Multiple Linear Regression - Estimated Regression Equation

Learning[t] = + 15.6101778789857 + 0.0771210908317657Happiness[t] -0.134840982774543Depression[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)	15.6101778789857	1.851841	8.4295	0	0
Happiness	0.0771210908317657	0.088525	0.8712	0.384973	0.192486
Depression	-0.134840982774543	0.06536	-2.0631	0.040732	0.020366

Multiple Linear Regression - Regression Statistics
Multiple R	0.242167285326478
R-squared	0.0586449940823957
Adjusted R-squared	0.0468040506117341
F-TEST (value)	4.95272984181543
F-TEST (DF numerator)	2
F-TEST (DF denominator)	159
p-value	0.00819215566757125
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	2.2028272449683
Sum Squared Residuals	771.539211516765

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	13	15.071781357336	-2.07178135733595
2	16	15.5151067034375	0.484893296562493
3	19	14.5707361192915	4.42926388070848
4	15	14.9175391756724	0.0824608243276288
5	14	14.0124546940286	-0.0124546940285505
6	13	15.380265720663	-2.38026572066297
7	19	13.7233715295905	5.27662847040952
8	15	15.2066223401104	-0.206622340110445
9	14	15.4185844137168	-1.41858441371675
10	15	15.0140614653931	-0.0140614653931256
11	16	15.5728265953803	0.427173404619715
12	16	15.9967507425929	0.00324925740709885
13	16	14.3587740456852	1.64122595431479
14	16	14.9563415734503	1.04365842654965
15	17	15.649947686212	1.35005231378795
16	15	14.8020993917868	0.197900608213183
17	15	14.8020993917868	0.197900608213183
18	20	15.4379856126057	4.56201438739426
19	18	15.341463322885	2.65853667711501
20	16	15.0911825562249	0.908817443775109
21	16	16.0544706345357	-0.0544706345356781
22	16	14.5707361192915	1.42926388070848
23	19	15.0717813573359	3.9282186426641
24	16	14.6478572101233	1.35214278987671
25	17	15.4379856126057	1.56201438739426
26	17	15.0906988515007	1.9093011484993
27	16	15.360864521774	0.639135478226024
28	15	14.6672584090123	0.332741590987725
29	16	14.8792204826186	1.12077951738142
30	14	14.7055771020661	-0.705577102066063
31	15	15.6305464873231	-0.630546487323062
32	12	14.5901373181805	-2.59013731818051
33	14	15.5728265953803	-1.57282659538028
34	16	15.2837434309422	0.716256569057789
35	14	14.9369403745614	-0.93694037456136
36	7	15.7653874700976	-8.7653874700976
37	10	13.6074480409807	-3.60744804098073
38	14	15.1489024481677	-1.14890244816767
39	16	15.5728265953803	0.427173404619715
40	16	15.2643422320532	0.735657767946778
41	16	15.5534253964913	0.446574603508704
42	14	14.9563415734503	-0.956341573450349
43	20	15.7653874700976	4.2346125299024
44	14	14.6478572101233	-0.647857210123286
45	14	15.0523801584469	-1.05238015844691
46	11	14.7055771020661	-3.70557710206606
47	14	15.5534253964913	-1.5534253964913
48	15	15.2837434309422	-0.283743430942211
49	16	14.8986216815076	1.10137831849243
50	14	15.1295012492787	-1.12950124927868
51	16	15.4957055045485	0.504294495451481
52	14	14.8020993917868	-0.802099391786817
53	12	14.0313721881933	-2.03137218819335
54	16	14.6478572101233	1.35214278987671
55	9	15.0523801584469	-6.05238015844691
56	14	15.1489024481677	-1.14890244816767
57	16	15.0911825562249	0.908817443775109
58	16	15.5534253964913	0.446574603508704
59	15	15.1872211412215	-0.187221141221456
60	16	14.5130162273487	1.48698377265126
61	12	13.530326950149	-1.53032695014897
62	16	14.9946602665041	1.00533973349586
63	16	14.8404180848406	1.15958191515939
64	14	14.8020993917868	-0.802099391786817
65	16	15.0140614653931	0.985938534606874
66	17	14.8981379767834	2.10186202321662
67	18	14.1662131709679	3.83378682903211
68	18	14.9175391756724	3.08246082432763
69	12	15.0140614653931	-3.01406146539313
70	16	14.8792204826186	1.12077951738142
71	10	14.9369403745614	-4.93694037456136
72	14	14.8215005906758	-0.821500590675806
73	18	15.0140614653931	2.98593853460687
74	18	15.4185844137168	2.58141558628325
75	16	15.1295012492787	0.87049875072132
76	17	13.9736522962506	3.02634770374943
77	16	15.1683036470567	0.831696352943343
78	16	14.3204553526314	1.67954464736858
79	13	15.0140614653931	-2.01406146539313
80	16	15.3991832148278	0.600816785172235
81	16	15.2837434309422	0.716256569057789
82	20	15.4957055045485	4.50429449545148
83	16	15.5534253964913	0.446574603508704
84	15	15.2260235389994	-0.226023538999434
85	15	15.1489024481677	-0.148902448167668
86	16	14.9369403745614	1.06305962543864
87	14	15.0140614653931	-1.01406146539313
88	16	15.0717813573359	0.928218642664098
89	16	14.5901373181805	1.40986268181949
90	15	13.1835238937681	1.81647610623188
91	12	15.1683036470567	-3.16830364705666
92	17	14.5901373181805	2.40986268181949
93	16	15.0140614653931	0.985938534606874
94	15	14.6672584090123	0.332741590987725
95	13	15.2643422320532	-2.26434223205322
96	16	15.360864521774	0.639135478226024
97	16	14.3781752445742	1.6218247554258
98	16	15.2066223401104	0.793377659889555
99	16	15.4379856126057	0.562014387394258
100	14	15.4185844137168	-1.41858441371675
101	16	15.5728265953803	0.427173404619715
102	16	14.3781752445742	1.6218247554258
103	20	15.2260235389994	4.77397646100057
104	15	14.9752590676151	0.024740932384852
105	16	14.6095385170695	1.3904614829305
106	13	13.7422890237553	-0.742289023755276
107	17	15.360864521774	1.63913547822602
108	16	14.6095385170695	1.3904614829305
109	16	14.3587740456852	1.64122595431479
110	12	13.1452052007143	-1.14520520071433
111	16	14.8792204826186	1.12077951738142
112	16	14.435895136517	1.56410486348302
113	17	15.1295012492787	1.87049875072132
114	13	14.6672584090123	-1.66725840901227
115	12	15.380265720663	-3.38026572066297
116	18	15.4957055045485	2.50429449545148
117	14	14.8020993917868	-0.802099391786817
118	14	14.9369403745614	-0.93694037456136
119	13	15.4763043056595	-2.47630430565953
120	16	14.6672584090123	1.33274159098773
121	13	14.5130162273487	-1.51301622734874
122	16	14.8020993917868	1.19790060821318
123	13	15.2837434309422	-2.28374343094221
124	16	15.6882663792658	0.311733620734161
125	15	15.2837434309422	-0.283743430942211
126	16	15.1295012492787	0.87049875072132
127	15	15.8425085609294	-0.84250856092937
128	17	15.5728265953803	1.42717340461972
129	15	15.5922277942693	-0.592227794269273
130	12	15.0140614653931	-3.01406146539313
131	16	15.1295012492787	0.87049875072132
132	10	13.6074480409807	-3.60744804098073
133	16	15.4185844137168	0.581415586283247
134	12	14.744379499844	-2.74437949984404
135	14	15.1489024481677	-1.14890244816767
136	15	14.9563415734503	0.0436584265496514
137	13	13.3571672743206	-0.357167274320637
138	15	14.8020993917868	0.197900608213183
139	11	14.3010541537424	-3.30105415374243
140	12	15.2837434309422	-3.28374343094221
141	8	14.9946602665041	-6.99466026650414
142	16	15.4185844137168	0.581415586283247
143	15	14.9563415734503	0.0436584265496514
144	17	15.0717813573359	1.9282186426641
145	16	15.1489024481677	0.851097551832332
146	10	15.360864521774	-5.36086452177398
147	18	15.2260235389994	2.77397646100057
148	13	14.7055771020661	-1.70557710206606
149	16	15.0523801584469	0.947619841553086
150	13	13.7422890237553	-0.742289023755276
151	10	15.2260235389994	-5.22602353899943
152	15	14.3204553526314	0.679544647368576
153	16	15.6305464873231	0.369453512676938
154	16	14.9175391756724	1.08246082432763
155	14	13.7422890237553	0.257710976244724
156	10	14.1856143698569	-4.18561436985688
157	17	14.5901373181805	2.40986268181949
158	13	14.8020993917868	-1.80209939178682
159	15	15.5922277942693	-0.592227794269273
160	16	15.3991832148278	0.600816785172235
161	12	14.1084932790251	-2.10849327902512
162	13	14.455296335406	-1.45529633540597

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
6	0.719190580471518	0.561618839056964	0.280809419528482
7	0.754991130995468	0.490017738009065	0.245008869004532
8	0.634047223171368	0.731905553657264	0.365952776828632
9	0.51483545153357	0.970329096932859	0.485164548466429
10	0.394927532406963	0.789855064813925	0.605072467593037
11	0.39684640129184	0.793692802583679	0.60315359870816
12	0.414074864529336	0.828149729058673	0.585925135470664
13	0.328932884644365	0.657865769288729	0.671067115355635
14	0.253850484494763	0.507700968989526	0.746149515505237
15	0.25956317487816	0.519126349756321	0.74043682512184
16	0.200984240912956	0.401968481825913	0.799015759087044
17	0.151616512823731	0.303233025647463	0.848383487176269
18	0.414444045888549	0.828888091777098	0.585555954111451
19	0.424784453120357	0.849568906240714	0.575215546879643
20	0.353812007939811	0.707624015879622	0.646187992060189
21	0.28894139851415	0.5778827970283	0.71105860148585
22	0.23251691897156	0.46503383794312	0.76748308102844
23	0.302834756169417	0.605669512338835	0.697165243830583
24	0.248679140154549	0.497358280309099	0.751320859845451
25	0.21309627133176	0.42619254266352	0.78690372866824
26	0.173450456692478	0.346900913384956	0.826549543307522
27	0.134582322416555	0.269164644833109	0.865417677583445
28	0.110652642758653	0.221305285517306	0.889347357241347
29	0.0841939028611541	0.168387805722308	0.915806097138846
30	0.0872356135517105	0.174471227103421	0.912764386448289
31	0.0690681591813435	0.138136318362687	0.930931840818656
32	0.134090161010501	0.268180322021002	0.865909838989499
33	0.125706276598077	0.251412553196154	0.874293723401923
34	0.0981732457664772	0.196346491532954	0.901826754233523
35	0.0898514035721476	0.179702807144295	0.910148596427852
36	0.767880097731987	0.464239804536027	0.232119902268013
37	0.900696534938096	0.198606930123807	0.0993034650619036
38	0.883730357755737	0.232539284488526	0.116269642244263
39	0.857076965153466	0.285846069693068	0.142923034846534
40	0.828659778109652	0.342680443780697	0.171340221890348
41	0.795349536968833	0.409300926062333	0.204650463031167
42	0.768713803166223	0.462572393667553	0.231286196833777
43	0.857927192708694	0.284145614582612	0.142072807291306
44	0.833758013127832	0.332483973744336	0.166241986872168
45	0.810255615727042	0.379488768545916	0.189744384272958
46	0.867681341130344	0.264637317739311	0.132318658869656
47	0.852143540423399	0.295712919153202	0.147856459576601
48	0.822267193689804	0.355465612620391	0.177732806310196
49	0.794256364381682	0.411487271236635	0.205743635618318
50	0.766967158679254	0.466065682641491	0.233032841320746
51	0.729845798891643	0.540308402216714	0.270154201108357
52	0.696293533199424	0.607412933601152	0.303706466800576
53	0.696688983956539	0.606622032086921	0.303311016043461
54	0.668184329691955	0.663631340616091	0.331815670308045
55	0.876934139620663	0.246131720758675	0.123065860379337
56	0.8583503107503	0.2832993784994	0.1416496892497
57	0.834446151161109	0.331107697677783	0.165553848838891
58	0.805609358075108	0.388781283849784	0.194390641924892
59	0.773643547928014	0.452712904143971	0.226356452071986
60	0.752516387524402	0.494967224951195	0.247483612475598
61	0.734020166758499	0.531959666483003	0.265979833241501
62	0.703371764790308	0.593256470419385	0.296628235209692
63	0.676144378869181	0.647711242261638	0.323855621130819
64	0.639936695546245	0.72012660890751	0.360063304453755
65	0.603743498774216	0.792513002451568	0.396256501225784
66	0.603081371410074	0.793837257179852	0.396918628589926
67	0.680159238499763	0.639681523000473	0.319840761500237
68	0.714446731481249	0.571106537037501	0.285553268518751
69	0.74889853078848	0.50220293842304	0.25110146921152
70	0.720171571860454	0.559656856279092	0.279828428139546
71	0.850870674857959	0.298258650284082	0.149129325142041
72	0.827506348984226	0.344987302031548	0.172493651015774
73	0.849230379954745	0.30153924009051	0.150769620045255
74	0.85810485809701	0.283790283805979	0.14189514190299
75	0.834993753246829	0.330012493506342	0.165006246753171
76	0.85706306965195	0.2858738606961	0.14293693034805
77	0.834900510800869	0.330198978398262	0.165099489199131
78	0.823536978704179	0.352926042591642	0.176463021295821
79	0.81867947775992	0.36264104448016	0.18132052224008
80	0.789393043870974	0.421213912258053	0.210606956129026
81	0.758840711033862	0.482318577932275	0.241159288966138
82	0.858094609351808	0.283810781296383	0.141905390648192
83	0.832156542892502	0.335686914214996	0.167843457107498
84	0.802769375605765	0.39446124878847	0.197230624394235
85	0.770078742506626	0.459842514986749	0.229921257493374
86	0.743608676336429	0.512782647327141	0.256391323663571
87	0.713637489033535	0.57272502193293	0.286362510966465
88	0.681574331373415	0.63685133725317	0.318425668626585
89	0.658874520792633	0.682250958414734	0.341125479207367
90	0.647873865747598	0.704252268504805	0.352126134252402
91	0.688836910930129	0.622326178139742	0.311163089069871
92	0.70200051803015	0.595998963939699	0.29799948196985
93	0.671829431920087	0.656341136159825	0.328170568079912
94	0.632767938465697	0.734464123068606	0.367232061534303
95	0.634915093575721	0.730169812848559	0.365084906424279
96	0.595730382448686	0.808539235102628	0.404269617551314
97	0.58193384173349	0.836132316533019	0.41806615826651
98	0.543264973042173	0.913470053915655	0.456735026957827
99	0.501963257592628	0.996073484814743	0.498036742407372
100	0.472953391935748	0.945906783871497	0.527046608064252
101	0.429488075465421	0.858976150930843	0.570511924534579
102	0.417000164031443	0.834000328062887	0.582999835968557
103	0.616248227995858	0.767503544008284	0.383751772004142
104	0.569999194848071	0.860001610303857	0.430000805151929
105	0.562082345319092	0.875835309361815	0.437917654680908
106	0.521951934008308	0.956096131983384	0.478048065991692
107	0.512957848902656	0.974084302194688	0.487042151097344
108	0.512188625312754	0.975622749374491	0.487811374687246
109	0.497751124760912	0.995502249521824	0.502248875239088
110	0.469413924311781	0.938827848623562	0.530586075688219
111	0.453932735988188	0.907865471976375	0.546067264011812
112	0.446114758544062	0.892229517088124	0.553885241455938
113	0.443311174952364	0.886622349904727	0.556688825047637
114	0.41147420297755	0.8229484059551	0.58852579702245
115	0.452572817158852	0.905145634317704	0.547427182841148
116	0.488309107971043	0.976618215942085	0.511690892028957
117	0.441763078310023	0.883526156620047	0.558236921689977
118	0.396257471511255	0.792514943022511	0.603742528488745
119	0.400744827466538	0.801489654933075	0.599255172533462
120	0.397745409397526	0.795490818795051	0.602254590602474
121	0.360094499146299	0.720188998292598	0.639905500853701
122	0.348984759006346	0.697969518012691	0.651015240993654
123	0.337347408706042	0.674694817412084	0.662652591293958
124	0.291023989527454	0.582047979054907	0.708976010472546
125	0.247368774681136	0.494737549362272	0.752631225318864
126	0.218352157456762	0.436704314913523	0.781647842543238
127	0.182651987085261	0.365303974170522	0.817348012914739
128	0.173644882495907	0.347289764991814	0.826355117504093
129	0.142288774199085	0.28457754839817	0.857711225800915
130	0.145837828321897	0.291675656643793	0.854162171678103
131	0.12521399497551	0.25042798995102	0.87478600502449
132	0.143312247864982	0.286624495729963	0.856687752135018
133	0.120572013203086	0.241144026406172	0.879427986796914
134	0.113430593685491	0.226861187370983	0.886569406314509
135	0.0888396703939153	0.177679340787831	0.911160329606085
136	0.0707437516820375	0.141487503364075	0.929256248317962
137	0.0560453093296539	0.112090618659308	0.943954690670346
138	0.0438137394058814	0.0876274788117627	0.956186260594119
139	0.0476847779332637	0.0953695558665275	0.952315222066736
140	0.0524143892280634	0.104828778456127	0.947585610771937
141	0.371126717846748	0.742253435693495	0.628873282153252
142	0.309868240526783	0.619736481053565	0.690131759473217
143	0.270610063025975	0.541220126051949	0.729389936974026
144	0.268799094160469	0.537598188320939	0.731200905839531
145	0.238581591223031	0.477163182446063	0.761418408776969
146	0.47745274984311	0.95490549968622	0.52254725015689
147	0.638517867519585	0.722964264960831	0.361482132480415
148	0.647844181325768	0.704311637348463	0.352155818674232
149	0.557414340753414	0.885171318493173	0.442585659246586
150	0.465179888644921	0.930359777289842	0.534820111355079
151	0.776729284581618	0.446541430836765	0.223270715418382
152	0.78189085110232	0.43621829779536	0.21810914889768
153	0.678290528126445	0.643418943747109	0.321709471873555
154	0.551531682759327	0.896936634481346	0.448468317240673
155	0.474314857790306	0.948629715580611	0.525685142209694
156	0.489370937599742	0.978741875199484	0.510629062400258

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	0	0	OK
10% type I error level	2	0.0132450331125828	OK