Multiple Linear Regression - Estimated Regression Equation

Time[t] = + 1.01138573870643 + 0.269255495850061Logins[t] + 0.404714263529591Reviewed_compendiums[t] + 0.176272052812395long_feedback[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)	1.01138573870643	2.460513	0.411	0.681588	0.340794
Logins	0.269255495850061	0.03539	7.6081	0	0
Reviewed_compendiums	0.404714263529591	0.659338	0.6138	0.540207	0.270103
long_feedback	0.176272052812395	0.172019	1.0247	0.30704	0.15352

Multiple Linear Regression - Regression Statistics
Multiple R	0.80587761427563
R-squared	0.64943872919058
Adjusted R-squared	0.642865705362904
F-TEST (value)	98.8036474865693
F-TEST (DF numerator)	3
F-TEST (DF denominator)	160
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	11.5445604323912
Sum Squared Residuals	21324.3000923411

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	47	41.3706426280056	5.62935737199436
2	24	35.6028828766555	-11.6028828766555
3	31	36.5514661629844	-5.55146616298437
4	42	48.2455215856906	-6.24552158569063
5	24	22.6561742283104	1.34382577168965
6	10	23.6148242604742	-13.6148242604742
7	85	43.773531195195	41.226468804805
8	9	24.4145579542705	-15.4145579542705
9	32	31.6242533905634	0.375746609436629
10	36	28.7882068706293	7.2117931293707
11	45	50.5731628426487	-5.57316284264868
12	36	60.4125355231286	-24.4125355231286
13	28	35.2944761351816	-7.29447613518161
14	54	48.5712925473988	5.42870745260122
15	39	46.9470774621813	-7.9470774621813
16	70	71.200482984148	-1.20048298414792
17	50	38.2502877478595	11.7497122521405
18	55	52.0097404964924	2.99025950350764
19	32	31.0857423988632	0.91425760113675
20	44	46.8868745105226	-2.88687451052256
21	46	42.3138678832354	3.68613211676464
22	80	42.8292932168195	37.1707067831805
23	25	22.0691890702955	2.93081092970446
24	30	42.9216358492834	-12.9216358492834
25	41	51.9371679489159	-10.9371679489159
26	40	50.8220074430376	-10.8220074430376
27	45	45.0693005560495	-0.069300556049528
28	45	44.9037445654354	0.0962554345646405
29	30	32.9431084095339	-2.94310840953386
30	52	43.4795365075094	8.52046349249056
31	53	47.6946409980727	5.30535900192726
32	36	48.0913224678484	-12.0913224678484
33	57	50.0346518509486	6.96534814905144
34	17	29.0574623664794	-12.0574623664794
35	68	45.1730000612854	22.8269999387146
36	46	37.4849965849511	8.51500341504886
37	73	55.5960338207622	17.4039661792378
38	34	35.9651218155433	-1.96512181554327
39	22	16.0090881649794	5.99091183502061
40	58	56.0211504739635	1.97884952603654
41	62	42.8604116686894	19.1395883313106
42	32	38.385746515539	-6.38574651553899
43	38	36.1005805832228	1.8994194167772
44	23	31.7827978163589	-8.78279781635889
45	26	32.7514115797873	-6.7514115797873
46	85	54.8334174205087	30.1665825794913
47	22	37.2969957467947	-15.2969957467947
48	44	47.8806078841481	-3.88060788414808
49	62	56.3586502210157	5.64134977898434
50	36	43.0437037921099	-7.04370379210992
51	36	36.3160038816591	-0.316003881659058
52	7	11.207639326975	-4.20763932697499
53	72	89.9269405613994	-17.9269405613994
54	18	24.6838134501205	-6.68381345012054
55	27	31.4603509336687	-4.46035093366874
56	48	29.7722454109919	18.2277545890081
57	50	55.5234612731857	-5.52346127318567
58	55	57.6366834490638	-2.63668344906382
59	59	48.121419690783	10.878580309217
60	39	38.2777102081393	0.722289791860728
61	68	57.5136027830915	10.4863972169085
62	57	43.8160065198369	13.1839934801631
63	40	51.7565590939396	-11.7565590939396
64	47	45.1402195699065	1.85978043009351
65	39	37.4425212603093	1.55747873969072
66	32	26.7298211095213	5.2701788904787
67	32	44.7247892441787	-12.7247892441787
68	40	57.9634671339178	-17.9634671339178
69	42	40.1350762188099	1.86492378119012
70	26	29.8829564810464	-3.88295648104642
71	33	36.7605187071757	-3.76051870717569
72	19	30.0415009068419	-11.0415009068419
73	35	39.7223291615264	-4.72232916152636
74	41	36.9040102686092	4.09598973139085
75	27	34.7171858104297	-7.71718581042974
76	53	39.9915846573764	13.0084153426236
77	55	37.8499102864937	17.1500897135063
78	29	41.2723011538689	-12.2723011538689
79	25	34.4151498232008	-9.41514982320076
80	33	39.1838181698262	-6.18381816982623
81	27	28.5366790017961	-1.53667900179611
82	76	51.4642179399736	24.5357820600264
83	37	38.8162211998394	-1.81622119983939
84	38	35.3001030642823	2.69989693571768
85	22	15.9161047219417	6.08389527805828
86	30	33.9368417831594	-3.93684178315938
87	27	34.2388777703884	-7.23887777038836
88	63	57.6366834490638	5.36331655093617
89	48	44.9672715961121	3.0327284038879
90	33	48.9425770031863	-15.9425770031863
91	37	40.1447710520728	-3.14477105207282
92	42	41.0686066407767	0.931393359223343
93	31	34.5683362178972	-3.56833621789716
94	47	40.67358721051	6.32641278949
95	52	40.67358721051	11.32641278949
96	36	29.7722454109919	6.22775458900813
97	40	28.7243079273804	11.2756920726196
98	53	41.4813536980602	11.5186463019398
99	56	68.5885418727672	-12.5885418727672
100	69	43.9320756209905	25.0679243790095
101	43	51.3207263785401	-8.32072637854012
102	51	39.8480930959429	11.1519069040571
103	30	52.389707062397	-22.389707062397
104	12	24.9858494373495	-12.9858494373495
105	35	29.2461040152095	5.75389598479048
106	36	47.9381275673625	-11.9381275673625
107	41	32.3540892994379	8.64591070056206
108	52	44.1739086565608	7.8260913434392
109	21	30.5375365739002	-9.53753657390019
110	26	44.971980310848	-18.971980310848
111	49	37.1404852730803	11.8595147269197
112	39	44.1986563541858	-5.19865635418578
113	6	4.10865496073664	1.89134503926336
114	35	41.0358261493977	-6.03582614939773
115	17	17.8353357237801	-0.835335723780074
116	25	38.6275795511092	-13.6275795511092
117	71	42.4928146987026	28.5071853012974
118	6	5.31947367230741	0.680526327692589
119	47	27.8917937422053	19.1082062577947
120	9	13.7717555884042	-4.77175558840418
121	52	47.0524305011367	4.94756949886327
122	38	43.2527563363012	-5.25275633630124
123	21	39.3273097312597	-18.3273097312597
124	21	29.42939613863	-8.42939613863002
125	11	18.1631321317799	-7.16313213177988
126	25	31.2770673160377	-6.2770673160377
127	54	49.5014988903476	4.49850110965245
128	38	46.6326718790345	-8.63267187903455
129	68	47.9966769853017	20.0033230146983
130	56	54.255114372611	1.74488562738902
131	71	58.006963687495	12.993036312505
132	39	29.6287538495584	9.3712461504416
133	21	30.310756402692	-9.310756402692
134	53	79.1771231170687	-26.1771231170687
135	78	62.6568796645225	15.3431203354775
136	14	26.5411794607911	-12.5411794607911
137	70	52.72184877835	17.2781512216499
138	29	39.522971450598	-10.522971450598
139	47	37.5177770763301	9.48222292366993
140	36	41.7425764001563	-5.74257640015631
141	21	33.7154111372608	-12.7154111372608
142	69	45.4218446616743	23.5781553383257
143	42	41.3050816452478	0.694918354752208
144	48	40.3989736835608	7.60102631643917
145	55	51.8264568788613	3.17354312113868
146	19	45.615852847293	-26.615852847293
147	39	39.6062600603727	-0.606260060372699
148	51	50.3544154651944	0.645584534805574
149	0	1.01138573870644	-1.01138573870644
150	4	3.70394069720705	0.296059302792954
151	0	1.2806412345565	-1.2806412345565
152	0	1.54989673040656	-1.54989673040656
153	0	1.01138573870644	-1.01138573870644
154	0	1.01138573870644	-1.01138573870644
155	38	37.766621676719	0.233378323281036
156	51	50.186176206136	0.813823793864031
157	0	1.01138573870644	-1.01138573870644
158	0	2.08840772210668	-2.08840772210668
159	2	2.35766321795674	-0.357663217956742
160	13	11.0641477655415	1.93585223445848
161	5	3.46746569273591	1.53253430726409
162	20	32.044020518455	-12.044020518455
163	0	1.54989673040656	-1.54989673040656
164	29	25.8909361701012	3.10906382989881

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
7	0.96207692639189	0.075846147216221	0.0379230736081105
8	0.925465960291248	0.149068079417504	0.0745340397087521
9	0.87199407616112	0.25601184767776	0.12800592383888
10	0.911138157182432	0.177723685635136	0.088861842817568
11	0.871944759579876	0.256110480840248	0.128055240420124
12	0.87143839077244	0.25712321845512	0.12856160922756
13	0.816651322067685	0.366697355864629	0.183348677932315
14	0.939269818787936	0.121460362424127	0.0607301812120635
15	0.911223335428172	0.177553329143657	0.0887766645718283
16	0.8981001758811	0.203799648237799	0.101899824118899
17	0.921308043113798	0.157383913772404	0.078691956886202
18	0.9060204228184	0.187959154363201	0.0939795771816004
19	0.871291577130131	0.257416845739738	0.128708422869869
20	0.835084694752395	0.32983061049521	0.164915305247605
21	0.80176470959453	0.396470580810939	0.19823529040547
22	0.979650915240188	0.0406981695196245	0.0203490847598122
23	0.970545755249396	0.058908489501207	0.0294542447506035
24	0.96151529601569	0.0769694079686205	0.0384847039843102
25	0.959675158173457	0.0806496836530851	0.0403248418265426
26	0.966503530472015	0.0669929390559701	0.0334964695279851
27	0.955491319926878	0.0890173601462437	0.0445086800731219
28	0.940438735917641	0.119122528164717	0.0595612640823585
29	0.920899404621115	0.158201190757771	0.0791005953788853
30	0.924951837006278	0.150096325987444	0.0750481629937218
31	0.913684347225034	0.172631305549932	0.086315652774966
32	0.909346955079058	0.181306089841884	0.0906530449209419
33	0.896804722751913	0.206390554496173	0.103195277248087
34	0.892781599948399	0.214436800103202	0.107218400051601
35	0.948788218597443	0.102423562805114	0.0512117814025572
36	0.942492675147835	0.115014649704329	0.0575073248521646
37	0.953687781779203	0.0926244364415937	0.0463122182207969
38	0.940252838842262	0.119494322315477	0.0597471611577383
39	0.924597145593598	0.150805708812803	0.0754028544064017
40	0.906802535022075	0.186394929955851	0.0931974649779254
41	0.935098238212821	0.129803523574357	0.0649017617871786
42	0.922615071216627	0.154769857566747	0.0773849287833733
43	0.902517000665791	0.194965998668418	0.097482999334209
44	0.890881301094965	0.218237397810069	0.109118698905035
45	0.885204262730588	0.229591474538823	0.114795737269412
46	0.956096439343672	0.0878071213126553	0.0439035606563276
47	0.961121817051731	0.0777563658965374	0.0388781829482687
48	0.950598867824034	0.0988022643519317	0.0494011321759658
49	0.94000231519326	0.119995369613478	0.0599976848067392
50	0.927831912832292	0.144336174335416	0.072168087167708
51	0.91184060280883	0.176318794382339	0.0881593971911694
52	0.896436543296406	0.207126913407187	0.103563456703594
53	0.951401519352678	0.0971969612946443	0.0485984806473222
54	0.942855032576292	0.114289934847415	0.0571449674237075
55	0.930913819287101	0.138172361425797	0.0690861807128987
56	0.948540898672683	0.102918202654635	0.0514591013273174
57	0.93778572095207	0.124428558095862	0.0622142790479309
58	0.923532662685974	0.152934674628052	0.076467337314026
59	0.921105481460337	0.157789037079326	0.0788945185396628
60	0.902438046394831	0.195123907210338	0.0975619536051691
61	0.897717735979958	0.204564528040083	0.102282264020042
62	0.901474673211026	0.197050653577947	0.0985253267889737
63	0.901945085864758	0.196109828270484	0.0980549141352422
64	0.880867662506878	0.238264674986244	0.119132337493122
65	0.856552020532742	0.286895958934515	0.143447979467258
66	0.833252111489989	0.333495777020023	0.166747888510011
67	0.842176281149986	0.315647437700028	0.157823718850014
68	0.875231651354847	0.249536697290306	0.124768348645153
69	0.850591596141263	0.298816807717473	0.149408403858737
70	0.826519406540154	0.346961186919692	0.173480593459846
71	0.79906007215042	0.401879855699162	0.200939927849581
72	0.796700424037265	0.40659915192547	0.203299575962735
73	0.76867001676047	0.462659966479059	0.23132998323953
74	0.73673673627046	0.52652652745908	0.26326326372954
75	0.715782455054406	0.568435089891189	0.284217544945594
76	0.724142946699361	0.551714106601278	0.275857053300639
77	0.76392277716672	0.472154445666561	0.23607722283328
78	0.768086739884262	0.463826520231476	0.231913260115738
79	0.756522942540368	0.486954114919264	0.243477057459632
80	0.730373383388873	0.539253233222253	0.269626616611127
81	0.692498407502595	0.61500318499481	0.307501592497405
82	0.814306870736141	0.371386258527718	0.185693129263859
83	0.783140127128316	0.433719745743368	0.216859872871684
84	0.753392141551103	0.493215716897793	0.246607858448897
85	0.725310854379231	0.549378291241538	0.274689145620769
86	0.690726365104271	0.618547269791458	0.309273634895729
87	0.665656391940953	0.668687216118093	0.334343608059047
88	0.634680382505629	0.730639234988742	0.365319617494371
89	0.59318635710413	0.81362728579174	0.40681364289587
90	0.628959481331797	0.742081037336406	0.371040518668203
91	0.58832630516859	0.82334738966282	0.41167369483141
92	0.543461929019511	0.913076141960978	0.456538070980489
93	0.502351051564523	0.995297896870954	0.497648948435477
94	0.470020373105604	0.940040746211208	0.529979626894396
95	0.467931617392938	0.935863234785877	0.532068382607062
96	0.434944671676348	0.869889343352696	0.565055328323652
97	0.428271506616665	0.85654301323333	0.571728493383335
98	0.428078747222221	0.856157494444442	0.571921252777779
99	0.429201965990938	0.858403931981875	0.570798034009062
100	0.601538641575809	0.796922716848382	0.398461358424191
101	0.57650657734167	0.84698684531666	0.42349342265833
102	0.57399860301392	0.85200279397216	0.42600139698608
103	0.687976837699785	0.62404632460043	0.312023162300215
104	0.698548793653746	0.602902412692508	0.301451206346254
105	0.666833403711181	0.666333192577638	0.333166596288819
106	0.668660986711618	0.662678026576764	0.331339013288382
107	0.649930383337565	0.70013923332487	0.350069616662435
108	0.626489814480188	0.747020371039624	0.373510185519812
109	0.609286601465008	0.781426797069984	0.390713398534992
110	0.68985981443037	0.62028037113926	0.31014018556963
111	0.690119104943272	0.619761790113456	0.309880895056728
112	0.65310213108556	0.69379573782888	0.34689786891444
113	0.609097974337151	0.781804051325698	0.390902025662849
114	0.574293493086888	0.851413013826224	0.425706506913112
115	0.526034265540485	0.94793146891903	0.473965734459515
116	0.545335616479451	0.909328767041097	0.454664383520549
117	0.775064676987366	0.449870646025269	0.224935323012634
118	0.735927093483233	0.528145813033534	0.264072906516767
119	0.820222524759636	0.359554950480727	0.179777475240364
120	0.786919609135392	0.426160781729216	0.213080390864608
121	0.757275457905492	0.485449084189016	0.242724542094508
122	0.721314406583802	0.557371186832396	0.278685593416198
123	0.795999897331229	0.408000205337542	0.204000102668771
124	0.77132957497826	0.45734085004348	0.22867042502174
125	0.73888737017699	0.522225259646021	0.26111262982301
126	0.71046143007327	0.579077139853461	0.28953856992673
127	0.663995687160441	0.672008625679117	0.336004312839559
128	0.660246374307609	0.679507251384782	0.339753625692391
129	0.736998435896218	0.526003128207563	0.263001564103782
130	0.687472878570577	0.625054242858847	0.312527121429423
131	0.703675365079409	0.592649269841182	0.296324634920591
132	0.692014744737851	0.615970510524298	0.307985255262149
133	0.667191879660298	0.665616240679403	0.332808120339702
134	0.990580976571655	0.0188380468566908	0.00941902342834542
135	0.986787568227788	0.0264248635444232	0.0132124317722116
136	0.981146746233544	0.0377065075329119	0.018853253766456
137	0.983312847728447	0.0333743045431061	0.0166871522715531
138	0.983023812404094	0.0339523751918123	0.0169761875959061
139	0.99496859258195	0.0100628148360989	0.00503140741804943
140	0.991824669020677	0.0163506619586464	0.00817533097932318
141	0.99999998324084	3.35183209871494e-08	1.67591604935747e-08
142	0.999999980678882	3.86422368929187e-08	1.93211184464593e-08
143	0.99999994460598	1.10788039574631e-07	5.53940197873153e-08
144	0.999999784925334	4.30149332853657e-07	2.15074666426829e-07
145	0.999999750926722	4.98146555459615e-07	2.49073277729808e-07
146	0.999999997603152	4.79369516161665e-09	2.39684758080832e-09
147	0.999999991494438	1.70111233888427e-08	8.50556169442134e-09
148	0.999999979062647	4.1874706272619e-08	2.09373531363095e-08
149	0.999999874870108	2.50259783162278e-07	1.25129891581139e-07
150	0.999999445810487	1.10837902668573e-06	5.54189513342863e-07
151	0.99999666266781	6.67466437867945e-06	3.33733218933973e-06
152	0.99998177779763	3.64444047389576e-05	1.82222023694788e-05
153	0.999903976163252	0.000192047673495973	9.60238367479864e-05
154	0.999527094309906	0.000945811380188266	0.000472905690094133
155	0.999237282158742	0.00152543568251519	0.000762717841257597
156	0.995904642889865	0.00819071422027045	0.00409535711013523
157	0.988309702666642	0.0233805946667154	0.0116902973333577

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	16	0.105960264900662	NOK
5% type I error level	25	0.165562913907285	NOK
10% type I error level	36	0.23841059602649	NOK