Repository of Reproducible Computations

Multiple Linear Regression - Estimated Regression Equation

log[t] = + 45.8494816429812 + 0.287132806589791blog[t] + 0.810720912550083PR[t] + 0.000104618328910731size[t] -1.29081107820149`age `[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)	45.8494816429812	34.736525	1.3199	0.188679	0.094339
blog	0.287132806589791	0.113336	2.5335	0.012221	0.00611
PR	0.810720912550083	0.392139	2.0674	0.040245	0.020123
size	0.000104618328910731	9e-05	1.1676	0.244629	0.122315
`age `	-1.29081107820149	1.745341	-0.7396	0.460602	0.230301

Multiple Linear Regression - Regression Statistics
Multiple R	0.540434446157205
R-squared	0.292069390593245
Adjusted R-squared	0.275010821691877
F-TEST (value)	17.1215646682899
F-TEST (DF numerator)	4
F-TEST (DF denominator)	166
p-value	8.94018192809654e-12
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	31.6975605241144
Sum Squared Residuals	166786.066967863

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	56	77.4946371595875	-21.4946371595874
2	56	64.3848848129825	-8.38488481298248
3	54	74.1831903488858	-20.1831903488858
4	92	84.931352009904	7.06864799009596
5	44	64.3218331532885	-20.3218331532885
6	33	63.5615017777661	-30.5615017777661
7	84	78.8717267288894	5.12827327111059
8	55	61.7441269499412	-6.74412694994117
9	154	112.431178279844	41.5688217201559
10	53	86.3520658975609	-33.3520658975609
11	119	74.0191738770034	44.9808261229966
12	41	71.3586135140746	-30.3586135140746
13	58	87.2914700333876	-29.2914700333876
14	75	71.8217382503609	3.17826174963913
15	33	58.9343463808753	-25.9343463808753
16	100	73.492972743207	26.507027256793
17	112	74.7680932230245	37.2319067769755
18	73	80.6645017191081	-7.66450171910806
19	40	54.4295100384608	-14.4295100384608
20	60	85.1077057250166	-25.1077057250166
21	62	73.1690594855008	-11.1690594855008
22	77	86.8375820944761	-9.83758209447611
23	99	80.334898530759	18.665101469241
24	17	20.1821319609914	-3.18213196099144
25	30	42.8195666747887	-12.8195666747887
26	76	41.8268411696978	34.1731588303022
27	146	80.9463523706904	65.0536476293096
28	56	69.5346872377854	-13.5346872377855
29	107	56.7981445153692	50.2018554846308
30	58	62.8692044396817	-4.86920443968166
31	34	55.2702308157947	-21.2702308157947
32	119	78.6649559962188	40.3350440037812
33	66	81.2874607637466	-15.2874607637466
34	66	70.8244483000659	-4.82444830006585
35	24	22.3232520042845	1.67674799571548
36	259	82.5732611457578	176.426738854242
37	41	72.5150093587552	-31.5150093587552
38	68	97.1425696020878	-29.1425696020878
39	168	76.3002124690347	91.6997875309653
40	43	45.8277680405375	-2.8277680405375
41	105	92.1495301821101	12.8504698178899
42	94	83.1462970265087	10.8537029734913
43	57	63.9917425469201	-6.99174254692008
44	53	62.8755649768449	-9.87556497684491
45	103	69.7387423661533	33.2612576338467
46	121	77.1539603233441	43.846039676656
47	62	83.8995250839964	-21.8995250839964
48	32	46.0722090976802	-14.0722090976802
49	45	68.7244121366443	-23.7244121366443
50	46	83.6844035371389	-37.6844035371389
51	75	76.7051382028695	-1.70513820286953
52	88	88.321405619617	-0.321405619617002
53	53	69.7188999687213	-16.7188999687213
54	78	83.3961966814028	-5.3961966814028
55	45	45.4725557878724	-0.472555787872419
56	46	72.7588869026628	-26.7588869026628
57	41	50.958913446772	-9.95891344677201
58	144	68.0032479786529	75.9967520213471
59	91	100.772468203735	-9.77246820373544
60	63	91.8617484437946	-28.8617484437946
61	53	52.6053802333821	0.394619766617861
62	62	78.6623406196998	-16.6623406196999
63	63	66.7323142228014	-3.73231422280141
64	32	72.2617069617152	-40.2617069617152
65	62	94.5280007318937	-32.5280007318937
66	117	104.612843430523	12.3871565694765
67	34	47.6393592992703	-13.6393592992703
68	92	91.2786350783103	0.721364921689652
69	93	90.175065400775	2.824934599225
70	54	89.0889116470051	-35.0889116470051
71	144	59.807931176796	84.192068823204
72	109	75.0241988921979	33.9758011078021
73	75	55.2077576526906	19.7922423473094
74	50	64.2837660024095	-14.2837660024095
75	61	45.1143075854729	15.8856924145271
76	55	56.6069467163905	-1.60694671639052
77	77	38.9052928720161	38.0947071279839
78	72	79.0517473064701	-7.05174730647014
79	53	43.2502902838872	9.74970971611277
80	42	61.1975324338246	-19.1975324338246
81	71	99.0015806630484	-28.0015806630484
82	10	17.9577134877393	-7.95771348773935
83	65	81.9811056725604	-16.9811056725604
84	66	53.736233273251	12.263766726749
85	41	72.5764587486068	-31.5764587486068
86	86	85.4548670767335	0.545132923266512
87	16	18.6896178201263	-2.68961782012634
88	42	63.5754547048229	-21.5754547048229
89	19	37.3660866285515	-18.3660866285515
90	19	31.8733991506708	-12.8733991506708
91	45	35.6688046021932	9.33119539780678
92	65	60.821000870772	4.17899912922801
93	95	80.3627056652059	14.6372943347941
94	64	68.4357941052356	-4.4357941052356
95	38	55.2943193725004	-17.2943193725004
96	65	92.1314974261429	-27.1314974261429
97	52	75.8806064218185	-23.8806064218185
98	62	46.6283951918442	15.3716048081558
99	65	100.064289226927	-35.0642892269274
100	95	115.33982215179	-20.3398221517901
101	29	66.975739185421	-37.975739185421
102	247	70.2690507727791	176.730949227221
103	29	57.4260550562079	-28.4260550562079
104	118	51.2596742127957	66.7403257872043
105	110	95.3898927542618	14.6101072457382
106	67	59.3669001077482	7.63309989225182
107	42	81.2927082732702	-39.2927082732702
108	64	55.3910558165252	8.60894418347485
109	81	56.4047225431444	24.5952774568556
110	95	77.7744534154452	17.2255465845548
111	67	86.4565263885187	-19.4565263885187
112	63	51.435810566461	11.564189433539
113	83	95.6729546087025	-12.6729546087025
114	32	42.752473211757	-10.752473211757
115	83	102.878187197887	-19.8781871978871
116	31	48.1974165427202	-17.1974165427202
117	67	36.4047328716332	30.5952671283668
118	66	52.6528564816627	13.3471435183373
119	70	63.3036434785318	6.69635652146816
120	103	80.6263162773854	22.3736837226146
121	34	56.3661215143004	-22.3661215143004
122	40	42.2499401394368	-2.2499401394368
123	31	46.7287181313678	-15.7287181313678
124	42	61.5135232179289	-19.5135232179289
125	46	49.7048129972374	-3.70481299723745
126	33	43.2683018046368	-10.2683018046368
127	18	42.386258489011	-24.386258489011
128	35	47.4949934357731	-12.4949934357731
129	66	47.9559886103195	18.0440113896805
130	60	46.2670770440466	13.7329229559534
131	54	47.7378460589957	6.26215394100425
132	53	48.1378688940631	4.86213110593688
133	39	47.6401225908201	-8.64012259082005
134	45	46.4040669837128	-1.40406698371283
135	36	44.4424579967652	-8.44245799676517
136	28	43.2395398105366	-15.2395398105366
137	30	39.0644006281726	-9.06440062817256
138	22	43.9996372250505	-21.9996372250505
139	31	46.5243759991944	-15.5243759991944
140	55	54.2554828110778	0.744517188922149
141	54	54.8643235447339	-0.864323544733919
142	14	34.3949530853455	-20.3949530853455
143	81	44.145959050121	36.854040949879
144	43	48.9559663501128	-5.95596635011279
145	30	54.3321891486305	-24.3321891486305
146	23	32.9581382507786	-9.95813825077856
147	38	44.9971539204147	-6.99715392041468
148	53	43.3448923392681	9.65510766073188
149	45	45.8553672212808	-0.855367221280782
150	39	43.3843523125892	-4.38435231258923
151	24	43.1786415072255	-19.1786415072255
152	35	42.5109716242747	-7.51097162427474
153	151	52.7285159183233	98.2714840816767
154	30	41.6549220748247	-11.6549220748247
155	57	52.6364970438593	4.36350295614071
156	40	39.980730522203	0.0192694777970285
157	77	50.3910463113601	26.6089536886399
158	35	56.1304392479749	-21.1304392479749
159	63	42.3331740932232	20.6668259067768
160	44	43.0853643131547	0.914635686845283
161	19	25.8164437965876	-6.81644379658758
162	13	38.2359223462737	-25.2359223462737
163	42	42.3932671307534	-0.39326713075337
164	42	47.5299929722979	-5.52999297229788
165	49	39.5455425146374	9.45445748536255
166	30	47.2526563856087	-17.2526563856087
167	49	53.5568560216332	-4.55685602163316
168	12	26.4186056760456	-14.4186056760456
169	20	42.0857049688355	-22.0857049688355
170	27	39.2754116247191	-12.2754116247191
171	14	41.2211056168964	-27.2211056168964

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
8	0.157731124789133	0.315462249578266	0.842268875210867
9	0.073574045137545	0.14714809027509	0.926425954862455
10	0.0957917103430906	0.191583420686181	0.904208289656909
11	0.228927654188976	0.457855308377951	0.771072345811024
12	0.144796023455196	0.289592046910391	0.855203976544804
13	0.14414159805288	0.28828319610576	0.85585840194712
14	0.0899525084210836	0.179905016842167	0.910047491578916
15	0.0567881380717251	0.11357627614345	0.943211861928275
16	0.119070274376211	0.238140548752421	0.880929725623789
17	0.148666152034982	0.297332304069964	0.851333847965018
18	0.153589833422343	0.307179666844686	0.846410166577657
19	0.107569282117596	0.215138564235191	0.892430717882404
20	0.110681228514064	0.221362457028127	0.889318771485936
21	0.0783009579218873	0.156601915843775	0.921699042078113
22	0.0535662708145977	0.107132541629195	0.946433729185402
23	0.0451724982672596	0.0903449965345192	0.95482750173274
24	0.0475630369315246	0.0951260738630491	0.952436963068475
25	0.0319279069468466	0.0638558138936932	0.968072093053153
26	0.0262301933208051	0.0524603866416102	0.973769806679195
27	0.110587555695831	0.221175111391662	0.889412444304169
28	0.0853333748239737	0.170666749647947	0.914666625176026
29	0.137261618051559	0.274523236103118	0.862738381948441
30	0.104403837395008	0.208807674790016	0.895596162604992
31	0.088450884539802	0.176901769079604	0.911549115460198
32	0.1368994385452	0.273798877090401	0.8631005614548
33	0.119152988834937	0.238305977669875	0.880847011165063
34	0.0935912286808173	0.187182457361635	0.906408771319183
35	0.0707534300406513	0.141506860081303	0.929246569959349
36	0.995048110010222	0.00990377997955704	0.00495188998977852
37	0.994762933888908	0.010474132222183	0.00523706611109149
38	0.994777155498569	0.0104456890028611	0.00522284450143055
39	0.999593486781096	0.00081302643780748	0.00040651321890374
40	0.999368058276875	0.00126388344625077	0.000631941723125384
41	0.999080129542779	0.00183974091444235	0.000919870457221176
42	0.99865758419129	0.00268483161742026	0.00134241580871013
43	0.998001988187876	0.00399602362424822	0.00199801181212411
44	0.997253924534704	0.00549215093059127	0.00274607546529564
45	0.997126189278933	0.00574762144213332	0.00287381072106666
46	0.997769059796512	0.00446188040697633	0.00223094020348817
47	0.997541718765067	0.00491656246986568	0.00245828123493284
48	0.996582677359409	0.00683464528118145	0.00341732264059073
49	0.996037339638524	0.0079253207229523	0.00396266036147615
50	0.996590560562881	0.00681887887423821	0.00340943943711911
51	0.995197668186468	0.00960466362706306	0.00480233181353153
52	0.993548481246486	0.0129030375070278	0.00645151875351392
53	0.991684050798889	0.0166318984022214	0.00831594920111071
54	0.988861700810044	0.0222765983799129	0.0111382991899564
55	0.984955586116695	0.0300888277666094	0.0150444138833047
56	0.983068117243227	0.0338637655135468	0.0169318827567734
57	0.977852369616989	0.0442952607660213	0.0221476303830107
58	0.994391277070793	0.0112174458584139	0.00560872292920695
59	0.992697777636511	0.0146044447269784	0.00730222236348921
60	0.992254578555694	0.0154908428886115	0.00774542144430577
61	0.989435200444378	0.021129599111244	0.010564799555622
62	0.986675143851631	0.0266497122967374	0.0133248561483687
63	0.982650439708326	0.0346991205833472	0.0173495602916736
64	0.985233601293121	0.0295327974137579	0.0147663987068789
65	0.985488571723294	0.0290228565534116	0.0145114282767058
66	0.981604647241105	0.0367907055177893	0.0183953527588946
67	0.976795774293363	0.0464084514132732	0.0232042257066366
68	0.969864213455835	0.0602715730883299	0.0301357865441649
69	0.961539424289606	0.0769211514207885	0.0384605757103942
70	0.962643882107922	0.0747122357841553	0.0373561178920777
71	0.992861918124637	0.0142761637507266	0.00713808187536328
72	0.993290181787938	0.0134196364241242	0.00670981821206209
73	0.991772665288045	0.0164546694239097	0.00822733471195484
74	0.989843242441897	0.0203135151162066	0.0101567575581033
75	0.987412077237504	0.0251758455249911	0.0125879227624955
76	0.983300317986732	0.033399364026535	0.0166996820132675
77	0.984876976334833	0.0302460473303342	0.0151230236651671
78	0.980431794564618	0.039136410870763	0.0195682054353815
79	0.974767079392991	0.0504658412140187	0.0252329206070094
80	0.970669545899335	0.0586609082013293	0.0293304541006647
81	0.967574105955131	0.0648517880897371	0.0324258940448685
82	0.959896149907758	0.0802077001844835	0.0401038500922418
83	0.951986605751823	0.0960267884963538	0.0480133942481769
84	0.942325636224836	0.115348727550329	0.0576743637751645
85	0.940461996291271	0.119076007417457	0.0595380037087286
86	0.926040293856162	0.147919412287676	0.0739597061438381
87	0.909952878179388	0.180094243641224	0.0900471218206122
88	0.90228974491733	0.195420510165339	0.0977102550826695
89	0.892106706520471	0.215786586959058	0.107893293479529
90	0.876413825150703	0.247172349698595	0.123586174849297
91	0.853655892371884	0.292688215256232	0.146344107628116
92	0.826337697444341	0.347324605111318	0.173662302555659
93	0.803963447408915	0.39207310518217	0.196036552591085
94	0.773897949276331	0.452204101447338	0.226102050723669
95	0.755010293367635	0.489979413264729	0.244989706632365
96	0.738130003133645	0.523739993732711	0.261869996866355
97	0.716310083550094	0.567379832899812	0.283689916449906
98	0.683110846810662	0.633778306378675	0.316889153189338
99	0.686943025560605	0.626113948878789	0.313056974439395
100	0.696818366585796	0.606363266828407	0.303181633414204
101	0.721614724548539	0.556770550902922	0.278385275451461
102	0.999992659228735	1.46815425296788e-05	7.34077126483939e-06
103	0.999993214436947	1.35711261055011e-05	6.78556305275053e-06
104	0.99999957445381	8.51092379462014e-07	4.25546189731007e-07
105	0.999999296642086	1.40671582776565e-06	7.03357913882824e-07
106	0.999998825133875	2.34973225079128e-06	1.17486612539564e-06
107	0.99999926194115	1.47611770065552e-06	7.38058850327759e-07
108	0.999998789027437	2.42194512526747e-06	1.21097256263373e-06
109	0.999998549539381	2.90092123717156e-06	1.45046061858578e-06
110	0.999997907071931	4.18585613881011e-06	2.09292806940505e-06
111	0.999997275841508	5.44831698446356e-06	2.72415849223178e-06
112	0.999995727708536	8.54458292802811e-06	4.27229146401405e-06
113	0.999993483691418	1.3032617164748e-05	6.51630858237401e-06
114	0.999989016336854	2.19673262916022e-05	1.09836631458011e-05
115	0.999993002488938	1.39950221233106e-05	6.99751106165532e-06
116	0.999990653923781	1.86921524377542e-05	9.34607621887712e-06
117	0.99999295520656	1.40895868809282e-05	7.04479344046412e-06
118	0.999988366066592	2.32678668167707e-05	1.16339334083854e-05
119	0.999979139459128	4.17210817441101e-05	2.0860540872055e-05
120	0.999969439710281	6.11205794375486e-05	3.05602897187743e-05
121	0.999959084471783	8.18310564342454e-05	4.09155282171227e-05
122	0.999929287365191	0.000141425269617704	7.07126348088522e-05
123	0.999893661466342	0.000212677067315397	0.000106338533657698
124	0.99989868381376	0.000202632372480284	0.000101316186240142
125	0.999830471261735	0.000339057476530224	0.000169528738265112
126	0.999721280129325	0.000557439741350135	0.000278719870675068
127	0.999715184532502	0.000569630934996084	0.000284815467498042
128	0.999609621140048	0.000780757719904268	0.000390378859952134
129	0.999460566469961	0.0010788670600774	0.000539433530038701
130	0.999173083706796	0.00165383258640833	0.000826916293204166
131	0.998656637733689	0.00268672453262302	0.00134336226631151
132	0.997886306777653	0.00422738644469461	0.00211369322234731
133	0.99674988756888	0.00650022486224019	0.00325011243112009
134	0.99490782110316	0.0101843577936805	0.00509217889684027
135	0.992383860184693	0.0152322796306143	0.00761613981530714
136	0.988877603158677	0.0222447936826467	0.0111223968413234
137	0.984105362403352	0.0317892751932956	0.0158946375966478
138	0.979809496156703	0.0403810076865938	0.0201905038432969
139	0.973045578393456	0.0539088432130882	0.0269544216065441
140	0.963420342628969	0.073159314742061	0.0365796573710305
141	0.948146182340279	0.103707635319441	0.0518538176597207
142	0.930882539924275	0.13823492015145	0.0691174600757248
143	0.963424790635483	0.0731504187290338	0.0365752093645169
144	0.948055835201647	0.103888329596707	0.0519441647983534
145	0.979725981600306	0.0405480367993884	0.0202740183996942
146	0.969252944697115	0.0614941106057694	0.0307470553028847
147	0.953865463290918	0.0922690734181639	0.0461345367090819
148	0.932796496431704	0.134407007136592	0.0672035035682961
149	0.907748981524922	0.184502036950157	0.0922510184750783
150	0.876524698422917	0.246950603154167	0.123475301577083
151	0.831624365380049	0.336751269239902	0.168375634619951
152	0.81981086814867	0.360378263702661	0.18018913185133
153	0.999632030564699	0.000735938870602674	0.000367969435301337
154	0.999125725841267	0.00174854831746671	0.000874274158733354
155	0.998813596762655	0.00237280647469087	0.00118640323734543
156	0.99700303375603	0.00599393248793947	0.00299696624396973
157	0.995877556498946	0.00824488700210729	0.00412244350105364
158	0.990249758506209	0.0195004829875829	0.00975024149379146
159	0.996495126202169	0.00700974759566157	0.00350487379783078
160	0.995634783956407	0.00873043208718529	0.00436521604359265
161	0.987931190691465	0.0241376186170706	0.0120688093085353
162	0.996805340404176	0.00638931919164895	0.00319465959582448
163	0.984904433369774	0.0301911332604513	0.0150955666302256

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	54	0.346153846153846	NOK
5% type I error level	89	0.57051282051282	NOK
10% type I error level	106	0.67948717948718	NOK