Multiple Linear Regression - Estimated Regression Equation

Happiness[t] = + 15.5161790562666 + 0.921967037106414Gender[t] + 0.0328499179784167Connected[t] + 0.0313861616355641Separate[t] -0.4011941225649Depression[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)	15.5161790562666	2.011915	7.7121	0	0
Gender	0.921967037106414	0.320831	2.8737	0.004619	0.00231
Connected	0.0328499179784167	0.048372	0.6791	0.498069	0.249034
Separate	0.0313861616355641	0.047079	0.6667	0.505964	0.252982
Depression	-0.4011941225649	0.048178	-8.3273	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.587100754320178
R-squared	0.344687295723323
Adjusted R-squared	0.32799143064621
F-TEST (value)	20.6450695505338
F-TEST (DF numerator)	4
F-TEST (DF denominator)	157
p-value	1.0946799022804e-13
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	1.91628880101747
Sum Squared Residuals	576.529554718081

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	14	15.0853044389672	-1.08530443896719
2	18	15.2324817557618	2.76751824423817
3	11	13.8274086111681	-2.82740861116807
4	12	13.6779074138987	-1.67790741389875
5	16	11.2132217483986	4.78677825160143
6	18	14.6057294763766	3.39427052362343
7	14	10.7879602459124	3.21203975408763
8	14	15.193776812412	-1.193776812412
9	15	15.6292846092982	-0.629284609298171
10	15	14.5527106444886	0.44728935551142
11	17	14.6474727616063	2.35252723839367
12	19	16.4002866927924	2.59971330720759
13	10	12.7670467953241	-2.76704679532409
14	16	14.2172163578805	1.78278364211949
15	18	15.593507178634	2.40649282136595
16	14	12.9083690867474	1.09163091325264
17	14	13.0083825970255	0.991617402974535
18	17	15.3879488075968	1.6120511924032
19	14	14.9000258110337	-0.9000258110337
20	16	14.2001440847831	1.79985591521689
21	18	15.7167279447017	2.28327205529834
22	11	13.7347138826042	-2.73471388260423
23	14	15.0196046030103	-1.01960460301031
24	12	14.1829026835592	-2.18290268355924
25	17	14.3105147186554	2.68948528134459
26	9	16.1005698368485	-7.10056983684846
27	16	14.3061234496269	1.69387655037314
28	14	13.5875365658096	0.41246343419045
29	15	13.8631860418322	1.13681395816781
30	11	13.3752630452691	-2.3752630452691
31	16	15.646526010522	0.353473989477962
32	13	12.3115392126548	0.688460787345185
33	17	15.5365898807343	1.46341011926567
34	15	15.2251629740476	-0.225162974047566
35	14	13.2811045603624	0.718895439637597
36	16	15.3155338221368	0.684466177863238
37	9	10.3398822741516	-1.33988227415159
38	15	13.8421570037908	1.15784299620917
39	17	15.273790536907	1.726209463093
40	13	14.6116953309422	-1.61169533094221
41	15	15.0472031278284	-0.0472031278283813
42	16	13.8960359598106	2.10396404018939
43	16	15.4812471683717	0.518752831628302
44	12	13.0069188406826	-1.00691884068261
45	12	15.0740871912412	-3.07408719124116
46	11	14.4585521595819	-3.45855215958189
47	15	16.2217232143622	-1.22172321436216
48	15	15.0981545711625	-0.0981545711624569
49	17	13.7174724813804	3.28252751861964
50	13	14.277664800677	-1.277664800677
51	16	15.5920434222912	0.407956577708803
52	14	12.8142106018407	1.18578939815933
53	11	11.3035925964878	-0.303592596487763
54	12	14.0529667679884	-2.05296676798843
55	12	14.0805652928065	-2.0805652928065
56	15	14.7655877972401	0.234412202759904
57	16	14.4928658339032	1.50713416609684
58	15	15.7691431443786	-0.76914314437859
59	12	14.7715536518057	-2.77155365180574
60	12	13.5590779168597	-1.55907791685969
61	8	10.2785737072233	-2.27857370722331
62	13	13.9392430013832	-0.939243001383227
63	11	14.7611965282115	-3.76119652821154
64	14	13.8602585291465	0.139741470853512
65	15	14.2344577591044	0.765542240895619
66	10	14.3360458549196	-4.33604585491957
67	11	12.8209257513439	-1.82092575134387
68	12	13.4567405261069	-1.45674052610694
69	15	14.6811828037165	0.318817196283458
70	15	13.1324634872249	1.86753651277513
71	14	13.6008212020895	0.399178797910545
72	16	13.5532228914883	2.44677710851172
73	15	14.4855470521889	0.514452947811105
74	15	14.961334377962	0.0386656220380246
75	13	13.9893343205855	-0.989334320585511
76	12	11.9601564519715	0.0398435480284988
77	17	14.521324482853	2.47867551714698
78	13	12.6296812688448	0.370318731155218
79	15	13.1153912141275	1.88460878587253
80	13	14.8902723196506	-1.89027231965056
81	15	14.2389598573272	0.761040142672828
82	16	14.8343259750769	1.16567402492313
83	15	16.0604011371558	-1.06040113715578
84	16	13.8750069217692	2.12499307823075
85	15	14.6641105306191	0.33588946938086
86	14	14.201607841126	-0.201607841125965
87	15	13.6949796869961	1.30502031300385
88	14	14.6969604485976	-0.696960448597557
89	13	13.2992060857181	-0.299206085718062
90	7	10.653633061313	-3.65363306131299
91	17	14.292838813347	2.70716118665305
92	13	13.529155511567	-0.529155511566979
93	15	14.5811692934384	0.41883070656156
94	14	13.2722111931111	0.727788806888944
95	13	15.2424043752714	-2.24240437527143
96	16	15.3580264023041	0.641973597695914
97	12	13.2549697918872	-1.25496979188719
98	14	15.0696959222126	-1.0696959222126
99	17	14.3075872059697	2.69241279403029
100	15	14.6073040619137	0.392695938086345
101	17	15.7263706068906	1.27362939310943
102	12	12.3330027547808	-0.333002754780774
103	16	14.8896686874395	1.1103313125605
104	11	13.9550206462642	-2.95502064626424
105	15	13.2491147665158	1.75088523348422
106	9	11.1338116561146	-2.13381165611463
107	16	15.2937903226901	0.706209677309895
108	15	12.5899470732367	2.4100529267633
109	10	12.7013469593673	-2.70134695936726
110	10	10.4622194506874	-0.462219450687438
111	15	13.7960224495325	1.20397755046749
112	11	13.3962920833105	-2.39629208331046
113	13	15.285007784633	-2.28500778463299
114	14	12.5071749641825	1.49282503581754
115	18	14.8283601205112	3.17163987948878
116	16	14.6460090052635	1.35399099473652
117	14	14.0828891732811	-0.0828891732811422
118	14	14.5169332138245	-0.516933213824459
119	14	15.9319289779278	-1.93192897792782
120	14	13.7203999940661	0.279600005933931
121	12	13.5875365658095	-1.58753656580955
122	14	13.609169236062	0.390830763938025
123	15	15.4193349692324	-0.419334969232361
124	15	16.5586812573131	-1.55868125731308
125	15	15.0039960862558	-0.00399608625576461
126	13	15.0010685735701	-2.00106857357006
127	17	15.5140970863501	1.48590291364989
128	17	16.0176285996678	0.982371400332239
129	19	15.1609268944336	3.83907310556642
130	15	14.3300800003539	0.669919999646073
131	13	14.1119514544421	-1.11195145444206
132	9	10.3384185178087	-1.33841851780873
133	15	15.823456604483	-0.823456604482966
134	15	12.2487668893837	2.75123311061631
135	15	14.0319377299471	0.968062270052934
136	16	13.7047914773115	2.29520852268848
137	11	8.82097453375839	2.17902546624161
138	14	13.0368412459753	0.963158754024676
139	11	13.0250203660383	-2.02502036603827
140	15	15.1638544071193	-0.163854407119291
141	13	13.7406797371699	-0.740679737169874
142	15	15.4664987757489	-0.46649877574894
143	16	12.8740554124261	3.12594458757391
144	14	14.6297968562979	-0.629796856297871
145	15	13.3640457975431	1.6359542024569
146	16	15.2339455121047	0.766054487895318
147	16	14.4444073991702	1.55559260082981
148	11	13.5351213661326	-2.53512136613262
149	12	14.0491791311709	-2.04917913117093
150	9	10.9695620662225	-1.96956206622255
151	16	15.0181408466675	0.981859153332539
152	13	13.0807975824855	-0.0807975824855003
153	16	15.1369703437065	0.863029656293483
154	12	14.9195910927322	-2.91959109273221
155	9	11.9543014266001	-2.95430142660009
156	13	12.1956372283015	0.804362771698535
157	13	13.529155511567	-0.529155511566979
158	14	13.955880770396	0.0441192296039669
159	19	15.1609268944336	3.83907310556642
160	13	15.8706204109995	-2.87062041099955
161	12	12.2883319568653	-0.288331956865305
162	13	13.1878061995875	-0.187806199587502

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
8	0.920807230872157	0.158385538255686	0.0791927691278432
9	0.851114092512778	0.297771814974444	0.148885907487222
10	0.776856844989784	0.446286310020432	0.223143155010216
11	0.741589556854519	0.516820886290961	0.258410443145481
12	0.813732740464925	0.37253451907015	0.186267259535075
13	0.860092588441525	0.27981482311695	0.139907411558475
14	0.831505963179878	0.336988073640244	0.168494036820122
15	0.88582212875917	0.22835574248166	0.11417787124083
16	0.872432998871994	0.255134002256012	0.127567001128006
17	0.827948283935497	0.344103432129005	0.172051716064503
18	0.798806228295754	0.402387543408492	0.201193771704246
19	0.743641345687905	0.512717308624191	0.256358654312095
20	0.685488865868744	0.629022268262512	0.314511134131256
21	0.753577708144983	0.492844583710033	0.246422291855017
22	0.901876254023419	0.196247491953163	0.0981237459765813
23	0.890852217134865	0.21829556573027	0.109147782865135
24	0.893706833261748	0.212586333476504	0.106293166738252
25	0.883991122009478	0.232017755981045	0.116008877990522
26	0.999509113796213	0.000981772407574107	0.000490886203787054
27	0.999354335118106	0.00129132976378716	0.000645664881893582
28	0.998938403967073	0.00212319206585482	0.00106159603292741
29	0.998377215751373	0.00324556849725397	0.00162278424862699
30	0.998920950801427	0.00215809839714549	0.00107904919857275
31	0.998294359572968	0.00341128085406477	0.00170564042703238
32	0.997400480959218	0.00519903808156316	0.00259951904078158
33	0.996554729505942	0.00689054098811558	0.00344527049405779
34	0.994828453389525	0.0103430932209499	0.00517154661047494
35	0.992559856798708	0.0148802864025839	0.00744014320129194
36	0.989758343334487	0.0204833133310259	0.0102416566655129
37	0.990410152143462	0.0191796957130752	0.00958984785653759
38	0.987413465678573	0.0251730686428544	0.0125865343214272
39	0.985122494430509	0.0297550111389813	0.0148775055694906
40	0.983460387761525	0.0330792244769505	0.0165396122384753
41	0.977302641655657	0.0453947166886867	0.0226973583443434
42	0.97541275634589	0.0491744873082196	0.0245872436541098
43	0.967561752994821	0.0648764940103588	0.0324382470051794
44	0.961142909306415	0.0777141813871707	0.0388570906935854
45	0.97881574373478	0.0423685125304391	0.0211842562652196
46	0.989243470731251	0.0215130585374985	0.0107565292687492
47	0.986391741005593	0.0272165179888147	0.0136082589944074
48	0.98149768480375	0.0370046303924992	0.0185023151962496
49	0.98833008263201	0.0233398347359803	0.0116699173679902
50	0.985863344409172	0.0282733111816557	0.0141366555908278
51	0.981008540168971	0.0379829196620575	0.0189914598310288
52	0.976344822617834	0.0473103547643325	0.0236551773821662
53	0.970083891969742	0.0598322160605162	0.0299161080302581
54	0.971779424748993	0.0564411505020136	0.0282205752510068
55	0.972905379220906	0.0541892415581876	0.0270946207790938
56	0.964569056898918	0.0708618862021634	0.0354309431010817
57	0.959802013374957	0.080395973250087	0.0401979866250435
58	0.950412921328598	0.0991741573428033	0.0495870786714017
59	0.959087603602512	0.0818247927949761	0.0409123963974881
60	0.957109363675889	0.0857812726482228	0.0428906363241114
61	0.964298971523184	0.0714020569536324	0.0357010284768162
62	0.95637662586831	0.0872467482633794	0.0436233741316897
63	0.978787729069104	0.0424245418617913	0.0212122709308957
64	0.972128540356846	0.0557429192863071	0.0278714596431536
65	0.964899885158164	0.0702002296836724	0.0351001148418362
66	0.987633077996399	0.024733844007203	0.0123669220036015
67	0.987362354077595	0.0252752918448091	0.0126376459224046
68	0.98606456016584	0.0278708796683202	0.0139354398341601
69	0.981647581214763	0.0367048375704748	0.0183524187852374
70	0.981784846123478	0.0364303077530439	0.018215153876522
71	0.976420112716207	0.0471597745675854	0.0235798872837927
72	0.980227640641098	0.0395447187178031	0.0197723593589016
73	0.9745226949669	0.0509546100662	0.0254773050331
74	0.967471820556919	0.0650563588861619	0.0325281794430809
75	0.961760712934971	0.0764785741300589	0.0382392870650294
76	0.951542632707978	0.0969147345840435	0.0484573672920217
77	0.958644765661677	0.0827104686766469	0.0413552343383235
78	0.948241675655034	0.103516648689932	0.0517583243449661
79	0.946871961441239	0.106256077117522	0.0531280385587611
80	0.950992347404568	0.0980153051908647	0.0490076525954323
81	0.939987275099938	0.120025449800125	0.0600127249000624
82	0.930024141280423	0.139951717439155	0.0699758587195773
83	0.919180911347924	0.161638177304153	0.0808190886520763
84	0.920257195177822	0.159485609644355	0.0797428048221775
85	0.902322601864887	0.195354796270225	0.0976773981351126
86	0.881106785181894	0.237786429636212	0.118893214818106
87	0.86617341276967	0.26765317446066	0.13382658723033
88	0.843262323276453	0.313475353447093	0.156737676723547
89	0.814796972281167	0.370406055437666	0.185203027718833
90	0.880832820102597	0.238334359794806	0.119167179897403
91	0.905231641640519	0.189536716718963	0.0947683583594813
92	0.885758324221205	0.22848335155759	0.114241675778795
93	0.864550353874785	0.27089929225043	0.135449646125215
94	0.841218018548849	0.317563962902302	0.158781981451151
95	0.852248557980598	0.295502884038804	0.147751442019402
96	0.825956508198679	0.348086983602642	0.174043491801321
97	0.807561416134531	0.384877167730937	0.192438583865468
98	0.787989198909473	0.424021602181054	0.212010801090527
99	0.81388679008307	0.37222641983386	0.18611320991693
100	0.781812669045498	0.436374661909005	0.218187330954503
101	0.759969047675397	0.480061904649207	0.240030952324603
102	0.722153609947202	0.555692780105596	0.277846390052798
103	0.695850041062525	0.60829991787495	0.304149958937475
104	0.772195809445104	0.455608381109791	0.227804190554896
105	0.78345839458003	0.43308321083994	0.21654160541997
106	0.810097433992434	0.379805132015132	0.189902566007566
107	0.778285162752322	0.443429674495357	0.221714837247678
108	0.802082456248161	0.395835087503678	0.197917543751839
109	0.84271377792745	0.3145724441451	0.15728622207255
110	0.815807780357136	0.368384439285729	0.184192219642864
111	0.801959765258296	0.396080469483407	0.198040234741704
112	0.818196084955799	0.363607830088402	0.181803915044201
113	0.816783438349614	0.366433123300772	0.183216561650386
114	0.800180276659188	0.399639446681625	0.199819723340812
115	0.858938155161603	0.282123689676794	0.141061844838397
116	0.836373205537833	0.327253588924334	0.163626794462167
117	0.806736847877555	0.386526304244889	0.193263152122445
118	0.770722155656694	0.458555688686611	0.229277844343306
119	0.773242490339986	0.453515019320029	0.226757509660014
120	0.735197796649601	0.529604406700798	0.264802203350399
121	0.707936709547127	0.584126580905746	0.292063290452873
122	0.661473825735942	0.677052348528116	0.338526174264058
123	0.610399060275168	0.779201879449664	0.389600939724832
124	0.589332286102407	0.821335427795187	0.410667713897593
125	0.537286746262387	0.925426507475226	0.462713253737613
126	0.56723273492304	0.86553453015392	0.43276726507696
127	0.526236185825098	0.947527628349804	0.473763814174902
128	0.507246652965093	0.985506694069814	0.492753347034907
129	0.678900700125149	0.642198599749702	0.321099299874851
130	0.630079045549175	0.73984190890165	0.369920954450825
131	0.605310791310286	0.789378417379428	0.394689208689714
132	0.586690663337756	0.826618673324488	0.413309336662244
133	0.526922122823941	0.946155754352118	0.473077877176059
134	0.536515952368432	0.926968095263135	0.463484047631568
135	0.511494365744413	0.977011268511175	0.488505634255587
136	0.508879845731804	0.982240308536392	0.491120154268196
137	0.495424971773408	0.990849943546816	0.504575028226592
138	0.460711707390821	0.921423414781642	0.539288292609179
139	0.451427059899147	0.902854119798293	0.548572940100853
140	0.381205417311631	0.762410834623261	0.618794582688369
141	0.319947969352088	0.639895938704176	0.680052030647912
142	0.267480713092611	0.534961426185222	0.732519286907389
143	0.42836301250069	0.856726025001381	0.571636987499309
144	0.363494472323189	0.726988944646378	0.636505527676811
145	0.35790464280598	0.715809285611959	0.64209535719402
146	0.295104848841584	0.590209697683167	0.704895151158416
147	0.296580538628444	0.593161077256887	0.703419461371557
148	0.263681855857712	0.527363711715424	0.736318144142288
149	0.207627285227489	0.415254570454978	0.792372714772511
150	0.159635685852194	0.319271371704389	0.840364314147806
151	0.122805054027991	0.245610108055983	0.877194945972009
152	0.174007193750615	0.348014387501229	0.825992806249385
153	0.102925906641113	0.205851813282225	0.897074093358887
154	0.0829870301386628	0.165974060277326	0.917012969861337

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	8	0.054421768707483	NOK
5% type I error level	33	0.224489795918367	NOK
10% type I error level	53	0.360544217687075	NOK