078573542598	0.441842852914804	0.220921426457402
51	0.75917975533735	0.481640489325301	0.24082024466265
52	0.719031255593119	0.561937488813763	0.280968744406881
53	0.697466891810785	0.605066216378429	0.302533108189215
54	0.663665234496091	0.672669531007817	0.336334765503909
55	0.626586009740418	0.746827980519163	0.373413990259582
56	0.608264810178879	0.783470379642242	0.391735189821121
57	0.573359652049934	0.853280695900132	0.426640347950066
58	0.696637129859221	0.606725740281559	0.303362870140779
59	0.742815065446648	0.514369869106704	0.257184934553352
60	0.718346650622552	0.563306698754895	0.281653349377448
61	0.82881347590712	0.34237304818576	0.17118652409288
62	0.797625689557857	0.404748620884287	0.202374310442143
63	0.835999069316943	0.328001861366115	0.164000930683057
64	0.810733414128572	0.378533171742857	0.189266585871428
65	0.824278207995298	0.351443584009405	0.175721792004702
66	0.794364340535087	0.411271318929826	0.205635659464913
67	0.779255028149405	0.441489943701191	0.220744971850595
68	0.755084406346462	0.489831187307076	0.244915593653538
69	0.71703175132376	0.565936497352481	0.28296824867624
70	0.678796377324234	0.642407245351532	0.321203622675766
71	0.739163366275099	0.521673267449802	0.260836633724901
72	0.706777081955762	0.586445836088475	0.293222918044238
73	0.724812366243379	0.550375267513242	0.275187633756621
74	0.7113513780464	0.5772972439072	0.2886486219536
75	0.671624446866397	0.656751106267205	0.328375553133603
76	0.67976365295041	0.64047269409918	0.32023634704959
77	0.647729761640041	0.704540476719917	0.352270238359959
78	0.637887833354607	0.724224333290787	0.362112166645394
79	0.601801381780583	0.796397236438833	0.398198618219417
80	0.580266274325615	0.839467451348771	0.419733725674385
81	0.563563057193848	0.872873885612305	0.436436942806152
82	0.538266419009837	0.923467161980327	0.461733580990163
83	0.55684205559152	0.88631588881696	0.44315794440848
84	0.524066887176402	0.951866225647196	0.475933112823598
85	0.577453449387449	0.845093101225101	0.422546550612551
86	0.530604605193589	0.938790789612822	0.469395394806411
87	0.507654626883798	0.984690746232405	0.492345373116202
88	0.524641619590204	0.950716760819592	0.475358380409796
89	0.484872088907936	0.969744177815871	0.515127911092064
90	0.458687668357164	0.917375336714328	0.541312331642836
91	0.424262209194188	0.848524418388377	0.575737790805812
92	0.408171170597148	0.816342341194296	0.591828829402852
93	0.409958025328813	0.819916050657626	0.590041974671187
94	0.369674196982022	0.739348393964043	0.630325803017978
95	0.467662663951366	0.935325327902731	0.532337336048635
96	0.452565201261816	0.905130402523632	0.547434798738184
97	0.557914272491674	0.884171455016652	0.442085727508326
98	0.513263238369817	0.973473523260365	0.486736761630183
99	0.471952214399598	0.943904428799196	0.528047785600402
100	0.431052613453887	0.862105226907773	0.568947386546113
101	0.426366891866742	0.852733783733485	0.573633108133258
102	0.379407129255473	0.758814258510947	0.620592870744527
103	0.475615453544102	0.951230907088204	0.524384546455898
104	0.463257009969662	0.926514019939324	0.536742990030338
105	0.428533515244968	0.857067030489936	0.571466484755032
106	0.394904880705232	0.789809761410465	0.605095119294768
107	0.361762904645391	0.723525809290782	0.638237095354609
108	0.373658055804471	0.747316111608942	0.626341944195529
109	0.362699948588944	0.725399897177887	0.637300051411057
110	0.344543837614863	0.689087675229726	0.655456162385137
111	0.375302018697563	0.750604037395126	0.624697981302437
112	0.380657932973118	0.761315865946235	0.619342067026882
113	0.405179974550073	0.810359949100146	0.594820025449927
114	0.366236235382511	0.732472470765023	0.633763764617489
115	0.317359015940394	0.634718031880789	0.682640984059606
116	0.270923102478316	0.541846204956632	0.729076897521684
117	0.242779756506607	0.485559513013214	0.757220243493393
118	0.205601254679578	0.411202509359156	0.794398745320422
119	0.181845793102527	0.363691586205053	0.818154206897473
120	0.172156265697003	0.344312531394006	0.827843734302997
121	0.149415258936711	0.298830517873422	0.850584741063289
122	0.141749976517617	0.283499953035233	0.858250023482383
123	0.115108719343467	0.230217438686935	0.884891280656533
124	0.0895245045083858	0.179049009016772	0.910475495491614
125	0.195018620023877	0.390037240047754	0.804981379976123
126	0.156973455866684	0.313946911733368	0.843026544133316
127	0.146494307461927	0.292988614923853	0.853505692538074
128	0.129005145622554	0.258010291245109	0.870994854377446
129	0.121586867844772	0.243173735689543	0.878413132155228
130	0.101675973662234	0.203351947324468	0.898324026337766
131	0.110112181239886	0.220224362479772	0.889887818760114
132	0.0845997947816791	0.169199589563358	0.915400205218321
133	0.174776190360106	0.349552380720212	0.825223809639894
134	0.162448520056386	0.324897040112772	0.837551479943614
135	0.159251547705655	0.31850309541131	0.840748452294345
136	0.137455888430431	0.274911776860863	0.862544111569569
137	0.13364395454383	0.267287909087661	0.86635604545617
138	0.13139582417798	0.26279164835596	0.86860417582202
139	0.0950992271603755	0.190198454320751	0.904900772839625
140	0.076468559144912	0.152937118289824	0.923531440855088
141	0.0583396995263591	0.116679399052718	0.941660300473641
142	0.042439578887735	0.08487915777547	0.957560421112265
143	0.927310583839807	0.145378832320386	0.0726894161601929
144	0.98841268585207	0.0231746282958606	0.0115873141479303
145	0.979309963776638	0.0413800724467236	0.0206900362233618
146	0.955489693565375	0.0890206128692501	0.0445103064346251
147	0.910813258802392	0.178373482395216	0.0891867411976082
148	0.8391423932382	0.321715213523601	0.1608576067618
149	0.717327175435281	0.565345649129438	0.282672824564719

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	2	0.0145985401459854	OK
10% type I error level	4	0.0291970802919708	OK