Multiple Linear Regression - Estimated Regression Equation

Learning[t] = + 6.78552844714587 + 0.0265247004285554Gender[t] + 0.562657311049385Software[t] + 0.137355388183658Happiness[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)	6.78552844714587	1.14544	5.924	0	0
Gender	0.0265247004285554	0.313841	0.0845	0.932753	0.466376
Software	0.562657311049385	0.070226	8.0121	0	0
Happiness	0.137355388183658	0.064551	2.1278	0.034902	0.017451

Multiple Linear Regression - Regression Statistics
Multiple R	0.563990472389244
R-squared	0.318085252945843
Adjusted R-squared	0.305137504584055
F-TEST (value)	24.5668392725793
F-TEST (DF numerator)	3
F-TEST (DF denominator)	158
p-value	4.21662704752634e-13
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	1.8807833914639
Sum Squared Residuals	558.90069416582

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	13	15.4869163147383	-2.48691631473827
2	16	15.4736805564235	0.526319443576509
3	19	16.7628220833354	2.23717791666457
4	15	11.8097369716461	3.19026302835394
5	14	16.3242844021549	-2.32428440215495
6	13	14.9110232453741	-1.91102324537411
7	19	15.4869163147382	3.51308368526175
8	15	16.612230936837	-1.61223093683702
9	14	15.6242717029219	-1.6242717029219
10	15	12.2483278366256	2.75167216337441
11	16	14.7471431567619	1.25285684323811
12	16	16.1736932556565	-0.173693255656533
13	16	14.9109700615751	1.08902993842494
14	16	15.1989697800562	0.801030219943824
15	17	17.724309800621	-0.724309800621031
16	15	15.4603916143097	-0.46039161430969
17	15	14.3350769922109	0.66492300778908
18	20	15.8989824792892	4.10101752071078
19	18	14.8977343032603	3.10226569673969
20	16	15.7616270911056	0.238372908894439
21	16	15.4471558559949	0.552844144005065
22	16	15.0748501501873	0.925149849812727
23	19	16.0495736257876	2.95042637421237
24	16	14.6495482273215	1.35045177267845
25	17	14.1844858457125	2.81551415428749
26	17	15.3627966848693	1.63720331513066
27	16	14.6097877685782	1.39021223142176
28	15	16.612230936837	-1.61223093683702
29	16	15.6242717029219	0.375728297078097
30	14	13.9230108276599	0.0769891723400525
31	15	15.7616270911056	-0.761627091105561
32	12	13.0724069819285	-1.07240698192849
33	14	14.7736678571904	-0.773667857190448
34	16	15.6242717029219	0.375728297078097
35	14	15.4603916143097	-1.46039161430969
36	7	12.9218158354301	-5.92181583543008
37	10	11.3976708070951	-1.39767080709509
38	14	15.5977470024933	-1.59774700249335
39	16	14.7736678571904	1.22633214280955
40	16	14.1977216040273	1.80227839597274
41	16	14.4724323803946	1.52756761960542
42	14	15.7616270911056	-1.76162709110556
43	20	17.4230743238252	2.57692567617484
44	14	14.0603662158436	-0.060366215843605
45	14	14.0868909162722	-0.0868909162721604
46	11	15.0748501501873	-4.07485015018727
47	14	16.1869290139713	-2.18692901397129
48	15	15.0616143918725	-0.0616143918725182
49	16	15.3363251682398	0.663674831760167
50	14	15.323036226126	-1.32303622612603
51	16	16.8869417132043	-0.886941713204331
52	14	14.3350769922109	-0.33507699221092
53	12	15.0483254497587	-3.04832544975872
54	16	15.7748628494203	0.225137150579684
55	9	11.2470796605967	-2.24707966059668
56	14	12.2483278366256	1.75167216337441
57	16	15.7616270911056	0.238372908894439
58	16	15.6242717029219	0.375728297078097
59	15	14.623023526893	0.37697647310701
60	16	14.0868909162722	1.91310908372784
61	12	11.8229727299608	0.17702727003918
62	16	15.323036226126	0.676963773873967
63	16	16.200164772286	-0.200164772286043
64	14	14.9242590036889	-0.924259003688861
65	16	15.6242717029219	0.375728297078097
66	17	15.4736273726244	1.52637262737555
67	18	16.200164772286	1.79983522771396
68	18	14.623023526893	3.37697647310701
69	12	15.6242717029219	-3.6242717029219
70	16	15.5977470024933	0.402252997506652
71	10	13.2097623701122	-3.20976237011215
72	14	15.1989697800562	-1.19896978005618
73	18	16.7495863250207	1.25041367497933
74	18	16.7230616245921	1.27693837540788
75	16	15.323036226126	0.676963773873967
76	17	13.5242336052228	3.47576639477722
77	16	16.4616397903386	-0.461639790338603
78	16	14.7869036155052	1.2130963844948
79	13	15.5977470024933	-2.59774700249335
80	16	15.323036226126	0.676963773873967
81	16	15.5977470024933	0.402252997506652
82	20	15.735102390677	4.26489760932299
83	16	15.6242717029219	0.375728297078097
84	15	15.735102390677	-0.735102390677005
85	15	15.0616143918725	-0.0616143918725182
86	16	14.3616016926395	1.63839830736052
87	14	13.9097750693452	0.0902249306548073
88	16	15.4869163147382	0.513083685261754
89	16	15.3495609265546	0.650439073445412
90	15	14.5254285974526	0.474571402547357
91	12	14.2110105461411	-2.21101054614106
92	17	17.0375328597027	-0.0375328597027434
93	16	15.6242717029219	0.375728297078097
94	15	15.4869163147382	-0.486916314738246
95	13	15.3495609265546	-2.34956092655459
96	16	14.6363124690068	1.36368753099321
97	16	15.7748628494203	0.225137150579684
98	16	13.7989443815901	2.20105561840991
99	16	15.8724577788607	0.127542221139337
100	14	14.4724323803946	-0.472432380394578
101	16	17.024297101388	-1.02429710138799
102	16	14.623023526893	1.37697647310701
103	20	17.4495990242537	2.55040097574628
104	15	14.4856681387093	0.514331861290667
105	16	15.0616143918725	0.938385608127482
106	13	14.7736146733914	-1.7736146733914
107	17	15.7616270911056	1.23837290889444
108	16	15.5977470024933	0.402252997506652
109	16	14.3483127505257	1.65168724947433
110	12	12.1242082067567	-0.124208206756691
111	16	15.6242717029219	0.375728297078097
112	16	16.200164772286	-0.200164772286043
113	17	14.7869036155052	2.2130963844948
114	13	14.8977343032603	-1.89773430326031
115	12	14.9110232453741	-2.91102324537411
116	18	16.2977597017264	1.70224029827361
117	14	16.0495736257876	-2.04957362578763
118	14	13.2362870705407	0.763712929459294
119	13	14.9242590036889	-1.92425900368886
120	16	15.4869163147382	0.513083685261754
121	13	14.6495482273215	-1.64954822732155
122	16	16.0495736257876	-0.0495736257876306
123	13	15.6242717029219	-2.6242717029219
124	16	16.7495863250207	-0.749586325020673
125	15	16.1869290139713	-1.18692901397129
126	16	17.0375328597027	-1.03753285970274
127	15	14.7471431567619	0.252856843238107
128	17	15.3363251682398	1.66367483176017
129	15	14.4857213225084	0.514278677491621
130	12	15.0616143918725	-3.06161439187252
131	16	14.1977216040273	1.80227839597274
132	10	14.210957362342	-4.21095736234202
133	16	13.3736424587244	2.62635754127564
134	12	15.035089691444	-3.03508969144396
135	14	15.5977470024933	-1.59774700249335
136	15	15.7616270911056	-0.761627091105561
137	13	13.3603535166106	-0.360353516610563
138	15	14.8977343032603	0.102265696739695
139	11	13.9495355280885	-2.9495355280885
140	12	13.3736424587244	-1.37364245872436
141	8	13.6350642929779	-5.63506429297788
142	16	13.3736424587244	2.62635754127564
143	15	14.0471304575288	0.95286954247115
144	17	17.1748882478864	-0.174888247886401
145	16	15.035089691444	0.964910308556037
146	10	13.510997846908	-3.51099784690802
147	18	16.3242844021549	1.67571559784505
148	13	15.0483254497587	-2.04832544975872
149	16	15.1856808379424	0.814319162057625
150	13	13.0856427402432	-0.0856427402432476
151	10	12.9483405358586	-2.94834053585864
152	15	15.912218237604	-0.912218237603973
153	16	14.0471304575288	1.95286954247115
154	16	11.8362616720746	4.16373832792538
155	14	12.5495101296224	1.45048987037758
156	10	13.098931682357	-3.09893168235705
157	17	17.0375328597027	-0.0375328597027434
158	13	12.1109724484419	0.889027551558064
159	15	14.4857213225084	0.514278677491621
160	16	14.7869036155052	1.2130963844948
161	12	12.9615762941734	-0.961576294173391
162	13	13.098931682357	-0.0989316823570487

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
7	0.93495111231262	0.130097775374761	0.0650488876873805
8	0.898305180164411	0.203389639671177	0.101694819835589
9	0.862939674635535	0.274120650728931	0.137060325364465
10	0.794644348491234	0.410711303017533	0.205355651508767
11	0.773973010418934	0.452053979162133	0.226026989581066
12	0.740642541801244	0.518714916397512	0.259357458198756
13	0.678864796713546	0.642270406572908	0.321135203286454
14	0.604578348386077	0.790843303227847	0.395421651613923
15	0.545092548594513	0.909814902810975	0.454907451405487
16	0.480099823062007	0.960199646124015	0.519900176937993
17	0.39869299786971	0.79738599573942	0.60130700213029
18	0.727779277637336	0.544441444725328	0.272220722362664
19	0.752933765737466	0.494132468525069	0.247066234262535
20	0.690051645962337	0.619896708075326	0.309948354037663
21	0.623856169697243	0.752287660605514	0.376143830302757
22	0.556138514328695	0.88772297134261	0.443861485671305
23	0.622035114161693	0.755929771676614	0.377964885838307
24	0.560522235424817	0.878955529150365	0.439477764575183
25	0.558146135545973	0.883707728908054	0.441853864454027
26	0.501120087593607	0.997759824812786	0.498879912406393
27	0.443316070540915	0.88663214108183	0.556683929459085
28	0.433287223833583	0.866574447667165	0.566712776166417
29	0.372254881308093	0.744509762616186	0.627745118691907
30	0.373611539771125	0.74722307954225	0.626388460228875
31	0.333314425931544	0.666628851863087	0.666685574068456
32	0.413393207437906	0.826786414875811	0.586606792562094
33	0.382043005593342	0.764086011186684	0.617956994406658
34	0.327501101806047	0.655002203612094	0.672498898193953
35	0.333455734029131	0.666911468058262	0.666544265970869
36	0.869855706927869	0.260288586144261	0.130144293072131
37	0.881763623117003	0.236472753765994	0.118236376882997
38	0.872854400100063	0.254291199799873	0.127145599899937
39	0.852392568230753	0.295214863538495	0.147607431769247
40	0.842348173896779	0.315303652206441	0.157651826103221
41	0.827266127595209	0.345467744809581	0.172733872404791
42	0.825807929174153	0.348384141651694	0.174192070825847
43	0.846354155867854	0.307291688264292	0.153645844132146
44	0.816903954100495	0.36619209179901	0.183096045899505
45	0.783214724881891	0.433570550236218	0.216785275118109
46	0.900289103511378	0.199421792977244	0.0997108964886221
47	0.906944569178987	0.186110861642026	0.093055430821013
48	0.88443377129161	0.23113245741678	0.11556622870839
49	0.861812974678489	0.276374050643023	0.138187025321511
50	0.851648033769338	0.296703932461324	0.148351966230662
51	0.828010523931024	0.343978952137953	0.171989476068976
52	0.79759733342977	0.404805333140459	0.20240266657023
53	0.84797992261536	0.30404015476928	0.15202007738464
54	0.818228199286441	0.363543601427118	0.181771800713559
55	0.830576668693324	0.338846662613353	0.169423331306676
56	0.824160571211721	0.351678857576557	0.175839428788279
57	0.791915967652274	0.416168064695452	0.208084032347726
58	0.757294279707214	0.485411440585573	0.242705720292787
59	0.720180897354494	0.559638205291012	0.279819102645506
60	0.717596639434902	0.564806721130196	0.282403360565098
61	0.676542006432028	0.646915987135945	0.323457993567972
62	0.638724031950571	0.722551936098857	0.361275968049429
63	0.594381693780996	0.811236612438008	0.405618306219004
64	0.560502185316244	0.878995629367512	0.439497814683756
65	0.515481167576048	0.969037664847905	0.484518832423952
66	0.498370509215808	0.996741018431615	0.501629490784192
67	0.491038719940695	0.98207743988139	0.508961280059305
68	0.585311340839393	0.829377318321215	0.414688659160608
69	0.700041287696187	0.599917424607625	0.299958712303813
70	0.660720630545424	0.678558738909152	0.339279369454576
71	0.734288766019717	0.531422467960566	0.265711233980283
72	0.710765853447397	0.578468293105206	0.289234146552603
73	0.687353566433155	0.62529286713369	0.312646433566845
74	0.664036870763036	0.671926258473929	0.335963129236964
75	0.627241552989536	0.745516894020929	0.372758447010464
76	0.722971860474803	0.554056279050395	0.277028139525198
77	0.685781055027984	0.628437889944031	0.314218944972016
78	0.661221869517528	0.677556260964945	0.338778130482472
79	0.6956811089571	0.608637782085801	0.3043188910429
80	0.660642359537075	0.678715280925851	0.339357640462925
81	0.620169290806925	0.75966141838615	0.379830709193075
82	0.785032571220345	0.429934857559311	0.214967428779655
83	0.751782882186007	0.496434235627987	0.248217117813993
84	0.719102537540499	0.561794924919001	0.280897462459501
85	0.679310146071563	0.641379707856874	0.320689853928437
86	0.669268797116718	0.661462405766564	0.330731202883282
87	0.627326968429038	0.745346063141924	0.372673031570962
88	0.587245936227317	0.825508127545367	0.412754063772683
89	0.548788127261392	0.902423745477217	0.451211872738608
90	0.511594436523254	0.976811126953492	0.488405563476746
91	0.52985930652865	0.940281386942701	0.47014069347135
92	0.48637515471167	0.972750309423339	0.51362484528833
93	0.443101234088436	0.886202468176873	0.556898765911564
94	0.400508979299959	0.801017958599918	0.599491020700041
95	0.420085574884142	0.840171149768283	0.579914425115858
96	0.398432760624365	0.796865521248731	0.601567239375634
97	0.357311495571727	0.714622991143453	0.642688504428273
98	0.374683880144906	0.749367760289812	0.625316119855094
99	0.331757953911505	0.66351590782301	0.668242046088495
100	0.292338510420127	0.584677020840254	0.707661489579873
101	0.2625711204629	0.525142240925801	0.7374288795371
102	0.2516902648336	0.5033805296672	0.7483097351664
103	0.293864157326792	0.587728314653583	0.706135842673209
104	0.263541894590628	0.527083789181256	0.736458105409372
105	0.237766087485371	0.475532174970742	0.762233912514629
106	0.225310271063129	0.450620542126259	0.774689728936871
107	0.209704257313494	0.419408514626988	0.790295742686506
108	0.181505501606199	0.363011003212398	0.818494498393801
109	0.188801448213286	0.377602896426571	0.811198551786714
110	0.158336052132715	0.31667210426543	0.841663947867285
111	0.133793514596905	0.267587029193811	0.866206485403095
112	0.112531548405138	0.225063096810277	0.887468451594862
113	0.132109599607623	0.264219199215246	0.867890400392377
114	0.12461892467174	0.249237849343479	0.87538107532826
115	0.164245183219019	0.328490366438038	0.835754816780981
116	0.170722774085961	0.341445548171922	0.829277225914039
117	0.163224057978837	0.326448115957674	0.836775942021163
118	0.138595557767404	0.277191115534808	0.861404442232596
119	0.131881952771348	0.263763905542696	0.868118047228652
120	0.111641900053911	0.223283800107821	0.888358099946089
121	0.0986279416111845	0.197255883222369	0.901372058388816
122	0.0792380351995677	0.158476070399135	0.920761964800432
123	0.0886842071751338	0.177368414350268	0.911315792824866
124	0.070212537769664	0.140425075539328	0.929787462230336
125	0.0572465816027218	0.114493163205444	0.942753418397278
126	0.0447605337882705	0.089521067576541	0.95523946621173
127	0.0338189324805803	0.0676378649611607	0.96618106751942
128	0.0309685244838327	0.0619370489676654	0.969031475516167
129	0.0227381741412486	0.0454763482824972	0.977261825858751
130	0.0324594205752058	0.0649188411504116	0.967540579424794
131	0.0374786482863863	0.0749572965727726	0.962521351713614
132	0.0672449971226517	0.134489994245303	0.932755002877348
133	0.0834018562659198	0.16680371253184	0.91659814373408
134	0.0996345688106725	0.199269137621345	0.900365431189327
135	0.0847866903661921	0.169573380732384	0.915213309633808
136	0.0652039243933199	0.13040784878664	0.93479607560668
137	0.0476862345857129	0.0953724691714257	0.952313765414287
138	0.0343004632081746	0.0686009264163492	0.965699536791825
139	0.0459322594871847	0.0918645189743694	0.954067740512815
140	0.0374355998517208	0.0748711997034415	0.962564400148279
141	0.258723944744224	0.517447889488447	0.741276055255776
142	0.305755890519708	0.611511781039417	0.694244109480292
143	0.251222058232584	0.502444116465169	0.748777941767416
144	0.194153534850751	0.388307069701502	0.805846465149249
145	0.153810845319308	0.307621690638616	0.846189154680692
146	0.26484405640291	0.52968811280582	0.73515594359709
147	0.262947170451942	0.525894340903885	0.737052829548058
148	0.293410165913392	0.586820331826783	0.706589834086608
149	0.219109833185366	0.438219666370732	0.780890166814634
150	0.220596569449806	0.441193138899612	0.779403430550194
151	0.316800530719288	0.633601061438576	0.683199469280712
152	0.231938329066368	0.463876658132735	0.768061670933632
153	0.153392302269617	0.306784604539234	0.846607697730383
154	0.389461526290244	0.778923052580488	0.610538473709756
155	0.386247076418083	0.772494152836166	0.613752923581917

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	0.00671140939597315	OK
10% type I error level	10	0.0671140939597315	OK