Multiple Linear Regression - Estimated Regression Equation

Connected[t] = + 31.7314276893716 + 0.206028458364907Happiness[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)	31.7314276893716	1.607567	19.7388	0	0
Happiness	0.206028458364907	0.112977	1.8236	0.070074	0.035037

Multiple Linear Regression - Regression Statistics
Multiple R	0.142695535921038
R-squared	0.0203620159717923
Adjusted R-squared	0.0142392785716159
F-TEST (value)	3.32563927553156
F-TEST (DF numerator)	1
F-TEST (DF denominator)	160
p-value	0.0700735573932146
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	3.35101318488899
Sum Squared Residuals	1796.68629844798

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	41	34.6158261064804	6.38417389351958
2	39	35.4399399399399	3.56006006006006
3	30	33.9977407313856	-3.99774073138559
4	31	34.2037691897505	-3.2037691897505
5	34	35.0278830232101	-1.02788302321012
6	35	35.4399399399399	-0.439939939939938
7	39	34.6158261064803	4.38417389351969
8	34	34.6158261064803	-0.615826106480312
9	36	34.8218545648452	1.17814543515478
10	37	34.8218545648452	2.17814543515478
11	38	35.233911481575	2.76608851842497
12	36	35.6459683983048	0.354031601695155
13	38	33.7917122730207	4.20828772697932
14	39	35.0278830232101	3.97211697678988
15	33	35.4399399399399	-2.43993993993994
16	32	34.6158261064803	-2.61582610648031
17	36	34.6158261064803	1.38417389351969
18	38	35.233911481575	2.76608851842497
19	39	34.6158261064803	4.38417389351969
20	32	35.0278830232101	-3.02788302321012
21	32	35.4399399399399	-3.43993993993994
22	31	33.9977407313856	-2.99774073138559
23	39	34.6158261064803	4.38417389351969
24	37	34.2037691897505	2.7962308102495
25	39	35.233911481575	3.76608851842497
26	41	33.5856838146558	7.41431618534422
27	36	35.0278830232101	0.972116976789875
28	33	34.6158261064803	-1.61582610648031
29	33	34.8218545648452	-1.82185456484522
30	34	33.9977407313856	0.00225926861440825
31	31	35.0278830232101	-4.02788302321012
32	27	34.4097976481154	-7.4097976481154
33	37	35.233911481575	1.76608851842497
34	34	34.8218545648452	-0.821854564845218
35	34	34.6158261064803	-0.615826106480312
36	32	35.0278830232101	-3.02788302321012
37	29	33.5856838146558	-4.58568381465578
38	36	34.8218545648452	1.17814543515478
39	29	35.233911481575	-6.23391148157503
40	35	34.4097976481154	0.590202351884595
41	37	34.8218545648452	2.17814543515478
42	34	35.0278830232101	-1.02788302321012
43	38	35.0278830232101	2.97211697678988
44	35	34.2037691897505	0.796230810249502
45	38	34.2037691897505	3.7962308102495
46	37	33.9977407313856	3.00225926861441
47	38	34.8218545648452	3.17814543515478
48	33	34.8218545648452	-1.82185456484522
49	36	35.233911481575	0.766088518424969
50	38	34.4097976481154	3.59020235188459
51	32	35.0278830232101	-3.02788302321012
52	32	34.6158261064803	-2.61582610648031
53	32	33.9977407313856	-1.99774073138559
54	34	34.2037691897505	-0.203769189750498
55	32	34.2037691897505	-2.2037691897505
56	37	34.8218545648452	2.17814543515478
57	39	35.0278830232101	3.97211697678988
58	29	34.8218545648452	-5.82185456484522
59	37	34.2037691897505	2.7962308102495
60	35	34.2037691897505	0.796230810249502
61	30	33.3796553562909	-3.37965535629087
62	38	34.4097976481154	3.59020235188459
63	34	33.9977407313856	0.00225926861440825
64	31	34.6158261064803	-3.61582610648031
65	34	34.8218545648452	-0.821854564845218
66	35	33.7917122730207	1.20828772697932
67	36	33.9977407313856	2.00225926861441
68	30	34.2037691897505	-4.2037691897505
69	39	34.8218545648452	4.17814543515478
70	35	34.8218545648452	0.178145435154782
71	38	34.6158261064803	3.38417389351969
72	31	35.0278830232101	-4.02788302321012
73	34	34.8218545648452	-0.821854564845218
74	38	34.8218545648452	3.17814543515478
75	34	34.4097976481154	-0.409797648115405
76	39	34.2037691897505	4.7962308102495
77	37	35.233911481575	1.76608851842497
78	34	34.4097976481154	-0.409797648115405
79	28	34.8218545648452	-6.82185456484522
80	37	34.4097976481154	2.59020235188459
81	33	34.8218545648452	-1.82185456484522
82	37	35.0278830232101	1.97211697678988
83	35	34.8218545648452	0.178145435154782
84	37	35.0278830232101	1.97211697678988
85	32	34.8218545648452	-2.82185456484522
86	33	34.6158261064803	-1.61582610648031
87	38	34.8218545648452	3.17814543515478
88	33	34.6158261064803	-1.61582610648031
89	29	34.4097976481154	-5.4097976481154
90	33	33.173626897926	-0.173626897925965
91	31	35.233911481575	-4.23391148157503
92	36	34.4097976481154	1.5902023518846
93	35	34.8218545648452	0.178145435154782
94	32	34.6158261064803	-2.61582610648031
95	29	34.4097976481154	-5.4097976481154
96	39	35.0278830232101	3.97211697678988
97	37	34.2037691897505	2.7962308102495
98	35	34.6158261064803	0.384173893519688
99	37	35.233911481575	1.76608851842497
100	32	34.8218545648452	-2.82185456484522
101	38	35.233911481575	2.76608851842497
102	37	34.2037691897505	2.7962308102495
103	36	35.0278830232101	0.972116976789875
104	32	33.9977407313856	-1.99774073138559
105	33	34.8218545648452	-1.82185456484522
106	40	33.5856838146558	6.41431618534422
107	38	35.0278830232101	2.97211697678988
108	41	34.8218545648452	6.17814543515478
109	36	33.7917122730207	2.20828772697932
110	43	33.7917122730207	9.20828772697931
111	30	34.8218545648452	-4.82185456484522
112	31	33.9977407313856	-2.99774073138559
113	32	34.4097976481154	-2.40979764811541
114	32	34.6158261064803	-2.61582610648031
115	37	35.4399399399399	1.56006006006006
116	37	35.0278830232101	1.97211697678988
117	33	34.6158261064803	-1.61582610648031
118	34	34.6158261064803	-0.615826106480312
119	33	34.6158261064803	-1.61582610648031
120	38	34.6158261064803	3.38417389351969
121	33	34.2037691897505	-1.2037691897505
122	31	34.6158261064803	-3.61582610648031
123	38	34.8218545648452	3.17814543515478
124	37	34.8218545648452	2.17814543515478
125	33	34.8218545648452	-1.82185456484522
126	31	34.4097976481154	-3.4097976481154
127	39	35.233911481575	3.76608851842497
128	44	35.233911481575	8.76608851842497
129	33	35.6459683983048	-2.64596839830484
130	35	34.8218545648452	0.178145435154782
131	32	34.4097976481154	-2.40979764811541
132	28	33.5856838146558	-5.58568381465578
133	40	34.8218545648452	5.17814543515478
134	27	34.8218545648452	-7.82185456484522
135	37	34.8218545648452	2.17814543515478
136	32	35.0278830232101	-3.02788302321012
137	28	33.9977407313856	-5.99774073138559
138	34	34.6158261064803	-0.615826106480312
139	30	33.9977407313856	-3.99774073138559
140	35	34.8218545648452	0.178145435154782
141	31	34.4097976481154	-3.4097976481154
142	32	34.8218545648452	-2.82185456484522
143	30	35.0278830232101	-5.02788302321012
144	30	34.6158261064803	-4.61582610648031
145	31	34.8218545648452	-3.82185456484522
146	40	35.0278830232101	4.97211697678988
147	32	35.0278830232101	-3.02788302321012
148	36	33.9977407313856	2.00225926861441
149	32	34.2037691897505	-2.2037691897505
150	35	33.5856838146558	1.41431618534422
151	38	35.0278830232101	2.97211697678988
152	42	34.4097976481154	7.5902023518846
153	34	35.0278830232101	-1.02788302321012
154	35	34.2037691897505	0.796230810249502
155	35	33.5856838146558	1.41431618534422
156	33	34.4097976481154	-1.4097976481154
157	36	34.4097976481154	1.5902023518846
158	32	34.6158261064803	-2.61582610648031
159	33	35.6459683983048	-2.64596839830484
160	34	34.4097976481154	-0.409797648115405
161	32	34.2037691897505	-2.2037691897505
162	34	34.4097976481154	-0.409797648115405

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
5	0.802234807079616	0.395530385840768	0.197765192920384
6	0.771705910675981	0.456588178648037	0.228294089324018
7	0.800859389374287	0.398281221251427	0.199140610625713
8	0.711145987113676	0.577708025772649	0.288854012886324
9	0.606723889234012	0.786552221531977	0.393276110765988
10	0.514092868210578	0.971814263578844	0.485907131789422
11	0.416793630790706	0.833587261581411	0.583206369209294
12	0.378758049658837	0.757516099317674	0.621241950341163
13	0.454738408918831	0.909476817837662	0.545261591081169
14	0.422395228975393	0.844790457950786	0.577604771024607
15	0.456059414554455	0.91211882910891	0.543940585445545
16	0.46475042882373	0.92950085764746	0.53524957117627
17	0.388898535348964	0.777797070697929	0.611101464651036
18	0.336469129594329	0.672938259188658	0.663530870405671
19	0.346019901895804	0.692039803791609	0.653980098104196
20	0.38448031413124	0.768960628262479	0.61551968586876
21	0.426057460104818	0.852114920209636	0.573942539895182
22	0.440371567576326	0.880743135152652	0.559628432423674
23	0.460934684467793	0.921869368935587	0.539065315532207
24	0.421176380519896	0.842352761039792	0.578823619480104
25	0.410134758014737	0.820269516029474	0.589865241985263
26	0.557598197058126	0.884803605883749	0.442401802941874
27	0.496298300553552	0.992596601107105	0.503701699446448
28	0.476286537717443	0.952573075434887	0.523713462282557
29	0.455155324713563	0.910310649427126	0.544844675286437
30	0.407323317108049	0.814646634216098	0.592676682891951
31	0.459927382568316	0.919854765136633	0.540072617431684
32	0.720696938231576	0.558606123536848	0.279303061768424
33	0.681138699248894	0.637722601502211	0.318861300751106
34	0.636511668556546	0.726976662886908	0.363488331443454
35	0.588732553477596	0.822534893044808	0.411267446522404
36	0.584904689508261	0.830190620983479	0.415095310491739
37	0.646378710275244	0.707242579449512	0.353621289724756
38	0.59935603608089	0.801287927838219	0.400643963919109
39	0.718197384829021	0.563605230341959	0.281802615170979
40	0.67289556045187	0.65420887909626	0.32710443954813
41	0.642318077956846	0.715363844086309	0.357681922043154
42	0.598073779873527	0.803852440252945	0.401926220126473
43	0.583611676956861	0.832776646086278	0.416388323043139
44	0.534528246199222	0.930943507601556	0.465471753800778
45	0.538514113111556	0.922971773776888	0.461485886888444
46	0.517988919398279	0.964022161203442	0.482011080601721
47	0.50635561791488	0.98728876417024	0.49364438208512
48	0.475179063620915	0.95035812724183	0.524820936379085
49	0.427909784450281	0.855819568900562	0.572090215549719
50	0.424831087184226	0.849662174368451	0.575168912815774
51	0.42012625493651	0.84025250987302	0.57987374506349
52	0.407872495845841	0.815744991691681	0.592127504154159
53	0.385836745832029	0.771673491664057	0.614163254167971
54	0.341727930027538	0.683455860055077	0.658272069972462
55	0.321862425551551	0.643724851103102	0.678137574448449
56	0.295589210130631	0.591178420261261	0.704410789869369
57	0.309629332391091	0.619258664782182	0.690370667608909
58	0.405004743535718	0.810009487071437	0.594995256464282
59	0.386737385552143	0.773474771104286	0.613262614447857
60	0.344051769466613	0.688103538933226	0.655948230533387
61	0.351765980238723	0.703531960477446	0.648234019761277
62	0.354853333500076	0.709706667000152	0.645146666499924
63	0.312663501009281	0.625327002018562	0.687336498990719
64	0.322308963670111	0.644617927340221	0.677691036329889
65	0.284744246947284	0.569488493894568	0.715255753052716
66	0.250814128847351	0.501628257694703	0.749185871152649
67	0.226521382786903	0.453042765573806	0.773478617213097
68	0.249725708325429	0.499451416650858	0.750274291674571
69	0.26845277088681	0.536905541773619	0.73154722911319
70	0.232145642339351	0.464291284678702	0.767854357660649
71	0.231318293155692	0.462636586311385	0.768681706844307
72	0.248802069546902	0.497604139093805	0.751197930453098
73	0.21640508988339	0.432810179766781	0.78359491011661
74	0.21209721626562	0.424194432531239	0.78790278373438
75	0.181364484143689	0.362728968287379	0.818635515856311
76	0.212530908771645	0.425061817543291	0.787469091228355
77	0.189247187655424	0.378494375310848	0.810752812344576
78	0.160890569004497	0.321781138008994	0.839109430995503
79	0.263796048684398	0.527592097368797	0.736203951315602
80	0.248556348904978	0.497112697809957	0.751443651095022
81	0.224208537852097	0.448417075704195	0.775791462147903
82	0.20256284853539	0.40512569707078	0.79743715146461
83	0.172349321519285	0.34469864303857	0.827650678480715
84	0.154126835571178	0.308253671142357	0.845873164428822
85	0.146424123879048	0.292848247758095	0.853575876120952
86	0.127502939148818	0.255005878297637	0.872497060851182
87	0.125027374425574	0.250054748851149	0.874972625574426
88	0.108055691271109	0.216111382542218	0.891944308728891
89	0.144590746275118	0.289181492550236	0.855409253724882
90	0.120544378864967	0.241088757729934	0.879455621135033
91	0.133641310783659	0.267282621567317	0.866358689216341
92	0.115633442765931	0.231266885531863	0.884366557234069
93	0.0950313521232469	0.190062704246494	0.904968647876753
94	0.0873167870262334	0.174633574052467	0.912683212973767
95	0.117997287406286	0.235994574812573	0.882002712593714
96	0.126405028702829	0.252810057405658	0.873594971297171
97	0.11921636479369	0.238432729587381	0.88078363520631
98	0.0982212142143053	0.196442428428611	0.901778785785695
99	0.0846021946284325	0.169204389256865	0.915397805371568
100	0.0787495043288549	0.15749900865771	0.921250495671145
101	0.0734033503798917	0.146806700759783	0.926596649620108
102	0.0686455186922206	0.137291037384441	0.931354481307779
103	0.05583168827495	0.1116633765499	0.94416831172505
104	0.0474868747279269	0.0949737494558538	0.952513125272073
105	0.0395434997988364	0.0790869995976727	0.960456500201164
106	0.0744006528077298	0.14880130561546	0.92559934719227
107	0.0708362948077511	0.141672589615502	0.929163705192249
108	0.1179688086065	0.235937617213	0.8820311913935
109	0.108545326424739	0.217090652849477	0.891454673575261
110	0.371308282770502	0.742616565541005	0.628691717229498
111	0.413064272743047	0.826128545486094	0.586935727256953
112	0.390165150303452	0.780330300606905	0.609834849696548
113	0.360160485861517	0.720320971723035	0.639839514138483
114	0.336042177608309	0.672084355216618	0.663957822391691
115	0.298927889208601	0.597855778417202	0.701072110791399
116	0.272299639528153	0.544599279056305	0.727700360471847
117	0.238118373814967	0.476236747629934	0.761881626185033
118	0.201590440463263	0.403180880926526	0.798409559536737
119	0.17263679671587	0.34527359343174	0.82736320328413
120	0.179671529439022	0.359343058878044	0.820328470560978
121	0.149935041836035	0.29987008367207	0.850064958163965
122	0.146426666704307	0.292853333408614	0.853573333295693
123	0.146700439761741	0.293400879523481	0.853299560238259
124	0.133333657220805	0.266667314441609	0.866666342779195
125	0.111459677648223	0.222919355296446	0.888540322351777
126	0.103705703594393	0.207411407188786	0.896294296405607
127	0.110933290586797	0.221866581173595	0.889066709413203
128	0.365952713201696	0.731905426403391	0.634047286798304
129	0.329818308176638	0.659636616353277	0.670181691823362
130	0.28510151737587	0.570203034751741	0.71489848262413
131	0.249827774308925	0.499655548617849	0.750172225691075
132	0.31064230428584	0.621284608571679	0.68935769571416
133	0.438681266718223	0.877362533436446	0.561318733281777
134	0.633231791025509	0.733536417948983	0.366768208974492
135	0.628537660388488	0.742924679223023	0.371462339611512
136	0.589444043235301	0.821111913529399	0.410555956764699
137	0.714150382231569	0.571699235536863	0.285849617768431
138	0.65555052988369	0.688898940232619	0.34444947011631
139	0.692811173244231	0.614377653511539	0.307188826755769
140	0.6374705071235	0.725058985753	0.3625294928765
141	0.63268654175217	0.734626916495659	0.36731345824783
142	0.590410353343973	0.819179293312053	0.409589646656027
143	0.632810917727821	0.734378164544357	0.367189082272179
144	0.697083633752116	0.605832732495768	0.302916366247884
145	0.721636912401483	0.556726175197035	0.278363087598517
146	0.839871029261703	0.320257941476595	0.160128970738297
147	0.819139261240645	0.361721477518709	0.180860738759355
148	0.765903499613604	0.468193000772791	0.234096500386396
149	0.749590292110946	0.500819415778109	0.250409707889054
150	0.667680272851888	0.664639454296225	0.332319727148112
151	0.694037392032578	0.611925215934844	0.305962607967422
152	0.99663835725986	0.00672328548028085	0.00336164274014043
153	0.991796797042496	0.0164064059150074	0.00820320295750369
154	0.983071273166669	0.0338574536666628	0.0169287268333314
155	0.962552053394678	0.0748958932106445	0.0374479466053223
156	0.913307265957957	0.173385468084086	0.0866927340420428
157	0.950444645327732	0.0991107093445358	0.0495553546722679

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	1	0.0065359477124183	OK
5% type I error level	3	0.0196078431372549	OK
10% type I error level	7	0.0457516339869281	OK