Repository of Reproducible Computations

Multiple Linear Regression - Estimated Regression Equation

Feedback_messages[t] = + 25.220510426338 + 0.266742323363293Blogged_Computations[t] + 0.000245643079172296Aantal_karakters[t] + 0.0674961137724305Logins[t] + 0.00202518167727737Pageviews[t] + 0.000102811188518391Time_Rfc[t] -0.0951477912474194t + 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)	25.220510426338	5.453481	4.6247	8e-06	4e-06
Blogged_Computations	0.266742323363293	0.08242	3.2364	0.001477	0.000738
Aantal_karakters	0.000245643079172296	6.5e-05	3.7597	0.00024	0.00012
Logins	0.0674961137724305	0.07698	0.8768	0.381936	0.190968
Pageviews	0.00202518167727737	0.006248	0.3242	0.746249	0.373125
Time_Rfc	0.000102811188518391	6.3e-05	1.6329	0.104495	0.052248
t	-0.0951477912474194	0.035515	-2.6791	0.008168	0.004084

Multiple Linear Regression - Regression Statistics
Multiple R	0.782854199460412
R-squared	0.612860697612803
Adjusted R-squared	0.598065565037496
F-TEST (value)	41.4231298363401
F-TEST (DF numerator)	6
F-TEST (DF denominator)	157
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	20.6795722070514
Sum Squared Residuals	67140.2189466642

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	84	89.012368300432	-5.012368300432
2	72	66.3380828843241	5.66191711567592
3	41	72.9944478029126	-31.9944478029126
4	85	95.512110438318	-10.512110438318
5	30	55.7574334137691	-25.7574334137691
6	53	43.2391243646259	9.7608756353741
7	74	118.846005550968	-44.846005550968
8	22	35.4741440494013	-13.4741440494013
9	68	70.5601074323198	-2.56010743231976
10	47	69.7215708302095	-22.7215708302095
11	102	77.9260862140226	24.0739137859774
12	123	79.0791140171838	43.9208859828162
13	69	62.6209011488721	6.37909885112788
14	108	85.7484162103747	22.2515837896253
15	59	70.5187316969736	-11.5187316969736
16	122	115.486504862221	6.51349513777915
17	91	96.5088070125774	-5.50880701257737
18	45	92.4912902385658	-47.4912902385658
19	53	80.2953565227343	-27.2953565227343
20	112	91.4359981140556	20.5640018859444
21	82	87.8059282303015	-5.80592823030152
22	92	94.254752214157	-2.25475221415708
23	51	56.2435269453392	-5.24352694533918
24	120	77.0525385200126	42.9474614799874
25	99	88.3593316272628	10.6406683727372
26	86	80.106006755162	5.89399324483799
27	59	84.6179868337647	-25.6179868337647
28	98	84.3466886202478	13.6533113797522
29	71	55.6725568462465	15.3274431537535
30	100	86.2550689658334	13.7449310341666
31	113	95.3857673079073	17.6142326920927
32	92	65.9566763597201	26.0433236402799
33	107	89.5049884520986	17.4950115479014
34	75	48.818421176558	26.181578823442
35	100	99.4223600032223	0.577639996777751
36	69	72.6807291141442	-3.68072911414421
37	106	91.9853440417181	14.0146559582819
38	51	63.4417626492197	-12.4417626492197
39	18	47.6120667759795	-29.6120667759795
40	91	93.2738362157617	-2.27383621576175
41	75	87.0039326173332	-12.0039326173332
42	63	60.7038693200914	2.29613067990862
43	72	69.5987418708713	2.4012581291287
44	59	50.6030454008312	8.39695459916877
45	29	57.8244240957646	-28.8244240957646
46	85	106.452194279279	-21.4521942792792
47	66	46.9929681096263	19.0070318903737
48	106	81.4569954204491	24.5430045795509
49	113	104.607253510296	8.39274648970368
50	101	74.61322275095	26.38677724905
51	65	72.2234978512811	-7.22349785128112
52	7	28.9795340598044	-21.9795340598044
53	111	103.251431492744	7.74856850725575
54	61	43.019924239932	17.980075760068
55	41	52.0035645001976	-11.0035645001976
56	70	78.980288413574	-8.980288413574
57	136	94.1535823794081	41.8464176205919
58	87	100.836532404124	-13.8365324041239
59	90	100.846562300324	-10.8465623003244
60	76	68.1450118668862	7.85498813311377
61	101	107.691934807307	-6.69193480730726
62	57	103.500508259903	-46.5005082599026
63	61	64.2206635723639	-3.22066357236389
64	92	75.2650630338763	16.7349369661237
65	80	66.4574417477215	13.5425582522785
66	35	63.1551784376346	-28.1551784376346
67	72	77.8743232292936	-5.87432322929357
68	88	76.2128369704556	11.7871630295444
69	80	83.551677666834	-3.55167766683403
70	62	73.7987817188218	-11.7987817188218
71	81	64.288109066832	16.711890933168
72	63	40.5215200623056	22.4784799376944
73	91	64.8720748627499	26.1279251372501
74	65	70.4781363912089	-5.47813639120887
75	79	71.5643249427148	7.43567505728524
76	85	87.2752164340664	-2.27521643406643
77	75	84.913899325966	-9.91389932596607
78	70	99.5390184666305	-29.5390184666305
79	78	62.2137687803098	15.7862312196902
80	75	60.060135222833	14.939864777167
81	55	53.8523719488108	1.14762805118923
82	80	104.030806566554	-24.0308065665542
83	83	53.5741845514555	29.4258154485445
84	38	76.07254552104	-38.07254552104
85	27	55.8843094916738	-28.8843094916738
86	62	44.0761156993453	17.9238843006547
87	82	61.0467021885023	20.9532978114977
88	88	81.0571586137128	6.94284138628719
89	59	64.7569955129399	-5.75699551293985
90	92	90.825946495529	1.17405350447097
91	40	54.4266974899099	-14.4266974899099
92	91	86.181235722078	4.81876427792195
93	63	49.8597616941857	13.1402383058143
94	88	74.129785703452	13.870214296548
95	85	73.5796981782786	11.4203018217214
96	76	71.407345999105	4.59265400089498
97	67	85.7132095689852	-18.7132095689852
98	69	106.052320235737	-37.0523202357373
99	150	93.1414400720567	56.8585599279433
100	77	108.398807708788	-31.3988077087877
101	103	81.0527558116722	21.9472441883278
102	81	94.6280011175136	-13.6280011175136
103	37	51.1777161909543	-14.1777161909543
104	64	36.1541679340477	27.8458320659523
105	22	61.0469194701329	-39.0469194701329
106	35	73.2059245204857	-38.2059245204857
107	61	74.382226455509	-13.382226455509
108	80	89.263586154752	-9.26358615475198
109	54	76.4254370972695	-22.4254370972695
110	76	64.7853818545767	11.2146181454233
111	87	73.94377519836	13.05622480164
112	75	72.2428752183564	2.75712478164363
113	0	21.781719227987	-21.781719227987
114	61	69.2803011096006	-8.28030110960062
115	30	35.7147998498237	-5.71479984982367
116	66	48.233896679138	17.766103320862
117	56	87.7821659630747	-31.7821659630747
118	0	19.2983350778194	-19.2983350778194
119	40	73.4056856742552	-33.4056856742552
120	9	27.4930784136735	-18.4930784136735
121	82	79.8052718782443	2.19472812175571
122	110	66.1941064003045	43.8058935996955
123	71	45.7096844666026	25.2903155333974
124	50	45.3012725270701	4.6987274729299
125	21	27.1239382467998	-6.12393824679976
126	78	52.9673101697854	25.0326898302146
127	118	76.5202823760439	41.4797176239561
128	102	57.4747484527157	44.5252515472843
129	109	91.599275871376	17.400724128624
130	104	94.689578882002	9.31042111799808
131	124	117.896813031119	6.1031869688805
132	76	59.2863387397508	16.7136612602492
133	57	40.2387375839314	16.7612624160686
134	91	81.498148050084	9.50185194991599
135	101	99.34379620275	1.65620379725002
136	66	36.0483880880962	29.9516119119038
137	98	99.6597943794446	-1.6597943794446
138	63	50.3843629069172	12.6156370930828
139	85	70.8986747709002	14.1013252290998
140	74	55.8932179913995	18.1067820086005
141	19	38.6357150870618	-19.6357150870618
142	57	84.7508966627353	-27.7508966627353
143	74	78.7240823534658	-4.72408235346578
144	78	57.7894871304416	20.2105128695584
145	91	80.7556033542347	10.2443966457653
146	112	70.8247948819089	41.1752051180911
147	79	75.3677481124972	3.63225188750278
148	100	95.7234119164028	4.27658808359723
149	0	11.0434895304725	-11.0434895304725
150	0	16.0990837804118	-16.0990837804118
151	0	10.9408914666113	-10.9408914666113
152	0	10.9560189284692	-10.9560189284692
153	0	10.6628983654828	-10.6628983654828
154	0	10.5677505742354	-10.5677505742354
155	48	52.8549638942558	-4.8549638942558
156	55	73.1919533029679	-18.1919533029679
157	0	10.2823072004931	-10.2823072004931
158	0	10.4861152623138	-10.4861152623138
159	0	13.7464658519755	-13.7464658519755
160	13	21.8226287400622	-8.82262874006221
161	4	13.2931698746243	-9.29316987462435
162	31	36.1979469425723	-5.19794694257233
163	0	10.0047669908688	-10.0047669908688
164	29	47.2637521558412	-18.2637521558412

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
10	0.00448188959607375	0.0089637791921475	0.995518110403926
11	0.00123233274606653	0.00246466549213305	0.998767667253934
12	0.0273803905945329	0.0547607811890659	0.972619609405467
13	0.0146081747206163	0.0292163494412325	0.985391825279384
14	0.0879042144391356	0.175808428878271	0.912095785560864
15	0.273285820479835	0.546571640959669	0.726714179520165
16	0.193993828186081	0.387987656372162	0.806006171813919
17	0.43962278569503	0.87924557139006	0.56037721430497
18	0.934484596493627	0.131030807012746	0.0655154035063731
19	0.961497590263594	0.0770048194728116	0.0385024097364058
20	0.95726921068106	0.0854615786378815	0.0427307893189407
21	0.937904292030622	0.124191415938756	0.0620957079693779
22	0.923885108646172	0.152229782707657	0.0761148913538284
23	0.899887792065417	0.200224415869167	0.100112207934583
24	0.929308891342332	0.141382217315335	0.0706911086576676
25	0.904891233216189	0.190217533567622	0.0951087667838109
26	0.87378923767508	0.25242152464984	0.12621076232492
27	0.89802826154071	0.20394347691858	0.10197173845929
28	0.86763684361305	0.2647263127739	0.13236315638695
29	0.836370696126798	0.327258607746404	0.163629303873202
30	0.796971222912976	0.406057554174049	0.203028777087024
31	0.765916794870308	0.468166410259384	0.234083205129692
32	0.755278246281064	0.489443507437872	0.244721753718936
33	0.712713289763376	0.574573420473248	0.287286710236624
34	0.679116511387558	0.641766977224885	0.320883488612442
35	0.626762834981821	0.746474330036357	0.373237165018179
36	0.600915941105616	0.798168117788767	0.399084058894384
37	0.564553429537005	0.87089314092599	0.435446570462995
38	0.605295904512632	0.789408190974735	0.394704095487367
39	0.740644979967731	0.518710040064537	0.259355020032269
40	0.702520229004128	0.594959541991744	0.297479770995872
41	0.666868771755333	0.666262456489334	0.333131228244667
42	0.620001299957803	0.759997400084393	0.379998700042197
43	0.571465918888555	0.85706816222289	0.428534081111445
44	0.520447906724343	0.959104186551313	0.479552093275657
45	0.535896340849687	0.928207318300627	0.464103659150313
46	0.529092395314194	0.941815209371613	0.470907604685806
47	0.506579373344476	0.986841253311047	0.493420626655524
48	0.485107990780875	0.97021598156175	0.514892009219125
49	0.451258568182245	0.90251713636449	0.548741431817755
50	0.432460151613638	0.864920303227275	0.567539848386363
51	0.446402824713045	0.89280564942609	0.553597175286955
52	0.481033160083526	0.962066320167053	0.518966839916474
53	0.436758091105581	0.873516182211162	0.563241908894419
54	0.407721349829119	0.815442699658237	0.592278650170881
55	0.382663183154956	0.765326366309912	0.617336816845044
56	0.365548850673145	0.731097701346291	0.634451149326855
57	0.43093284951793	0.86186569903586	0.56906715048207
58	0.431286068540924	0.862572137081848	0.568713931459076
59	0.464484050830649	0.928968101661297	0.535515949169351
60	0.419014765674392	0.838029531348784	0.580985234325608
61	0.387277410628482	0.774554821256963	0.612722589371518
62	0.626430497424148	0.747139005151703	0.373569502575851
63	0.58427128868682	0.83145742262636	0.41572871131318
64	0.563940371229411	0.872119257541178	0.436059628770589
65	0.52950511285837	0.94098977428326	0.47049488714163
66	0.608409909446572	0.783180181106855	0.391590090553428
67	0.57297333186556	0.85405333626888	0.42702666813444
68	0.538066358695752	0.923867282608495	0.461933641304248
69	0.501733240434618	0.996533519130763	0.498266759565382
70	0.490658750777045	0.98131750155409	0.509341249222955
71	0.464303006914235	0.92860601382847	0.535696993085765
72	0.457226306829342	0.914452613658683	0.542773693170658
73	0.466948613554898	0.933897227109796	0.533051386445102
74	0.431437451692957	0.862874903385915	0.568562548307042
75	0.392816357029838	0.785632714059676	0.607183642970162
76	0.355619064371255	0.71123812874251	0.644380935628745
77	0.32684194088055	0.6536838817611	0.67315805911945
78	0.363932272617255	0.72786454523451	0.636067727382745
79	0.341852092819378	0.683704185638755	0.658147907180622
80	0.317520963782999	0.635041927565998	0.682479036217001
81	0.278651901363757	0.557303802727515	0.721348098636243
82	0.294583378884283	0.589166757768567	0.705416621115717
83	0.327327283405512	0.654654566811025	0.672672716594488
84	0.440284857150523	0.880569714301045	0.559715142849477
85	0.492947102205617	0.985894204411233	0.507052897794383
86	0.468625489843314	0.937250979686627	0.531374510156686
87	0.467040996620808	0.934081993241615	0.532959003379192
88	0.424652509787628	0.849305019575256	0.575347490212372
89	0.385622921520881	0.771245843041761	0.614377078479119
90	0.346334849992586	0.692669699985173	0.653665150007414
91	0.330017385271633	0.660034770543267	0.669982614728367
92	0.291175814877219	0.582351629754438	0.708824185122781
93	0.263447411857806	0.526894823715612	0.736552588142194
94	0.238437522801836	0.476875045603673	0.761562477198164
95	0.215412500183207	0.430825000366414	0.784587499816793
96	0.184814716626669	0.369629433253339	0.81518528337333
97	0.178604596076156	0.357209192152311	0.821395403923844
98	0.252501741549574	0.505003483099147	0.747498258450426
99	0.534055472372186	0.931889055255628	0.465944527627814
100	0.607606884266083	0.784786231467833	0.392393115733917
101	0.60763993356752	0.78472013286496	0.39236006643248
102	0.593148224197773	0.813703551604453	0.406851775802227
103	0.573970301757331	0.852059396485338	0.426029698242669
104	0.615031916541328	0.769936166917344	0.384968083458672
105	0.727395574625361	0.545208850749278	0.272604425374639
106	0.832259660599413	0.335480678801173	0.167740339400587
107	0.825114068624865	0.349771862750271	0.174885931375135
108	0.813962457600079	0.372075084799842	0.186037542399921
109	0.930051918865813	0.139896162268375	0.0699480811341874
110	0.912630470432404	0.174739059135191	0.0873695295675956
111	0.894624319712522	0.210751360574957	0.105375680287478
112	0.869771232024312	0.260457535951375	0.130228767975688
113	0.880872696473436	0.238254607053127	0.119127303526564
114	0.876159888000105	0.247680223999791	0.123840111999895
115	0.858171188693428	0.283657622613144	0.141828811306572
116	0.84169288447221	0.31661423105558	0.15830711552779
117	0.89917303053828	0.201653938923439	0.100826969461719
118	0.914938545855688	0.170122908288623	0.0850614541443117
119	0.989140605149331	0.0217187897013371	0.0108593948506686
120	0.996792918612199	0.0064141627756029	0.00320708138780145
121	0.996795919633452	0.00640816073309679	0.00320408036654839
122	0.998001857372908	0.00399628525418408	0.00199814262709204
123	0.997261244064162	0.00547751187167672	0.00273875593583836
124	0.997161393349958	0.00567721330008376	0.00283860665004188
125	0.999131848605342	0.00173630278931609	0.000868151394658045
126	0.998776183075662	0.00244763384867515	0.00122381692433757
127	0.999315353647625	0.00136929270474984	0.000684646352374921
128	0.999933417806208	0.000133164387584774	6.65821937923869e-05
129	0.99987886564723	0.00024226870553893	0.000121134352769465
130	0.99984804094669	0.000303918106618648	0.000151959053309324
131	0.999740144952428	0.00051971009514456	0.00025985504757228
132	0.999580925999768	0.000838148000463284	0.000419074000231642
133	0.99922827831135	0.00154344337729876	0.000771721688649379
134	0.999097315549983	0.00180536890003362	0.00090268445001681
135	0.998394344169224	0.00321131166155286	0.00160565583077643
136	0.999505444537162	0.000989110925675594	0.000494555462837797
137	0.999039815906133	0.00192036818773391	0.000960184093866956
138	0.998235014680094	0.00352997063981184	0.00176498531990592
139	0.998524520237709	0.00295095952458255	0.00147547976229127
140	0.998367292419458	0.00326541516108392	0.00163270758054196
141	0.998797109409979	0.00240578118004284	0.00120289059002142
142	0.999916979281884	0.000166041436232923	8.30207181164617e-05
143	0.999810615767893	0.00037876846421491	0.000189384232107455
144	0.999915819272447	0.000168361455106708	8.4180727553354e-05
145	0.999998966206093	2.06758781503065e-06	1.03379390751533e-06
146	0.999998799583424	2.40083315127487e-06	1.20041657563744e-06
147	0.999999744688022	5.10623955105238e-07	2.55311977552619e-07
148	0.999998840168888	2.31966222353481e-06	1.15983111176741e-06
149	0.999993660299179	1.2679401642328e-05	6.33970082116398e-06
150	0.999973802121946	5.23957561090209e-05	2.61978780545104e-05
151	0.999842481499175	0.000315037001649374	0.000157518500824687
152	0.999107441683689	0.00178511663262227	0.000892558316311134
153	0.995430750793059	0.00913849841388277	0.00456924920694139
154	0.97960900972725	0.0407819805455023	0.0203909902727511

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	36	0.248275862068966	NOK
5% type I error level	39	0.268965517241379	NOK
10% type I error level	42	0.289655172413793	NOK