Multiple Linear Regression - Estimated Regression Equation

PR_Messages[t] = + 22.2207582333543 + 1.1174250730475TT_Hours[t] + 0.0699667926281474Logins[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)	22.2207582333543	4.040678	5.4993	0	0
TT_Hours	1.1174250730475	0.131351	8.5071	0	0
Logins	0.0699667926281474	0.082705	0.846	0.398821	0.199411

Multiple Linear Regression - Regression Statistics
Multiple R	0.707705386827691
R-squared	0.500846914544932
Adjusted R-squared	0.494646255098285
F-TEST (value)	80.7731691853807
F-TEST (DF numerator)	2
F-TEST (DF denominator)	161
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	23.2372477380735
Sum Squared Residuals	86935.1188729369

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	84	77.9582091274814	6.04179087251857
2	72	52.3973660326454	19.6026339673546
3	37	59.4497068250682	-22.4497068250682
4	85	74.4001207484603	10.5998792515397
5	30	51.2079305579668	-21.2079305579668
6	53	34.6544112311359	18.3455887688641
7	74	122.729266060015	-48.7292660600154
8	22	33.3970525728321	-11.3970525728321
9	68	60.6370986907438	7.36290130925615
10	47	64.1272638861398	-17.1272638861398
11	102	77.0527280413213	24.9472719586787
12	123	67.6256035175471	55.3743964824529
13	69	56.5172323616946	12.4827676383054
14	108	85.5003174683014	22.4996825316986
15	59	69.6485096767549	-10.6485096767548
16	122	108.906495254685	13.0935047453149
17	91	81.0306171761114	9.96938282388858
18	45	90.8157500990378	-45.8157500990378
19	53	60.4971651054876	-7.49716510548755
20	112	74.8858010788516	37.1141989211484
21	82	76.9807176396903	5.01928236030969
22	92	115.53290446433	-23.5329044643305
23	51	51.4857541194765	-0.485754119476549
24	120	57.98244778888	62.01755221112
25	99	73.4226292606691	25.5773707393309
26	86	73.2147724917875	12.7852275082125
27	59	78.1721967233717	-19.1721967233717
28	98	76.3530601150398	21.6469398849602
29	71	58.1223813741363	12.8776186258637
30	100	82.9856001516938	17.0143998483062
31	113	85.1525271141635	27.8474728858365
32	92	65.8064669092153	26.1935330907847
33	107	90.321895332635	16.678104667365
34	75	42.9661542908654	32.0338457091346
35	100	102.12380358776	-2.12380358776048
36	69	76.2110829207807	-7.21108292078069
37	106	109.600032353958	-3.60003235395795
38	51	63.7115503483766	-12.7115503483766
39	18	48.6232464487311	-30.6232464487311
40	91	94.5878260739491	-3.58782607394915
41	75	95.3492863568473	-20.3492863568473
42	63	60.8469990686283	2.15300093137171
43	72	68.1112838479385	3.88871615206154
44	59	50.0905054849193	8.90949451508068
45	29	54.7021829713685	-25.7021829713685
46	85	123.918701534694	-38.9187015346939
47	66	49.7427151307814	16.2572848692186
48	106	75.2356350419923	30.7643649580077
49	113	96.3987882462695	16.6012117537305
50	101	65.176765775562	35.823234224438
51	65	66.1563008723561	-1.15630087235606
52	7	31.7219367677623	-24.7219367677623
53	111	117.298423152057	-6.29842315205703
54	61	43.5238450228878	17.4761549771122
55	41	56.4493091780693	-15.4493091780693
56	70	77.7462651405942	-7.74626514059421
57	136	82.1500858581618	53.8499141418382
58	87	91.6553516105755	-4.65535161057553
59	90	93.3963469902678	-3.39634699026778
60	76	69.3686425062423	6.63135749375774
61	101	104.222807366605	-3.2228073666049
62	57	91.3014304294291	-34.3014304294291
63	61	71.2557022981994	-10.2557022981994
64	92	78.9377442242756	13.0622557757244
65	80	68.5290409947045	11.4709590052955
66	35	60.4271983128594	-25.4271983128594
67	72	63.9955047368949	8.00449526310508
68	88	74.0543740033253	13.9456259966747
69	80	72.5809841401285	7.41901585987154
70	62	53.7226478745744	8.27735212542559
71	81	61.4046898006506	19.5953101993494
72	63	45.4109048148449	17.5890951851551
73	91	64.4091746656552	26.5908253343448
74	65	70.6239575555432	-5.62395755554319
75	79	54.7001393623656	24.2998606376344
76	85	84.5927927731384	0.407207226861635
77	75	87.6672444307711	-12.6672444307711
78	70	58.6841593241643	11.3158406758357
79	78	52.6751895941551	25.3248104058449
80	75	62.0343909343039	12.9656090656961
81	55	54.4902389844812	0.50976101551883
82	80	111.83283889105	-31.8328388910501
83	83	67.2737259454036	15.7262740545964
84	38	68.8109517742199	-30.8109517742199
85	27	48.5532796561029	-21.5532796561029
86	62	58.472215337277	3.52778466272301
87	82	54.9100397402501	27.0899602597499
88	88	100.594752194956	-12.5947521949555
89	59	79.6353685415542	-20.6353685415542
90	92	63.9934611278921	28.0065388721079
91	40	67.1337923601473	-27.1337923601473
92	91	72.5809841401285	18.4190158598715
93	63	59.7995407882089	3.20045921179106
94	88	78.3080430906222	9.69195690937775
95	85	83.8951684558597	1.10483154414025
96	76	64.3371642640242	11.6628357359758
97	67	68.9467981414705	-1.94679814147052
98	69	85.2224939067917	-16.2224939067917
99	150	91.2335072458038	58.7664927541962
100	77	104.360697342858	-27.3606973428583
101	103	74.67794430997	28.32205569003
102	81	82.0780754565308	-1.07807545653078
103	37	63.5098244065036	-26.5098244065036
104	64	36.6093942067183	27.3906057932817
105	22	64.4791414582834	-42.4791414582834
106	35	68.8150389922257	-33.8150389922257
107	61	70.064223214518	-9.06422321451801
108	80	84.8047367600257	-4.80473676002566
109	54	47.9256221314525	6.07437786854753
110	76	55.8216516534188	20.1783483465812
111	87	79.9131921030639	7.08680789693608
112	75	69.6485096767549	5.35149032324515
113	0	29.6249765979207	-29.6249765979207
114	61	65.0388757993086	-4.03887579930856
115	30	42.9661542908654	-12.9661542908654
116	66	52.4652892162706	13.5347107837294
117	56	106.175746733184	-50.1757467331845
118	0	30.0447773536896	-30.0447773536896
119	32	77.1885744085719	-45.1885744085719
120	9	33.6069529507166	-24.6069529507166
121	82	85.6443382715634	-3.64433827156343
122	110	67.1317487511444	42.8682512488556
123	71	48.9051572282465	22.0948427717535
124	50	47.715721753568	2.28427824643197
125	21	36.8913049862338	-15.8913049862338
126	78	51.9055548752454	26.0944451247546
127	118	85.9201182240703	32.0798817759297
128	102	67.3416491290288	34.6583508709712
129	109	101.704002831992	7.29599716800841
130	104	89.3444038448438	14.6555961551562
131	124	106.595547488953	17.4044525110467
132	76	67.4095723126541	8.59042768734587
133	57	47.715721753568	9.28427824643197
134	91	95.0178448747323	-4.01784487473233
135	101	117.356128290668	-16.356128290668
136	66	38.9142111454415	27.0857888545585
137	98	106.4576575127	-8.4576575126999
138	63	58.1244249831391	4.87557501686088
139	85	77.0486408233156	7.9513591766844
140	74	65.9464004944716	8.05359950552839
141	19	50.7242938365784	-31.7242938365784
142	57	104.990398476512	-47.9903984765117
143	74	72.9308181032692	1.0691818967308
144	78	80.2650696752075	-2.26506967520752
145	91	88.5068459423089	2.4931540576911
146	112	46.1805395337545	65.8194604662455
147	79	69.228708920986	9.77129107901404
148	100	83.8972120648626	16.1027879351374
149	0	22.2207582333543	-22.2207582333543
150	0	27.3901264518257	-27.3901264518257
151	0	22.2907250259824	-22.2907250259824
152	0	22.3606918186106	-22.3606918186106
153	0	22.2207582333543	-22.2207582333543
154	0	22.2207582333543	-22.2207582333543
155	48	68.7409849815918	-20.7409849815918
156	55	84.2470460280033	-29.2470460280033
157	0	22.2207582333543	-22.2207582333543
158	0	22.5006254038669	-22.5006254038669
159	0	24.80544234259	-24.80544234259
160	13	38.1466200355347	-25.1466200355347
161	4	28.1577175617325	-24.1577175617325
162	31	46.4583630952642	-15.4583630952642
163	0	22.3606918186106	-22.3606918186106
164	29	56.9349895084606	-27.9349895084606

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
6	0.536096610116002	0.927806779767996	0.463903389883998
7	0.422181236398474	0.844362472796948	0.577818763601526
8	0.34729962342152	0.694599246843041	0.65270037657848
9	0.285548744736929	0.571097489473858	0.714451255263071
10	0.195844645515238	0.391689291030476	0.804155354484762
11	0.213521461955959	0.427042923911917	0.786478538044041
12	0.248545219834595	0.497090439669189	0.751454780165405
13	0.175953264751943	0.351906529503887	0.824046735248057
14	0.496693560402938	0.993387120805875	0.503306439597062
15	0.469602217303957	0.939204434607914	0.530397782696043
16	0.421047833581278	0.842095667162557	0.578952166418722
17	0.418623237824724	0.837246475649448	0.581376762175276
18	0.782686466414364	0.434627067171272	0.217313533585636
19	0.731383110419514	0.537233779160972	0.268616889580486
20	0.811326397786133	0.377347204427734	0.188673602213867
21	0.764135957701874	0.471728084596253	0.235864042298126
22	0.718066708206778	0.563866583586445	0.281933291793222
23	0.65887659836843	0.68224680326314	0.34112340163157
24	0.880923763785441	0.238152472429119	0.119076236214559
25	0.865100433004183	0.269799133991633	0.134899566995816
26	0.831079321673481	0.337841356653037	0.168920678326519
27	0.835884764999057	0.328230470001886	0.164115235000943
28	0.823325385837401	0.353349228325197	0.176674614162599
29	0.785954592880033	0.428090814239933	0.214045407119967
30	0.771748356770677	0.456503286458646	0.228251643229323
31	0.787513024624063	0.424973950751874	0.212486975375937
32	0.775283147827343	0.449433704345314	0.224716852172657
33	0.751767057466126	0.496465885067749	0.248232942533874
34	0.743870458128624	0.512259083742752	0.256129541871376
35	0.697447650209003	0.605104699581993	0.302552349790997
36	0.657024912894023	0.685950174211954	0.342975087105977
37	0.605547149700882	0.788905700598237	0.394452850299118
38	0.596192047437173	0.807615905125654	0.403807952562827
39	0.68970461572634	0.620590768547321	0.31029538427366
40	0.646491785057423	0.707016429885155	0.353508214942577
41	0.626550650824431	0.746898698351137	0.373449349175569
42	0.578553924009476	0.842892151981048	0.421446075990524
43	0.527949260194248	0.944101479611505	0.472050739805752
44	0.479499044636003	0.958998089272006	0.520500955363997
45	0.533749554172537	0.932500891654926	0.466250445827463
46	0.582758630835234	0.834482738329531	0.417241369164766
47	0.544176347530893	0.911647304938215	0.455823652469107
48	0.571824587226505	0.85635082554699	0.428175412773495
49	0.554715513334791	0.890568973330418	0.445284486665209
50	0.600360031453171	0.799279937093658	0.399639968546829
51	0.556866743435567	0.886266513128866	0.443133256564433
52	0.61966278709752	0.760674425804961	0.38033721290248
53	0.575917188810118	0.848165622379765	0.424082811189883
54	0.543585411545539	0.912829176908922	0.456414588454461
55	0.534063381040634	0.931873237918731	0.465936618959366
56	0.492932782839154	0.985865565678309	0.507067217160846
57	0.685671114317305	0.62865777136539	0.314328885682695
58	0.644643344764226	0.710713310471548	0.355356655235774
59	0.600614577223107	0.798770845553786	0.399385422776893
60	0.557068110506564	0.885863778986873	0.442931889493436
61	0.510802096448179	0.978395807103641	0.489197903551821
62	0.565607832841866	0.868784334316267	0.434392167158134
63	0.53296338241024	0.934073235179519	0.46703661758976
64	0.499310803889692	0.998621607779384	0.500689196110308
65	0.461477369909187	0.922954739818375	0.538522630090813
66	0.486106066208113	0.972212132416226	0.513893933791887
67	0.444058866332517	0.888117732665035	0.555941133667483
68	0.412720816604836	0.825441633209671	0.587279183395164
69	0.372013470001	0.744026940002	0.627986529999
70	0.333662654105133	0.667325308210266	0.666337345894867
71	0.316579295437488	0.633158590874976	0.683420704562512
72	0.294016399596508	0.588032799193015	0.705983600403492
73	0.300877540467227	0.601755080934454	0.699122459532773
74	0.26678871169368	0.533577423387359	0.73321128830632
75	0.264381719461902	0.528763438923804	0.735618280538098
76	0.228625242391258	0.457250484782515	0.771374757608742
77	0.204924768983822	0.409849537967644	0.795075231016178
78	0.180609859401898	0.361219718803797	0.819390140598102
79	0.182012481960201	0.364024963920401	0.8179875180398
80	0.161497295178423	0.322994590356845	0.838502704821577
81	0.137940543392736	0.275881086785473	0.862059456607264
82	0.155265917327632	0.310531834655264	0.844734082672368
83	0.140649892908193	0.281299785816386	0.859350107091807
84	0.169249773423584	0.338499546847169	0.830750226576416
85	0.177037548178462	0.354075096356923	0.822962451821538
86	0.150989783967015	0.301979567934031	0.849010216032985
87	0.159534945926535	0.31906989185307	0.840465054073465
88	0.139475577918642	0.278951155837283	0.860524422081358
89	0.135201018138903	0.270402036277805	0.864798981861097
90	0.147693724272244	0.295387448544489	0.852306275727756
91	0.162321224792928	0.324642449585856	0.837678775207072
92	0.15281066014848	0.305621320296961	0.84718933985152
93	0.129335192954631	0.258670385909262	0.870664807045369
94	0.111011443731831	0.222022887463661	0.888988556268169
95	0.0910349341812753	0.182069868362551	0.908965065818725
96	0.0781185610150672	0.156237122030134	0.921881438984933
97	0.0631334313136574	0.126266862627315	0.936866568686343
98	0.0558110838734978	0.111622167746996	0.944188916126502
99	0.184502810432359	0.369005620864718	0.815497189567641
100	0.193713723690073	0.387427447380146	0.806286276309927
101	0.216593419595268	0.433186839190536	0.783406580404732
102	0.1841662717519	0.3683325435038	0.8158337282481
103	0.195014193291778	0.390028386583557	0.804985806708222
104	0.217371068034931	0.434742136069861	0.782628931965069
105	0.308608849536612	0.617217699073225	0.691391150463388
106	0.35143887524342	0.70287775048684	0.64856112475658
107	0.315061247537795	0.63012249507559	0.684938752462205
108	0.275372268559248	0.550744537118495	0.724627731440752
109	0.245231667420474	0.490463334840949	0.754768332579526
110	0.247271912269256	0.494543824538513	0.752728087730744
111	0.214777568876265	0.429555137752531	0.785222431123735
112	0.185159836197521	0.370319672395042	0.814840163802479
113	0.207215808447598	0.414431616895195	0.792784191552402
114	0.175546574037912	0.351093148075825	0.824453425962088
115	0.155073732127461	0.310147464254923	0.844926267872539
116	0.141903936202304	0.283807872404608	0.858096063797696
117	0.28528495879944	0.57056991759888	0.71471504120056
118	0.303895729630208	0.607791459260415	0.696104270369792
119	0.462252120671067	0.924504241342135	0.537747879328933
120	0.456079988724498	0.912159977448996	0.543920011275502
121	0.407198199812263	0.814396399624527	0.592801800187737
122	0.53063866430821	0.93872267138358	0.46936133569179
123	0.5597381879045	0.880523624191	0.4402618120955
124	0.514599715312542	0.970800569374915	0.485400284687458
125	0.47603032657288	0.95206065314576	0.52396967342712
126	0.514292950179031	0.971414099641937	0.485707049820969
127	0.558755813761854	0.882488372476291	0.441244186238146
128	0.656161751696783	0.687676496606434	0.343838248303217
129	0.606453298113188	0.787093403773624	0.393546701886812
130	0.581055034618769	0.837889930762462	0.418944965381231
131	0.562410751257402	0.875178497485197	0.437589248742598
132	0.530046588763835	0.93990682247233	0.469953411236165
133	0.512501944630695	0.97499611073861	0.487498055369305
134	0.455041357555214	0.910082715110429	0.544958642444786
135	0.415719781401855	0.831439562803709	0.584280218598145
136	0.532036617702739	0.935926764594521	0.467963382297261
137	0.474395587073144	0.948791174146287	0.525604412926856
138	0.43723195229477	0.87446390458954	0.56276804770523
139	0.413988464862208	0.827976929724417	0.586011535137791
140	0.391142138448519	0.782284276897038	0.608857861551481
141	0.794493238245028	0.411013523509943	0.205506761754972
142	0.833332953729276	0.333334092541448	0.166667046270724
143	0.794155920807265	0.41168815838547	0.205844079192735
144	0.736732187389172	0.526535625221656	0.263267812610828
145	0.698315938711843	0.603368122576313	0.301684061288157
146	0.999430891153075	0.00113821769385035	0.000569108846925177
147	0.999674855203335	0.000650289593329947	0.000325144796664973
148	0.999999998478037	3.04392655454672e-09	1.52196327727336e-09
149	0.999999990461819	1.90763624562444e-08	9.53818122812219e-09
150	0.999999981922549	3.6154902072847e-08	1.80774510364235e-08
151	0.999999875977201	2.48045597735473e-07	1.24022798867737e-07
152	0.999999177809055	1.64438188971159e-06	8.22190944855796e-07
153	0.999994750092798	1.04998144045822e-05	5.24990720229108e-06
154	0.999967948738703	6.41025225947803e-05	3.20512612973902e-05
155	0.999873083728258	0.000253832543483142	0.000126916271741571
156	0.999581620585456	0.00083675882908826	0.00041837941454413
157	0.997802838349933	0.00439432330013367	0.00219716165006683
158	0.987449175885188	0.0251016482296246	0.0125508241148123

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	12	0.0784313725490196	NOK
5% type I error level	13	0.0849673202614379	NOK
10% type I error level	13	0.0849673202614379	OK