Repository of Reproducible Computations

Multiple Linear Regression - Estimated Regression Equation

Feedback_messages[t] = + 14.8287304310732 + 0.281855284357363Blogged_Computations[t] + 0.000112098518088704Time_Rfc[t] + 0.000244889814505626Aantal_karakters[t] + 0.0680182231106363Logins[t] + 0.00233086927254974`Pageviews `[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)	14.8287304310732	3.907678	3.7948	0.00021	0.000105
Blogged_Computations	0.281855284357363	0.083819	3.3627	0.000968	0.000484
Time_Rfc	0.000112098518088704	6.4e-05	1.7492	0.082192	0.041096
Aantal_karakters	0.000244889814505626	6.7e-05	3.677	0.000323	0.000161
Logins	0.0680182231106363	0.078471	0.8668	0.387366	0.193683
`Pageviews `	0.00233086927254974	0.006367	0.3661	0.714808	0.357404

Multiple Linear Regression - Regression Statistics
Multiple R	0.771467128673908
R-squared	0.595161530624364
Adjusted R-squared	0.582350186656781
F-TEST (value)	46.4558232243474
F-TEST (DF numerator)	5
F-TEST (DF denominator)	158
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	21.0799748616074
Sum Squared Residuals	70209.7237462282

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	84	81.5919888294553	2.40801117054468
2	72	57.9456405028783	14.0543594971217
3	41	65.1744774212813	-24.1744774212813
4	85	88.9853108913039	-3.98531089130394
5	30	47.4623711374985	-17.4623711374984
6	53	33.8322332251988	19.1677667748012
7	74	114.428530059645	-40.4285300596454
8	22	26.2594556510653	-4.2594556510653
9	68	63.0452337111406	4.95476628885942
10	47	62.7309746439266	-15.7309746439266
11	102	71.469479638316	30.530520361684
12	123	72.4375028949934	50.5624971050066
13	69	55.3478698333588	13.6521301666412
14	108	80.1250779460539	27.8749220539461
15	59	64.1700681694315	-5.17006816943153
16	122	111.841643644631	10.1583563553692
17	91	91.0580963800797	-0.0580963800797066
18	45	87.3494618972875	-42.3494618972875
19	53	74.1745038420302	-21.1745038420302
20	112	86.4118623536766	25.5881376463234
21	82	82.5507995367806	-0.550799536780629
22	92	90.3361625960294	1.66383740397063
23	51	49.7951277288541	1.20487227114595
24	120	71.4138018382619	48.5861981617381
25	99	83.9072895677815	15.0927104322185
26	86	75.1662062295285	10.8337937704715
27	59	79.9683961069061	-20.9683961069061
28	98	79.9211831649289	18.0788168350711
29	71	49.9813250333893	21.0186749666107
30	100	82.3560335689005	17.6439664310995
31	113	91.439004352149	21.560995647851
32	92	60.8352268579449	31.1647731420551
33	107	85.8808065092801	21.1191934907199
34	75	42.8951184424687	32.1048815575313
35	100	96.5417921062362	3.45820789376379
36	69	68.8080088236302	0.191991176369846
37	106	89.255911828918	16.744088171082
38	51	58.8885727273081	-7.88857272730808
39	18	42.3393187141965	-24.3393187141965
40	91	90.5751883788679	0.424811621132071
41	75	84.4443385441915	-9.44433854419147
42	63	56.4183521207219	6.58164787927807
43	72	65.7841386862969	6.21586131370312
44	59	45.920519400937	13.079480599063
45	29	53.5502229689367	-24.5502229689367
46	85	105.45226905171	-20.4522690517097
47	66	42.3849030592076	23.6150969407924
48	106	78.8418684044073	27.1581315955928
49	113	102.984067928091	10.015932071909
50	101	71.8253353842757	29.1746646157243
51	65	69.2934014803319	-4.29340148033188
52	7	24.0406545716101	-17.0406545716101
53	111	101.891532221782	9.10846777821767
54	61	38.8992308189987	22.1007691810013
55	41	48.552038255818	-7.55203825581801
56	70	77.0401071852553	-7.04010718525532
57	136	92.6783777253238	43.3216222746762
58	87	99.8451665984755	-12.8451665984755
59	90	100.274672679858	-10.274672679858
60	76	65.9548557560536	10.0451442439464
61	101	107.518511372393	-6.51851137239309
62	57	102.978130788474	-45.9781307884739
63	61	62.4512890341976	-1.45128903419756
64	92	73.8329433894791	18.1670566105209
65	80	64.4016414714774	15.5983585285226
66	35	61.4511535059928	-26.4511535059928
67	72	76.2413315196953	-4.24133151969532
68	88	75.2483873817207	12.7516126182793
69	80	83.0363031112961	-3.03630311129613
70	62	72.7224126310302	-10.7224126310302
71	81	62.9887918101039	18.0112081898961
72	63	38.2115084897858	24.7884915102142
73	91	63.7523132552707	27.2476867447293
74	65	69.7243184487279	-4.72431844872789
75	79	70.9196009494515	8.08039905054848
76	85	87.7457005982164	-2.74570059821639
77	75	85.2578642368306	-10.2578642368306
78	70	98.5874043397146	-28.5874043397146
79	78	61.5650650941161	16.4349349058839
80	75	59.4492786394	15.5507213606
81	55	53.1684219800175	1.83157801998249
82	80	106.481095223435	-26.481095223435
83	83	53.0792822071106	29.9207177928894
84	38	76.5794475229364	-38.5794475229364
85	27	55.3088136212406	-28.3088136212406
86	62	43.7032940537081	18.2967059462919
87	82	60.7374914490043	21.2625085509957
88	88	82.5577838957891	5.44221610421092
89	59	65.5989827544201	-6.59898275442009
90	92	92.2918462224622	-0.291846222462182
91	40	54.9454427902458	-14.9454427902458
92	91	88.0017826098721	2.99821739012789
93	63	50.1403232858307	12.8596767141693
94	88	76.0444234002621	11.9555765997379
95	85	75.1157073996068	9.88429260039323
96	76	72.5940875881459	3.40591241185413
97	67	87.276873148532	-20.276873148532
98	69	109.076760348343	-40.0767603483433
99	150	96.1468977454142	53.8531022545858
100	77	112.049670263443	-35.0496702634432
101	103	83.2119836651434	19.7880163348566
102	81	97.701835724526	-16.701835724526
103	37	52.3689260147516	-15.3689260147516
104	64	36.4146254904697	27.5853745095303
105	22	63.2915741162398	-41.2915741162398
106	35	75.5776356894607	-40.5776356894607
107	61	77.1646181086349	-16.1646181086349
108	80	93.024103842269	-13.024103842269
109	54	77.6053557372178	-23.6053557372178
110	76	67.3313477642748	8.66865223572522
111	87	76.8485752228204	10.1514247771796
112	75	75.5812661733255	-0.581266173325455
113	0	22.6598930712962	-22.6598930712962
114	61	72.5950957158956	-11.5950957158956
115	30	37.3432138095134	-7.34321380951339
116	66	50.8909131586288	15.1090868413712
117	56	92.8767293530754	-36.8767293530754
118	0	20.5159925379915	-20.5159925379915
119	40	77.2080628865606	-37.2080628865606
120	9	29.2193595607826	-20.2193595607826
121	82	84.6351055364839	-2.6351055364839
122	110	69.584471193785	40.415528806215
123	71	48.2013102108342	22.7986897891658
124	50	47.9353972449007	2.06460275509929
125	21	29.4071194262605	-8.40711942626052
126	78	56.2841112885237	21.7158887114763
127	118	81.6551938753486	36.3448061246514
128	102	61.2139729574448	40.7860270425552
129	109	97.9752383193169	11.0247616806831
130	104	100.817553757149	3.18244624285113
131	124	124.602177792803	-0.602177792802503
132	76	63.8303179435964	12.1696820564036
133	57	43.8706005183111	13.1293994816889
134	91	87.114195308736	3.88580469126399
135	101	106.521266302174	-5.5212663021738
136	66	39.2407812354963	26.7592187645037
137	98	106.810866552056	-8.81086655205554
138	63	55.0921063537373	7.9078936462627
139	85	76.8737652294282	8.12623477057184
140	74	61.2963152751148	12.7036847248852
141	19	42.6434167931114	-23.6434167931114
142	57	92.0554869068078	-35.0554869068078
143	74	85.1162422456983	-11.1162422456983
144	78	63.9546602719433	14.0453397280567
145	91	87.9362399716061	3.06376002839392
146	112	76.8548709710878	35.1451290289122
147	79	81.7755392140493	-2.77553921404931
148	100	103.285761619248	-3.28576161924808
149	0	14.8287304310732	-14.8287304310732
150	0	20.2402981254811	-20.2402981254811
151	0	14.9193886553193	-14.9193886553193
152	0	15.0344186572053	-15.0344186572053
153	0	14.8287304310732	-14.8287304310732
154	0	14.8287304310732	-14.8287304310732
155	48	59.5220336000925	-11.5220336000925
156	55	81.3634891446148	-26.3634891446148
157	0	14.8287304310732	-14.8287304310732
158	0	15.132882799778	-15.132882799778
159	0	18.7033658840508	-18.7033658840508
160	13	27.4198813586121	-14.4198813586121
161	4	18.4259042227075	-14.4259042227075
162	31	42.6746320031438	-11.6746320031438
163	0	15.1409855502264	-15.1409855502264
164	29	54.3371191114577	-25.3371191114577

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
9	0.0171834634456642	0.0343669268913283	0.982816536554336
10	0.118281390650413	0.236562781300825	0.881718609349587
11	0.370817520754173	0.741635041508346	0.629182479245827
12	0.35699603423629	0.71399206847258	0.64300396576371
13	0.255143350417033	0.510286700834066	0.744856649582967
14	0.82416231122252	0.351675377554959	0.17583768877748
15	0.779039070521781	0.441921858956437	0.220960929478219
16	0.705289227714023	0.589421544571955	0.294710772285977
17	0.627073805205921	0.745852389588158	0.372926194794079
18	0.909039891700057	0.181920216599887	0.0909601082999435
19	0.92086446413915	0.158271071721701	0.0791355358608504
20	0.921453550562406	0.157092898875189	0.0785464494375945
21	0.890276647119306	0.219446705761387	0.109723352880694
22	0.876612258934323	0.246775482131353	0.123387741065677
23	0.836993709472341	0.326012581055318	0.163006290527659
24	0.906859992261498	0.186280015477005	0.0931400077385024
25	0.879213674396657	0.241572651206687	0.120786325603343
26	0.847831678515673	0.304336642968654	0.152168321484327
27	0.846933091652952	0.306133816694095	0.153066908347047
28	0.813371120111018	0.373257759777965	0.186628879888982
29	0.790095328096615	0.41980934380677	0.209904671903385
30	0.752182620205201	0.495634759589597	0.247817379794799
31	0.75076173553577	0.49847652892846	0.24923826446423
32	0.795043417261265	0.40991316547747	0.204956582738735
33	0.774401383602343	0.451197232795314	0.225598616397657
34	0.781418633477521	0.437162733044958	0.218581366522479
35	0.741758423562655	0.516483152874689	0.258241576437345
36	0.699526041381344	0.600947917237312	0.300473958618656
37	0.701736938161891	0.596526123676219	0.298263061838109
38	0.678966753855005	0.642066492289989	0.321033246144995
39	0.736167896304803	0.527664207390394	0.263832103695197
40	0.690476994941889	0.619046010116222	0.309523005058111
41	0.644474830226433	0.711050339547135	0.355525169773567
42	0.594979807214265	0.81004038557147	0.405020192785735
43	0.544156766286172	0.911686467427657	0.455843233713828
44	0.50557045817295	0.988859083654099	0.49442954182705
45	0.492292523233292	0.984585046466584	0.507707476766708
46	0.482346046800686	0.964692093601373	0.517653953199314
47	0.486894216429289	0.973788432858578	0.513105783570711
48	0.495859080994311	0.991718161988623	0.504140919005689
49	0.48740576206833	0.974811524136659	0.51259423793167
50	0.499607255202626	0.999214510405252	0.500392744797374
51	0.47150357957274	0.94300715914548	0.52849642042726
52	0.472565405518764	0.945130811037527	0.527434594481236
53	0.439311788805029	0.878623577610059	0.560688211194971
54	0.435200194194523	0.870400388389046	0.564799805805477
55	0.395723073066247	0.791446146132494	0.604276926933753
56	0.358631711131862	0.717263422263724	0.641368288868138
57	0.476455810579437	0.952911621158875	0.523544189420563
58	0.454258390750008	0.908516781500016	0.545741609249992
59	0.452483968653107	0.904967937306213	0.547516031346894
60	0.413411255493042	0.826822510986084	0.586588744506958
61	0.373421364601424	0.746842729202847	0.626578635398576
62	0.577007398567246	0.845985202865509	0.422992601432754
63	0.530427257436449	0.939145485127103	0.469572742563551
64	0.522078009146072	0.955843981707855	0.477921990853928
65	0.500263447594606	0.999473104810788	0.499736552405394
66	0.556241680244551	0.887516639510897	0.443758319755449
67	0.517539003924246	0.964921992151508	0.482460996075754
68	0.486903869096822	0.973807738193644	0.513096130903178
69	0.449295854557754	0.898591709115508	0.550704145442246
70	0.436181936660387	0.872363873320774	0.563818063339613
71	0.416971674071026	0.833943348142053	0.583028325928974
72	0.423670507111981	0.847341014223961	0.576329492888019
73	0.446947357999721	0.893894715999443	0.553052642000278
74	0.409562532694529	0.819125065389058	0.590437467305471
75	0.375486825484386	0.750973650968773	0.624513174515614
76	0.339619815761292	0.679239631522584	0.660380184238708
77	0.310366180513038	0.620732361026075	0.689633819486962
78	0.341814590748842	0.683629181497684	0.658185409251158
79	0.32755303777272	0.65510607554544	0.67244696222728
80	0.308371102397712	0.616742204795424	0.691628897602288
81	0.271243342948888	0.542486685897776	0.728756657051112
82	0.285637376604582	0.571274753209164	0.714362623395418
83	0.323945617611238	0.647891235222476	0.676054382388762
84	0.435813108134746	0.871626216269493	0.564186891865254
85	0.48581394200767	0.971627884015341	0.51418605799233
86	0.466717979941857	0.933435959883714	0.533282020058143
87	0.46886497809189	0.93772995618378	0.53113502190811
88	0.426072649884901	0.852145299769801	0.573927350115099
89	0.38930995668384	0.778619913367681	0.61069004331616
90	0.348328918947624	0.696657837895248	0.651671081052376
91	0.333808505200266	0.667617010400532	0.666191494799734
92	0.296443117802545	0.59288623560509	0.703556882197455
93	0.271315524993758	0.542631049987517	0.728684475006242
94	0.246686730523021	0.493373461046042	0.753313269476979
95	0.223323043409234	0.446646086818469	0.776676956590766
96	0.192301339183116	0.384602678366231	0.807698660816884
97	0.18733832668734	0.37467665337468	0.81266167331266
98	0.267241436732928	0.534482873465857	0.732758563267072
99	0.548169930546561	0.903660138906877	0.451830069453439
100	0.62381312405209	0.75237375189582	0.37618687594791
101	0.623033274216026	0.753933451567948	0.376966725783974
102	0.608928449689971	0.782143100620058	0.391071550310029
103	0.595446710117259	0.809106579765481	0.404553289882741
104	0.634784453167527	0.730431093664947	0.365215546832473
105	0.752128750983483	0.495742498033035	0.247871249016517
106	0.849547285842511	0.300905428314979	0.150452714157489
107	0.839502718293014	0.320994563413972	0.160497281706986
108	0.823135314215215	0.35372937156957	0.176864685784785
109	0.922656798833652	0.154686402332696	0.077343201166348
110	0.906332881487095	0.18733423702581	0.0936671185129049
111	0.886106805030065	0.22778638993987	0.113893194969935
112	0.860252315282283	0.279495369435434	0.139747684717717
113	0.861883642743212	0.276232714513576	0.138116357256788
114	0.84102731686729	0.31794536626542	0.15897268313271
115	0.812721020313997	0.374557959372006	0.187278979686003
116	0.822562311303369	0.354875377393262	0.177437688696631
117	0.860275705040592	0.279448589918817	0.139724294959408
118	0.850816539175407	0.298366921649186	0.149183460824593
119	0.942662636671337	0.114674726657325	0.0573373633286626
120	0.937369742458783	0.125260515082434	0.0626302575412168
121	0.919835528196638	0.160328943606723	0.0801644718033615
122	0.94383957313203	0.112320853735941	0.0561604268679704
123	0.94534001965257	0.109319960694859	0.0546599803474297
124	0.927533530207425	0.144932939585149	0.0724664697925746
125	0.908556707902166	0.182886584195668	0.0914432920978338
126	0.908213798186406	0.183572403627189	0.0917862018135944
127	0.959080590687033	0.0818388186259348	0.0409194093129674
128	0.993167734041513	0.0136645319169734	0.00683226595848669
129	0.993045665313146	0.0139086693737071	0.00695433468685354
130	0.989384326716884	0.0212313465662324	0.0106156732831162
131	0.986151829711341	0.0276963405773172	0.0138481702886586
132	0.990502581190994	0.0189948376180122	0.00949741880900612
133	0.991878082216301	0.0162438355673979	0.00812191778369897
134	0.990474604105565	0.0190507917888692	0.00952539589443461
135	0.985911103889915	0.0281777922201698	0.0140888961100849
136	0.997385059879791	0.00522988024041794	0.00261494012020897
137	0.995404414131013	0.0091911717379739	0.00459558586898695
138	0.994533885186137	0.0109322296277256	0.00546611481386281
139	0.99848988806778	0.00302022386443917	0.00151011193221958
140	0.99887580665737	0.00224838668526062	0.00112419334263031
141	0.999009313482653	0.00198137303469476	0.00099068651734738
142	0.999861193240401	0.000277613519198877	0.000138806759599439
143	0.999662775570255	0.000674448859490309	0.000337224429745154
144	0.999947442138975	0.000105115722050482	5.2557861025241e-05
145	0.999999706957917	5.86084167075737e-07	2.93042083537868e-07
146	0.999999757644952	4.84710096364685e-07	2.42355048182343e-07
147	0.999999934930211	1.30139577892931e-07	6.50697889464656e-08
148	0.99999973530324	5.29393519873766e-07	2.64696759936883e-07
149	0.999998358917973	3.28216405404184e-06	1.64108202702092e-06
150	0.999995496320262	9.00735947589039e-06	4.5036797379452e-06
151	0.999971671234698	5.665753060362e-05	2.832876530181e-05
152	0.999837018244616	0.000325963510768052	0.000162981755384026
153	0.999081962496951	0.00183607500609792	0.000918037503048958
154	0.995214343129975	0.00957131374004952	0.00478565687002476
155	0.980786485554518	0.0384270288909637	0.0192135144454819

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	18	0.122448979591837	NOK
5% type I error level	29	0.197278911564626	NOK
10% type I error level	30	0.204081632653061	NOK