Multiple Linear Regression - Estimated Regression Equation

Happiness[t] = + 16.8555988203748 -0.0786345448628769Month[t] + 0.0176147950614903Age[t] -0.0124312897250591Concern_over_mistakes[t] -0.249744352622465Doubts_about_actions[t] + 0.0885995494564707Parental_expectations[t] -0.0926244834865925Parental_criticism[t] + 0.0351359704360569Popularity[t] + 0.0421600459244758Perceived_learning_competence[t] -0.142798650718867Amotivation[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)	16.8555988203748	4.614883	3.6524	0.000372	0.000186
Month	-0.0786345448628769	0.384686	-0.2044	0.838341	0.419171
Age	0.0176147950614903	0.062789	0.2805	0.779497	0.389748
Concern_over_mistakes	-0.0124312897250591	0.038788	-0.3205	0.749091	0.374545
Doubts_about_actions	-0.249744352622465	0.07832	-3.1888	0.001779	0.000889
Parental_expectations	0.0885995494564707	0.069585	1.2733	0.205132	0.102566
Parental_criticism	-0.0926244834865925	0.086807	-1.067	0.287883	0.143941
Popularity	0.0351359704360569	0.063796	0.5508	0.582718	0.291359
Perceived_learning_competence	0.0421600459244758	0.089618	0.4704	0.638805	0.319402
Amotivation	-0.142798650718867	0.073836	-1.934	0.055223	0.027611

Multiple Linear Regression - Regression Statistics
Multiple R	0.419882877183372
R-squared	0.176301630551787
Adjusted R-squared	0.120978605738101
F-TEST (value)	3.18676773631822
F-TEST (DF numerator)	9
F-TEST (DF denominator)	134
p-value	0.00159616503008553
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	2.23501532220863
Sum Squared Residuals	669.369327727986

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	14	15.1187435064363	-1.11874350643635
2	18	15.3197177628732	2.68028223712679
3	11	14.5166062869294	-3.51660628692941
4	12	12.6223785088577	-0.622378508857652
5	16	14.4187382854617	1.58126171453826
6	18	14.9066512829686	3.09334871703138
7	14	14.9845927958550	-0.984592795854973
8	14	14.5672631956204	-0.567263195620417
9	15	14.6661274705030	0.33387252949702
10	15	12.9864847379961	2.01351526200391
11	17	13.4339209797357	3.56607902026433
12	19	13.9470256899615	5.05297431003849
13	10	13.0759897716792	-3.07598977167917
14	18	16.2809923692112	1.71900763078882
15	14	11.8475945932063	2.15240540679370
16	14	14.6680001054871	-0.668000105487062
17	17	15.1656065387259	1.83439346127412
18	14	15.0726934805885	-1.07269348058852
19	16	15.0003963050803	0.999603694919672
20	18	13.5468798928006	4.4531201071994
21	14	13.4194064009629	0.58059359903707
22	12	12.9566609593639	-0.956660959363893
23	17	13.8614391821468	3.13856081785317
24	9	14.7086687735221	-5.70866877352209
25	16	14.6067730280030	1.39322697199697
26	14	13.2589375799070	0.741062420092959
27	11	14.6250951812076	-3.62509518120762
28	16	15.4824302340688	0.517569765931228
29	13	13.2596440265179	-0.259644026517915
30	17	14.5851985698176	2.41480143018237
31	15	14.6025193610647	0.397480638935307
32	14	14.9146205464400	-0.914620546439961
33	16	12.2113003175449	3.78869968245507
34	9	12.5608275480887	-3.56082754808873
35	15	13.2061779641678	1.79382203583218
36	17	15.5893022058277	1.41069779417228
37	13	13.5373064284695	-0.537306428469528
38	15	13.8073552501306	1.19264474986939
39	16	13.9592857926279	2.04071420737206
40	16	17.0569149648932	-1.05691496489316
41	12	13.9100914487873	-1.91009144878734
42	11	13.4714638472947	-2.47146384729472
43	15	15.2844491754492	-0.284449175449200
44	17	14.9468723775083	2.05312762249165
45	13	14.3551518351716	-1.35515183517163
46	16	11.8117219792692	4.18827802073083
47	14	14.2388318808711	-0.238831880871055
48	11	13.5181277155191	-2.51812771551909
49	12	13.2180225913502	-1.21802259135017
50	12	14.0125858833841	-2.01258588338413
51	15	14.0645261074146	0.935473892585384
52	16	15.1643394313368	0.835660568663244
53	15	14.8656445409333	0.134355459066687
54	12	15.0194526107514	-3.01945261075140
55	12	14.4780397816004	-2.47803978160035
56	8	12.8834643798061	-4.88346437980607
57	13	15.4410597590180	-2.44105975901798
58	11	14.9545700845368	-3.95457008453676
59	14	14.726401615604	-0.726401615604001
60	15	13.2075779158707	1.79242208412926
61	10	14.0220843152958	-4.02208431529579
62	11	12.741917967334	-1.74191796733400
63	12	13.8374257407787	-1.83742574077869
64	15	13.1224673399753	1.87753266002472
65	15	14.4842436573547	0.515756342645343
66	14	13.7531639125390	0.246836087460958
67	16	13.1925020617359	2.80749793826409
68	15	14.9277012822455	0.0722987177544991
69	15	15.2427298471073	-0.242729847107324
70	13	14.8170685028367	-1.81706850283673
71	17	14.8375496606220	2.16245033937797
72	13	13.3745828755644	-0.37458287556444
73	15	13.7439756906725	1.25602430932753
74	13	14.554042127295	-1.55404212729500
75	15	14.0671102094667	0.932889790533274
76	16	14.5215787074808	1.47842129251923
77	15	14.5461563228556	0.453843677144362
78	16	14.2117358221213	1.78826417787872
79	15	14.3180395985345	0.681960401465486
80	14	14.7377088005423	-0.737708800542279
81	15	12.2990048976007	2.70099510239928
82	7	11.6715508490726	-4.67155084907257
83	17	14.9805113422822	2.0194886577178
84	13	14.5147066422741	-1.51470664227414
85	15	13.6307527450909	1.36924725490912
86	14	13.8463059794131	0.153694020586945
87	13	13.7154514978716	-0.715451497871638
88	16	15.2664000925737	0.733599907426265
89	12	14.1509407882566	-2.15094078825657
90	14	15.5285006361618	-1.52850063616180
91	17	14.6738923371139	2.32610766288613
92	15	15.4878392217852	-0.487839221785187
93	17	13.2265010734638	3.77349892653621
94	12	13.9346446367192	-1.93464463671918
95	16	15.3600481944662	0.639951805533752
96	11	14.0844254755203	-3.08442547552025
97	15	13.2341424332127	1.76585756678735
98	9	14.0630057963438	-5.06300579634381
99	16	14.722995177714	1.27700482228601
100	10	13.0708203937425	-3.07082039374252
101	10	13.2045645870976	-3.20456458709756
102	15	14.8764284007164	0.123571599283556
103	11	13.9252878062601	-2.92528780626008
104	13	15.1863686071566	-2.18636860715656
105	14	13.225325560287	0.774674439713003
106	18	14.6184280211542	3.38157197884583
107	16	15.0834959090075	0.916504090992459
108	14	12.3008999283921	1.69910007160793
109	14	13.1771891454181	0.82281085458187
110	14	13.1981807063311	0.801819293668948
111	14	14.3127438182216	-0.312743818221648
112	12	13.7001098309657	-1.70010983096573
113	14	14.4638814051687	-0.463881405168717
114	15	14.3118047763015	0.68819522369848
115	15	14.9646733966296	0.0353266033704079
116	13	13.5736718031087	-0.573671803108669
117	17	14.8819899432468	2.11801005675318
118	17	15.3550100799349	1.64498992006510
119	19	14.9387016044131	4.06129839558688
120	15	13.8607229834053	1.13927701659474
121	13	14.0527081029942	-1.05270810299424
122	9	12.1771991614099	-3.17719916140986
123	15	15.0418790087624	-0.0418790087624142
124	15	14.5587721624333	0.441227837566655
125	16	13.8499906545279	2.15000934547209
126	11	13.2810069511133	-2.28100695111328
127	14	14.5860703071595	-0.58607030715945
128	11	12.6338756957475	-1.63387569574755
129	15	13.3679284248399	1.63207157516014
130	13	13.3853231292893	-0.385323129289257
131	16	12.6870887460228	3.31291125397724
132	14	14.6631349353270	-0.663134935327046
133	15	14.7954102298823	0.204589770117651
134	16	13.0148193934049	2.98518060659512
135	16	15.4402781789436	0.559721821056384
136	11	12.4000225370024	-1.4000225370024
137	13	13.9992080202958	-0.999208020295785
138	16	14.6067730280030	1.39322697199697
139	12	13.9855072458696	-1.98550724586963
140	9	11.4645641357693	-2.46456413576929
141	13	11.4594581978043	1.54054180219571
142	13	14.5147066422741	-1.51470664227414
143	19	14.9387016044131	4.06129839558688
144	13	15.4912077042297	-2.49120770422968

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
13	0.332278062883377	0.664556125766754	0.667721937116623
14	0.295505094733614	0.591010189467229	0.704494905266386
15	0.228416901523891	0.456833803047782	0.771583098476109
16	0.261121833634578	0.522243667269157	0.738878166365422
17	0.884431059973162	0.231137880053677	0.115568940026838
18	0.843921394026472	0.312157211947055	0.156078605973528
19	0.824776882105781	0.350446235788438	0.175223117894219
20	0.860960494113242	0.278079011773517	0.139039505886758
21	0.843748075539599	0.312503848920803	0.156251924460402
22	0.82654426363689	0.346911472726218	0.173455736363109
23	0.836077440852032	0.327845118295936	0.163922559147968
24	0.924246692022634	0.151506615954733	0.0757533079773663
25	0.901739028678314	0.196521942643371	0.0982609713216856
26	0.898535233509654	0.202929532980691	0.101464766490346
27	0.943489967583227	0.113020064833546	0.0565100324167729
28	0.922590784666578	0.154818430666843	0.0774092153334216
29	0.912634920089224	0.174730159821552	0.0873650799107759
30	0.925164844196968	0.149670311606065	0.0748351558030323
31	0.900628869249186	0.198742261501628	0.0993711307508142
32	0.874256879583196	0.251486240833608	0.125743120416804
33	0.885792935024182	0.228414129951637	0.114207064975819
34	0.906320118824906	0.187359762350187	0.0936798811750935
35	0.891506398545788	0.216987202908424	0.108493601454212
36	0.880855517417588	0.238288965164824	0.119144482582412
37	0.855898870610863	0.288202258778273	0.144101129389137
38	0.840426252433594	0.319147495132812	0.159573747566406
39	0.84207409826136	0.315851803477281	0.157925901738640
40	0.837475990488177	0.325048019023646	0.162524009511823
41	0.805920422317453	0.388159155365094	0.194079577682547
42	0.834945394105331	0.330109211789338	0.165054605894669
43	0.801186426351701	0.397627147296597	0.198813573648299
44	0.79435379379866	0.41129241240268	0.20564620620134
45	0.754491407692555	0.49101718461489	0.245508592307445
46	0.819080862136607	0.361838275726786	0.180919137863393
47	0.799173564935804	0.401652870128391	0.200826435064195
48	0.892226016548225	0.215547966903549	0.107773983451775
49	0.879757641557083	0.240484716885833	0.120242358442917
50	0.87990299974386	0.240194000512280	0.120097000256140
51	0.868398696380083	0.263202607239833	0.131601303619917
52	0.857658415489145	0.284683169021709	0.142341584510855
53	0.839327503092114	0.321344993815772	0.160672496907886
54	0.842816682998975	0.314366634002050	0.157183317001025
55	0.826099425844712	0.347801148310576	0.173900574155288
56	0.910381742128437	0.179236515743127	0.0896182578715633
57	0.917085760533073	0.165828478933855	0.0829142394669274
58	0.944988871811837	0.110022256376326	0.0550111281881629
59	0.93238184747905	0.135236305041900	0.0676181525209498
60	0.927572558546979	0.144854882906042	0.072427441453021
61	0.937782115615568	0.124435768768863	0.0622178843844316
62	0.920651465742824	0.158697068514352	0.0793485342571758
63	0.908431510228342	0.183136979543316	0.0915684897716579
64	0.940854480285124	0.118291039429753	0.0591455197148765
65	0.932229649946383	0.135540700107234	0.0677703500536172
66	0.916984455513197	0.166031088973605	0.0830155444868027
67	0.932598346573652	0.134803306852696	0.0674016534263478
68	0.91969883244119	0.160602335117620	0.0803011675588101
69	0.899387258213529	0.201225483572942	0.100612741786471
70	0.891899662513842	0.216200674972317	0.108100337486158
71	0.892126967880445	0.215746064239109	0.107873032119555
72	0.867820450648947	0.264359098702107	0.132179549351053
73	0.852301858326413	0.295396283347174	0.147698141673587
74	0.844643314403429	0.310713371193142	0.155356685596571
75	0.818948091770497	0.362103816459005	0.181051908229503
76	0.807130665022627	0.385738669954745	0.192869334977373
77	0.771359269855301	0.457281460289398	0.228640730144699
78	0.752492149474444	0.495015701051112	0.247507850525556
79	0.712436002554289	0.575127994891422	0.287563997445711
80	0.672959108075029	0.654081783849943	0.327040891924971
81	0.700061118112297	0.599877763775406	0.299938881887703
82	0.807544175119132	0.384911649761737	0.192455824880868
83	0.793712724519645	0.41257455096071	0.206287275480355
84	0.773534561777308	0.452930876445385	0.226465438222692
85	0.747685614415519	0.504628771168962	0.252314385584481
86	0.704196134917091	0.591607730165818	0.295803865082909
87	0.663140050183279	0.673719899633442	0.336859949816721
88	0.628883910644597	0.742232178710806	0.371116089355403
89	0.620765658591415	0.75846868281717	0.379234341408585
90	0.597005118575495	0.805989762849009	0.402994881424505
91	0.597801551007749	0.804396897984503	0.402198448992251
92	0.55132156124337	0.89735687751326	0.44867843875663
93	0.713061860297512	0.573876279404977	0.286938139702488
94	0.692747603692481	0.614504792615038	0.307252396307519
95	0.657547700722988	0.684904598554023	0.342452299277012
96	0.68922083076564	0.621558338468722	0.310779169234361
97	0.69662568658985	0.6067486268203	0.303374313410150
98	0.892004909359708	0.215990181280584	0.107995090640292
99	0.875642516759372	0.248714966481255	0.124357483240628
100	0.87071551816381	0.258568963672382	0.129284481836191
101	0.878420926066322	0.243158147867355	0.121579073933678
102	0.845658568751792	0.308682862496416	0.154341431248208
103	0.87024353047592	0.259512939048161	0.129756469524080
104	0.900482731424374	0.199034537151253	0.0995172685756264
105	0.891792211055875	0.216415577888250	0.108207788944125
106	0.894855860948435	0.21028827810313	0.105144139051565
107	0.875135934749661	0.249728130500679	0.124864065250339
108	0.907712113682479	0.184575772635042	0.092287886317521
109	0.884350719660121	0.231298560679758	0.115649280339879
110	0.889643851268033	0.220712297463934	0.110356148731967
111	0.85856910446366	0.28286179107268	0.14143089553634
112	0.840803532972898	0.318392934054203	0.159196467027101
113	0.799621730450113	0.400756539099774	0.200378269549887
114	0.747514767842477	0.504970464315045	0.252485232157523
115	0.705217094645946	0.589565810708109	0.294782905354054
116	0.639214549676832	0.721570900646335	0.360785450323168
117	0.702154641374285	0.595690717251431	0.297845358625716
118	0.731722811242165	0.536554377515670	0.268277188757835
119	0.732951866394142	0.534096267211715	0.267048133605858
120	0.744571664272433	0.510856671455133	0.255428335727567
121	0.745066899254621	0.509866201490757	0.254933100745379
122	0.69973076191612	0.600538476167759	0.300269238083879
123	0.629417056057465	0.74116588788507	0.370582943942535
124	0.544788343120138	0.910423313759723	0.455211656879862
125	0.504397976868921	0.991204046262158	0.495602023131079
126	0.419394281792616	0.838788563585232	0.580605718207384
127	0.327636924176015	0.65527384835203	0.672363075823985
128	0.298051624859243	0.596103249718486	0.701948375140757
129	0.221925946962777	0.443851893925553	0.778074053037223
130	0.229217071237245	0.45843414247449	0.770782928762755
131	0.981168985904672	0.0376620281906566	0.0188310140953283

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	1	0.00840336134453781	OK
10% type I error level	1	0.00840336134453781	OK