Multiple Linear Regression - Estimated Regression Equation

Happiness[t] = + 19.3158785241537 -0.398870553790956Depression[t] -0.00154027507600006t + 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)	19.3158785241537	0.679856	28.4117	0	0
Depression	-0.398870553790956	0.049503	-8.0575	0	0
t	-0.00154027507600006	0.003341	-0.461	0.645435	0.322717

Multiple Linear Regression - Regression Statistics
Multiple R	0.545101721019329
R-squared	0.297135886258234
Adjusted R-squared	0.288294828223746
F-TEST (value)	33.6086342945779
F-TEST (DF numerator)	2
F-TEST (DF denominator)	159
p-value	6.7035266226867e-13
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	1.97207585944176
Sum Squared Residuals	618.364228067478

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	14	14.5278916035863	-0.527891603586283
2	18	14.9252218823012	3.07477811769882
3	11	13.7270699458523	-2.72706994585232
4	12	14.5232707783582	-2.52327077835823
5	16	10.9318955191636	5.06810448083637
6	18	14.5201902282062	3.47980977179377
7	14	10.5299444152207	3.47005558477933
8	14	14.9159802318452	-0.915980231845184
9	15	15.3133105105601	-0.31331051056014
10	15	14.1151585741113	0.884841425888727
11	17	15.3102299604081	1.68977003959186
12	19	16.1064307929141	2.89356920708595
13	10	13.3127966413014	-3.31279664130136
14	16	13.7101269200163	2.28987307998368
15	18	15.3040688601041	2.69593113989586
16	14	13.7070463698643	0.292953630135683
17	14	13.7055060947883	0.294493905211683
18	17	14.9005774810852	2.09942251891482
19	14	15.2979077598001	-1.29790775980014
20	16	14.0997558233513	1.90024417664873
21	18	16.491438871021	1.50856112897899
22	11	13.6978047194083	-2.69780471940832
23	14	14.4940055519142	-0.494005551914228
24	12	13.6947241692563	-1.69472416925632
25	17	14.8897955555532	2.11020444444682
26	9	15.6859963880591	-6.68599638805909
27	16	14.8867150054012	1.11328499459882
28	14	13.2896925151614	0.710307484838639
29	15	13.6870227938763	1.31297720612368
30	11	14.0843530725913	-3.08435307259127
31	16	15.6782950126791	0.321704987320906
32	13	13.2835314148574	-0.28353141485736
33	17	15.2763439087361	1.72365609126386
34	15	14.8759330798692	0.124066920130817
35	14	14.0766516972113	-0.0766516972112713
36	16	16.06946419109	-0.069464191090049
37	9	11.2814772705226	-2.28147727052258
38	15	14.4709014257742	0.529098574225773
39	17	15.2671022582801	1.73289774171986
40	13	15.2655619832041	-2.26556198320414
41	15	15.6628922619191	-0.662892261919093
42	16	13.6669992178883	2.33300078211168
43	16	16.058682265558	-0.0586822655580486
44	12	13.6639186677363	-1.66391866773632
45	12	14.8589900540332	-2.85899005403318
46	11	14.0597086713753	-3.05970867137527
47	15	15.6536506114631	-0.653650611463093
48	15	14.8543692288052	0.145630771194818
49	17	13.2573467385654	3.74265326143464
50	13	14.8512886786532	-1.85128867865318
51	16	15.2486189573681	0.751381042631863
52	14	13.6515964671283	0.348403532871685
53	11	12.0545739768885	-1.05457397688849
54	12	13.6485159169763	-1.64851591697631
55	12	14.8435873032732	-2.84358730327318
56	15	14.4431764744062	0.556823525593774
57	16	14.0427656455393	1.95723435446073
58	15	15.6367075856271	-0.636707585627092
59	12	15.2362967567601	-3.23629675676014
60	12	13.2404037127294	-1.24040371272936
61	8	11.2445106686986	-3.24451066869858
62	13	14.4339348239502	-1.43393482395023
63	11	14.4323945488742	-3.43239454887423
64	14	13.6331131662163	0.366886833783686
65	15	14.0304434449313	0.969556555068731
66	10	14.8266442774372	-4.82664427743718
67	11	12.4318806796154	-1.43188067961545
68	12	14.4246931734942	-2.42469317349422
69	15	14.0242823446273	0.975717655372731
70	15	13.6238715157603	1.37612848423969
71	14	14.0212017944753	-0.0212017944752693
72	16	13.2219204118174	2.77807958818264
73	15	14.0181212443233	0.981878755676731
74	15	15.2131926306201	-0.213192630620136
75	13	14.8127818017532	-1.81278180175318
76	12	11.6202770963495	0.379722903650464
77	17	14.0119601440193	2.98803985598073
78	13	12.4149376537794	0.585062346220553
79	15	14.0088795938673	0.991120406132731
80	13	15.6028215339551	-2.60282153395509
81	15	14.8035401512972	0.19645984870282
82	16	15.2008704300121	0.799129569987865
83	15	15.5982007087271	-0.598200708727091
84	16	14.4000487722782	1.59995122772178
85	15	14.3985084972022	0.601491502797776
86	14	13.9980976683353	0.00190233166473155
87	15	13.9965573932593	1.00344260674073
88	14	14.3938876719742	-0.393887671974224
89	13	13.1957357355254	-0.195735735525357
90	7	10.4021015839127	-3.40210158391267
91	17	13.9903962929553	3.00960370704473
92	13	13.1911149102974	-0.191114910297357
93	15	13.9873157428033	1.01268425719673
94	14	13.1880343601454	0.811965639854643
95	13	15.1808468540241	-2.18084685402413
96	16	14.7804360251572	1.21956397484282
97	12	12.7845429811264	-0.784542981126401
98	14	14.7773554750052	-0.777355475005179
99	17	14.7758151999292	2.22418480007082
100	15	15.1731454786441	-0.173145478644134
101	17	15.1716052035681	1.82839479643187
102	12	12.7768416057464	-0.7768416057464
103	16	14.3707835458342	1.62921645416578
104	11	14.7681138245492	-3.76811382454918
105	15	12.7722207805184	2.2277792194816
106	9	11.5740688440695	-2.57406884406953
107	16	14.7634929993212	1.23650700067882
108	15	12.7675999552904	2.2324000447096
109	10	13.1649302340054	-3.16493023400536
110	10	9.57355497481076	0.426445025189244
111	15	13.5607202376443	1.43927976235569
112	11	13.1603094087774	-2.16030940877736
113	13	14.7542513488652	-1.75425134886518
114	14	13.1572288586254	0.842771141374644
115	18	14.3523002449222	3.64769975507778
116	16	15.1485010774281	0.851498922571867
117	14	13.5514785871883	0.448521412811689
118	14	13.9488088659033	0.0511911340967334
119	14	15.5427508059911	-1.54275080599109
120	14	13.1479872081694	0.852012791830645
121	12	13.1464469330934	-1.14644693309336
122	14	13.5437772118083	0.456222788191689
123	15	14.7388485981052	0.261151401894822
124	15	15.933919984402	-0.933919984402044
125	15	14.7357680479532	0.264231952046823
126	13	14.7342277728772	-1.73422777287718
127	17	15.929299159174	1.07070084082596
128	17	15.1300177765161	1.86998222348387
129	19	14.7296069476492	4.27039305235082
130	15	13.9303255649913	1.06967443500873
131	13	14.7265263974972	-1.72652639749718
132	9	11.1351511383026	-2.13515113830258
133	15	15.1223164011361	-0.122316401136132
134	15	13.1264233571054	1.87357664289465
135	15	14.3214947434022	0.678505256597779
136	16	13.5222133607443	2.47778663925569
137	11	9.93083810154971	1.06916189845029
138	14	13.5191328105923	0.48086718940769
139	11	12.7198514279344	-1.7198514279344
140	15	14.7126639218132	0.287336078186823
141	13	14.3122530929462	-1.31225309294622
142	15	15.1084539254521	-0.108453925452132
143	16	13.5114314352123	2.48856856478769
144	14	14.3076322677182	-0.307632267718221
145	15	14.3060919926422	0.693908007357779
146	16	14.7034222713572	1.29657772864282
147	16	14.3030114424902	1.69698855750978
148	11	13.9026006136233	-2.90260061362326
149	12	14.6988014461292	-2.69880144612918
150	9	11.5062967407255	-2.50629674072553
151	16	14.2968503421862	1.70314965781378
152	13	12.3009572981554	0.699042701844558
153	16	15.4903814534071	0.509618546592913
154	12	14.2922295169582	-2.29222951695822
155	9	11.4985953653455	-2.49859536534553
156	13	11.8959256440605	1.10407435593951
157	13	13.0909970303574	-0.0909970303573532
158	14	13.4883273090723	0.511672690927691
159	19	14.6833986953692	4.31660130463082
160	13	15.4795995278751	-2.47959952787509
161	12	11.8882242686805	0.111775731319514
162	13	12.6844251011864	0.315574898813603

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
6	0.987817914429478	0.0243641711410433	0.0121820855705216
7	0.978799101065826	0.0424017978683479	0.021200898934174
8	0.969972867390968	0.0600542652180637	0.0300271326090319
9	0.945141412801351	0.109717174397298	0.0548585871986492
10	0.909692690883509	0.180614618232983	0.0903073091164913
11	0.884285213586655	0.231429572826689	0.115714786413345
12	0.892772475681159	0.214455048637682	0.107227524318841
13	0.985838765650988	0.0283224686980236	0.0141612343490118
14	0.980642777558507	0.0387144448829867	0.0193572224414933
15	0.978691004592318	0.0426179908153643	0.0213089954076821
16	0.971688046096355	0.0566239078072903	0.0283119539036451
17	0.96123645846265	0.0775270830747003	0.0387635415373502
18	0.951580578015594	0.0968388439688116	0.0484194219844058
19	0.947952110547308	0.104095778905384	0.0520478894526919
20	0.93413468744584	0.13173062510832	0.0658653125541601
21	0.919093781593838	0.161812436812325	0.0809062184061624
22	0.95679404073824	0.0864119185235207	0.0432059592617603
23	0.942616488875755	0.11476702224849	0.0573835111242452
24	0.938410953712928	0.123178092574145	0.0615890462870724
25	0.940117877721599	0.119764244556803	0.0598821222784013
26	0.996238891084436	0.00752221783112859	0.0037611089155643
27	0.995652171981348	0.00869565603730352	0.00434782801865176
28	0.993922801063638	0.0121543978727244	0.00607719893636221
29	0.992663983882902	0.0146720322341969	0.00733601611709846
30	0.994159836988509	0.011680326022982	0.00584016301149102
31	0.99239070926903	0.0152185814619404	0.00760929073097018
32	0.988960366277855	0.0220792674442892	0.0110396337221446
33	0.990100356502774	0.0197992869944518	0.00989964349722591
34	0.98632079844806	0.0273584031038791	0.0136792015519395
35	0.980984904479454	0.0380301910410923	0.0190150955205462
36	0.97461326797168	0.0507734640566395	0.0253867320283198
37	0.974797636529453	0.0504047269410947	0.0252023634705473
38	0.968893079204518	0.0622138415909639	0.0311069207954819
39	0.971049671576997	0.0579006568460069	0.0289503284230035
40	0.968200843584667	0.0635983128306664	0.0317991564153332
41	0.957927108383638	0.084145783232724	0.042072891616362
42	0.967256179630056	0.0654876407398876	0.0327438203699438
43	0.957600081829373	0.0847998363412539	0.0423999181706269
44	0.94968381337016	0.100632373259679	0.0503161866298397
45	0.952315721828215	0.0953685563435706	0.0476842781717853
46	0.956555070952271	0.0868898580954587	0.0434449290477294
47	0.944647892199961	0.110704215600078	0.055352107800039
48	0.933378323659924	0.133243352680152	0.0666216763400759
49	0.973850109484612	0.0522997810307755	0.0261498905153878
50	0.968957062888485	0.0620858742230302	0.0310429371115151
51	0.964435265970101	0.0711294680597976	0.0355647340298988
52	0.95599947347064	0.0880010530587195	0.0440005265293598
53	0.94513716194923	0.10972567610154	0.0548628380507702
54	0.934983518865746	0.130032962268508	0.0650164811342539
55	0.937706571090041	0.124586857819918	0.0622934289099589
56	0.928681681169874	0.142636637660253	0.0713183188301263
57	0.938743730979267	0.122512538041466	0.061256269020733
58	0.923690830912815	0.15261833817437	0.0763091690871852
59	0.935182050326002	0.129635899347995	0.0648179496739976
60	0.921109948557209	0.157780102885582	0.0788900514427912
61	0.933972077840953	0.132055844318094	0.066027922159047
62	0.921546130789095	0.15690773842181	0.0784538692109048
63	0.93777619758796	0.12444760482408	0.0622238024120401
64	0.928920454357311	0.142159091285378	0.0710795456426888
65	0.925631894017057	0.148736211965885	0.0743681059829425
66	0.970115135580862	0.0597697288382766	0.0298848644191383
67	0.964364180567471	0.0712716388650578	0.0356358194325289
68	0.966012247150212	0.0679755056995754	0.0339877528497877
69	0.964891018057195	0.0702179638856101	0.0351089819428051
70	0.965948157017577	0.068103685964846	0.034051842982423
71	0.958798258507951	0.0824034829840975	0.0412017414920487
72	0.97398671206807	0.0520265758638599	0.0260132879319299
73	0.971085183233607	0.0578296335327862	0.0289148167663931
74	0.964257184954312	0.0714856300913762	0.0357428150456881
75	0.961910179134602	0.0761796417307959	0.038089820865398
76	0.953057392707905	0.0938852145841894	0.0469426072920947
77	0.971068803727479	0.0578623925450415	0.0289311962725207
78	0.964572366555452	0.0708552668890968	0.0354276334445484
79	0.959636221419054	0.0807275571618925	0.0403637785809463
80	0.965755295507023	0.068489408985954	0.034244704492977
81	0.957826957373046	0.0843460852539084	0.0421730426269542
82	0.951070644053666	0.0978587118926676	0.0489293559463338
83	0.941446804157151	0.117106391685699	0.0585531958428495
84	0.939557206354822	0.120885587290355	0.0604427936451777
85	0.927644825202128	0.144710349595743	0.0723551747978716
86	0.911198436505408	0.177603126989184	0.088801563494592
87	0.898838649260032	0.202322701479937	0.101161350739968
88	0.878470558879803	0.243058882240394	0.121529441120197
89	0.853903146825496	0.292193706349008	0.146096853174504
90	0.894054896276326	0.211890207447348	0.105945103723674
91	0.923118710593495	0.15376257881301	0.0768812894065049
92	0.905337525903053	0.189324948193893	0.0946624740969465
93	0.891697943665671	0.216604112668659	0.108302056334329
94	0.874207133721673	0.251585732556654	0.125792866278327
95	0.881122519303679	0.237754961392643	0.118877480696321
96	0.867408873206239	0.265182253587522	0.132591126793761
97	0.844502595838231	0.310994808323538	0.155497404161769
98	0.821832760457777	0.356334479084445	0.178167239542223
99	0.830499182754001	0.339001634491998	0.169500817245999
100	0.800683133909045	0.398633732181911	0.199316866090955
101	0.795813871600861	0.408372256798277	0.204186128399139
102	0.765239413878399	0.469521172243203	0.234760586121601
103	0.754369131366516	0.491261737266969	0.245630868633484
104	0.849772736560882	0.300454526878236	0.150227263439118
105	0.85896467422787	0.282070651544259	0.14103532577213
106	0.876821736506131	0.246356526987738	0.123178263493869
107	0.859593630931477	0.280812738137046	0.140406369068523
108	0.868553618831469	0.262892762337061	0.131446381168531
109	0.910589582026535	0.178820835946931	0.0894104179734655
110	0.890269923389084	0.219460153221832	0.109730076610916
111	0.878222494520362	0.243555010959276	0.121777505479638
112	0.888213955755804	0.223572088488391	0.111786044244196
113	0.89383942723785	0.212321145524299	0.10616057276215
114	0.871561004659623	0.256877990680754	0.128438995340377
115	0.922000392284613	0.155999215430774	0.0779996077153869
116	0.904085021561346	0.191829956877307	0.0959149784386536
117	0.880845330477098	0.238309339045805	0.119154669522902
118	0.852612798532208	0.294774402935584	0.147387201467792
119	0.850738561758183	0.298522876483635	0.149261438241817
120	0.822705455381351	0.354589089237299	0.177294544618649
121	0.802943792654645	0.39411241469071	0.197056207345355
122	0.764063462474434	0.471873075051131	0.235936537525566
123	0.720920176695385	0.558159646609229	0.279079823304615
124	0.702339506801058	0.595320986397885	0.297660493198942
125	0.654837789859388	0.690324420281223	0.345162210140611
126	0.679312105377192	0.641375789245616	0.320687894622808
127	0.632391509898461	0.735216980203078	0.367608490101539
128	0.600094537847773	0.799810924304454	0.399905462152227
129	0.754059305959485	0.491881388081029	0.245940694040515
130	0.718160863557028	0.563678272885944	0.281839136442972
131	0.717902964827487	0.564194070345026	0.282097035172513
132	0.737538876156159	0.524922247687683	0.262461123843841
133	0.69144699154871	0.617106016902581	0.30855300845129
134	0.668625061940244	0.662749876119512	0.331374938059756
135	0.611118195482257	0.777763609035486	0.388881804517743
136	0.639628750587274	0.720742498825451	0.360371249412726
137	0.625953314356307	0.748093371287387	0.374046685643693
138	0.575278978290611	0.849442043418777	0.424721021709389
139	0.532348951277772	0.935302097444455	0.467651048722228
140	0.465083383119468	0.930166766238937	0.534916616880531
141	0.422313371341597	0.844626742683194	0.577686628658403
142	0.355189355622378	0.710378711244755	0.644810644377622
143	0.416517931143702	0.833035862287403	0.583482068856298
144	0.344369700065698	0.688739400131395	0.655630299934302
145	0.295864230948808	0.591728461897616	0.704135769051192
146	0.286495275364905	0.572990550729811	0.713504724635095
147	0.363815044602544	0.727630089205088	0.636184955397456
148	0.333514589758546	0.667029179517091	0.666485410241454
149	0.338938866007399	0.677877732014798	0.661061133992601
150	0.327106748442129	0.654213496884258	0.672893251557871
151	0.299350096283865	0.59870019256773	0.700649903716135
152	0.250874642055153	0.501749284110306	0.749125357944847
153	0.197814050952882	0.395628101905764	0.802185949047118
154	0.16144440171477	0.322888803429539	0.83855559828523
155	0.20449008287777	0.40898016575554	0.79550991712223
156	0.114992131646046	0.229984263292091	0.885007868353954

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	2	0.0132450331125828	NOK
5% type I error level	15	0.0993377483443709	NOK
10% type I error level	51	0.337748344370861	NOK