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Multiple Regression - NWWZ

*The author of this computation has been verified*

R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Mon, 27 Dec 2010 14:46:53 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/27/t1293461163n6mtrcko4y55n8g.htm/, Retrieved Mon, 27 Dec 2010 15:46:15 +0100

BibTeX entries for LaTeX users:

@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Dec/27/t1293461163n6mtrcko4y55n8g.htm/},
    year = {2010},
}
@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Development Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2010},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

206010 198112 194519 185705 180173 176142 203401 221902 197378 185001 176356 180449 180144 173666 165688 161570 156145 153730 182698 200765 176512 166618 158644 159585 163095 159044 155511 153745 150569 150605 179612 194690 189917 184128 175335 179566 181140 177876 175041 169292 166070 166972 206348 215706 202108 195411 193111 195198 198770 194163 190420 189733 186029 191531 232571 243477 227247 217859 208679 213188 216234 213586 209465 204045 200237 203666 241476 260307 243324 244460 233575 237217 235243 230354 227184 221678 217142 219452 256446 265845 248624 241114 229245 231805 219277 219313 212610 214771 211142 211457 240048 240636 230580 208795 197922 194596 194581 185686 178106 172608 167302 168053 202300 202388 182516 173476 166444 171297 169701 164182 161914 159612 151001 158114 186530 187069 174330 169362 166827 178037 186413 189226 191563 188906 186005 195309 223532 226899 etc...

Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits!

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	8 seconds
R Server	'George Udny Yule' @ 72.249.76.132
R Framework error message	The field 'Names of X columns' contains a hard return which cannot be interpreted. Please, resubmit your request without hard returns in the 'Names of X columns'.

Multiple Linear Regression - Estimated Regression Equation

NWWZ [t] = + 186373.429232739 + 147.663133228274t + 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)	186373.429232739	4318.351284	43.1585	0	0
t	147.663133228274	52.032105	2.8379	0.005211	0.002606

Multiple Linear Regression - Regression Statistics
Multiple R	0.232449780503641
R-squared	0.0540329004561911
Adjusted R-squared	0.0473239139346038
F-TEST (value)	8.05380965997339
F-TEST (DF numerator)	1
F-TEST (DF denominator)	141
p-value	0.00521133953200614
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	25684.6831505770
Sum Squared Residuals	93018115744.9204

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	206010	186521.092365967	19488.9076340333
2	198112	186668.755499196	11443.2445008044
3	194519	186816.418632424	7702.58136757607
4	185705	186964.081765652	-1259.08176565221
5	180173	187111.744898880	-6938.74489888048
6	176142	187259.408032109	-11117.4080321088
7	203401	187407.071165337	15993.9288346630
8	221902	187554.734298565	34347.2657014347
9	197378	187702.397431794	9675.60256820642
10	185001	187850.060565022	-2849.06056502185
11	176356	187997.72369825	-11641.7236982501
12	180449	188145.386831478	-7696.3868314784
13	180144	188293.049964707	-8149.04996470667
14	173666	188440.713097935	-14774.7130979349
15	165688	188588.376231163	-22900.3762311632
16	161570	188736.039364392	-27166.0393643915
17	156145	188883.70249762	-32738.7024976198
18	153730	189031.365630848	-35301.3656308480
19	182698	189179.028764076	-6481.02876407631
20	200765	189326.691897305	11438.3081026954
21	176512	189474.355030533	-12962.3550305329
22	166618	189622.018163761	-23004.0181637611
23	158644	189769.681296989	-31125.6812969894
24	159585	189917.344430218	-30332.3444302177
25	163095	190065.007563446	-26970.0075634460
26	159044	190212.670696674	-31168.6706966742
27	155511	190360.333829903	-34849.3338299025
28	153745	190507.996963131	-36762.9969631308
29	150569	190655.660096359	-40086.6600963591
30	150605	190803.323229587	-40198.3232295873
31	179612	190950.986362816	-11338.9863628156
32	194690	191098.649496044	3591.35050395612
33	189917	191246.312629272	-1329.31262927215
34	184128	191393.975762500	-7265.97576250042
35	175335	191541.638895729	-16206.6388957287
36	179566	191689.302028957	-12123.3020289570
37	181140	191836.965162185	-10696.9651621852
38	177876	191984.628295414	-14108.6282954135
39	175041	192132.291428642	-17091.2914286418
40	169292	192279.95456187	-22987.9545618701
41	166070	192427.617695098	-26357.6176950983
42	166972	192575.280828327	-25603.2808283266
43	206348	192722.943961555	13625.0560384451
44	215706	192870.607094783	22835.3929052168
45	202108	193018.270228011	9089.72977198856
46	195411	193165.933361240	2245.06663876029
47	193111	193313.596494468	-202.596494467984
48	195198	193461.259627696	1736.74037230374
49	198770	193608.922760925	5161.07723907547
50	194163	193756.585894153	406.414105847194
51	190420	193904.249027381	-3484.24902738108
52	189733	194051.912160609	-4318.91216060935
53	186029	194199.575293838	-8170.57529383763
54	191531	194347.238427066	-2816.2384270659
55	232571	194494.901560294	38076.0984397058
56	243477	194642.564693522	48834.4353064775
57	227247	194790.227826751	32456.7721732493
58	217859	194937.890959979	22921.109040021
59	208679	195085.554093207	13593.4459067927
60	213188	195233.217226436	17954.7827735645
61	216234	195380.880359664	20853.1196403362
62	213586	195528.543492892	18057.4565071079
63	209465	195676.206626120	13788.7933738796
64	204045	195823.869759349	8221.13024065136
65	200237	195971.532892577	4265.46710742309
66	203666	196119.196025805	7546.80397419481
67	241476	196266.859159033	45209.1408409665
68	260307	196414.522292262	63892.4777077383
69	243324	196562.18542549	46761.81457451
70	244460	196709.848558718	47750.1514412817
71	233575	196857.511691947	36717.4883080534
72	237217	197005.174825175	40211.8251748252
73	235243	197152.837958403	38090.1620415969
74	230354	197300.501091631	33053.4989083686
75	227184	197448.164224860	29735.8357751403
76	221678	197595.827358088	24082.1726419121
77	217142	197743.490491316	19398.5095086838
78	219452	197891.153624544	21560.8463754555
79	256446	198038.816757773	58407.1832422272
80	265845	198186.479891001	67658.520108999
81	248624	198334.143024229	50289.8569757707
82	241114	198481.806157458	42632.1938425424
83	229245	198629.469290686	30615.5307093142
84	231805	198777.132423914	33027.8675760859
85	219277	198924.795557142	20352.2044428576
86	219313	199072.458690371	20240.5413096293
87	212610	199220.121823599	13389.8781764011
88	214771	199367.784956827	15403.2150431728
89	211142	199515.448090055	11626.5519099445
90	211457	199663.111223284	11793.8887767162
91	240048	199810.774356512	40237.225643488
92	240636	199958.437489740	40677.5625102597
93	230580	200106.100622969	30473.8993770314
94	208795	200253.763756197	8541.23624380314
95	197922	200401.426889425	-2479.42688942513
96	194596	200549.090022653	-5953.0900226534
97	194581	200696.753155882	-6115.75315588168
98	185686	200844.41628911	-15158.4162891100
99	178106	200992.079422338	-22886.0794223382
100	172608	201139.742555567	-28531.7425555665
101	167302	201287.405688795	-33985.4056887948
102	168053	201435.068822023	-33382.0688220231
103	202300	201582.731955251	717.26804474868
104	202388	201730.395088480	657.604911520405
105	182516	201878.058221708	-19362.0582217079
106	173476	202025.721354936	-28549.7213549361
107	166444	202173.384488164	-35729.3844881644
108	171297	202321.047621393	-31024.0476213927
109	169701	202468.710754621	-32767.710754621
110	164182	202616.373887849	-38434.3738878492
111	161914	202764.037021078	-40850.0370210775
112	159612	202911.700154306	-43299.7001543058
113	151001	203059.363287534	-52058.3632875341
114	158114	203207.026420762	-45093.0264207623
115	186530	203354.689553991	-16824.6895539906
116	187069	203502.352687219	-16433.3526872189
117	174330	203650.015820447	-29320.0158204472
118	169362	203797.678953675	-34435.6789536754
119	166827	203945.342086904	-37118.3420869037
120	178037	204093.005220132	-26056.005220132
121	186413	204240.668353360	-17827.6683533603
122	189226	204388.331486589	-15162.3314865885
123	191563	204535.994619817	-12972.9946198168
124	188906	204683.657753045	-15777.6577530451
125	186005	204831.320886273	-18826.3208862733
126	195309	204978.984019502	-9669.98401950162
127	223532	205126.64715273	18405.3528472701
128	226899	205274.310285958	21624.6897140418
129	214126	205421.973419186	8704.02658081356
130	206903	205569.636552415	1333.36344758528
131	204442	205717.299685643	-1275.29968564299
132	220375	205864.962818871	14510.0371811287
133	214320	206012.625952100	8307.37404790046
134	212588	206160.289085328	6427.71091467219
135	205816	206307.952218556	-491.952218556083
136	202196	206455.615351784	-4259.61535178436
137	195722	206603.278485013	-10881.2784850126
138	198563	206750.941618241	-8187.9416182409
139	229139	206898.604751469	22240.3952485308
140	229527	207046.267884697	22480.7321153025
141	211868	207193.931017926	4674.06898207427
142	203555	207341.594151154	-3786.594151154
143	195770	207489.257284382	-11719.2572843823

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
5	0.000156825104176465	0.000313650208352931	0.999843174895824
6	1.58451001642136e-05	3.16902003284273e-05	0.999984154899836
7	0.0332434588980504	0.0664869177961007	0.96675654110195
8	0.1081994724814	0.2163989449628	0.8918005275186
9	0.0575896874057742	0.115179374811548	0.942410312594226
10	0.0374018737555102	0.0748037475110203	0.96259812624449
11	0.028339408701517	0.056678817403034	0.971660591298483
12	0.015214969940076	0.030429939880152	0.984785030059924
13	0.00752835002876513	0.0150567000575303	0.992471649971235
14	0.00396062709217456	0.00792125418434912	0.996039372907825
15	0.00246853038539525	0.00493706077079049	0.997531469614605
16	0.00151523458085045	0.00303046916170091	0.99848476541915
17	0.000989392520920072	0.00197878504184014	0.99901060747908
18	0.000591472201356869	0.00118294440271374	0.999408527798643
19	0.000807910530294742	0.00161582106058948	0.999192089469705
20	0.00408764783898785	0.0081752956779757	0.995912352161012
21	0.00248940956129275	0.0049788191225855	0.997510590438707
22	0.00138122596841354	0.00276245193682708	0.998618774031586
23	0.000851306516411584	0.00170261303282317	0.999148693483588
24	0.000494538768530013	0.000989077537060025	0.99950546123147
25	0.00027780065383873	0.00055560130767746	0.99972219934616
26	0.000160044482833618	0.000320088965667236	0.999839955517166
27	9.74894948378204e-05	0.000194978989675641	0.999902510505162
28	6.19737939443299e-05	0.000123947587888660	0.999938026206056
29	4.32402884095745e-05	8.6480576819149e-05	0.99995675971159
30	3.11349484509474e-05	6.22698969018948e-05	0.99996886505155
31	8.97113314477987e-05	0.000179422662895597	0.999910288668552
32	0.000709508712441844	0.00141901742488369	0.999290491287558
33	0.00160067783145424	0.00320135566290848	0.998399322168546
34	0.00198413592559482	0.00396827185118964	0.998015864074405
35	0.00172525608103221	0.00345051216206441	0.998274743918968
36	0.00164535178339809	0.00329070356679619	0.998354648216602
37	0.00159331184088086	0.00318662368176171	0.998406688159119
38	0.00140366607167428	0.00280733214334856	0.998596333928326
39	0.00119817056233340	0.00239634112466681	0.998801829437667
40	0.00104487208143264	0.00208974416286529	0.998955127918567
41	0.000992975976423108	0.00198595195284622	0.999007024023577
42	0.000993197703039455	0.00198639540607891	0.99900680229696
43	0.0034830560027257	0.0069661120054514	0.996516943997274
44	0.0127341744722212	0.0254683489444424	0.987265825527779
45	0.0165291326635165	0.033058265327033	0.983470867336484
46	0.0168147552777237	0.0336295105554474	0.983185244722276
47	0.0160872287799884	0.0321744575599768	0.983912771220012
48	0.0154894418298713	0.0309788836597426	0.98451055817013
49	0.0152813299368063	0.0305626598736126	0.984718670063194
50	0.0140503510560774	0.0281007021121548	0.985949648943923
51	0.0128105291304503	0.0256210582609007	0.98718947086955
52	0.0118559452902764	0.0237118905805527	0.988144054709724
53	0.011561222553173	0.023122445106346	0.988438777446827
54	0.0111005055097051	0.0222010110194103	0.988899494490295
55	0.0281949019090086	0.0563898038180171	0.971805098090991
56	0.0776876569974815	0.155375313994963	0.922312343002519
57	0.0922300982580656	0.184460196516131	0.907769901741934
58	0.0875685756795725	0.175137151359145	0.912431424320427
59	0.0759469137598846	0.151893827519769	0.924053086240115
60	0.0661878309418792	0.132375661883758	0.93381216905812
61	0.0577907823715217	0.115581564743043	0.942209217628478
62	0.048630483776352	0.097260967552704	0.951369516223648
63	0.0400139566802516	0.0800279133605032	0.959986043319748
64	0.0334575503364963	0.0669151006729926	0.966542449663504
65	0.0291982964900847	0.0583965929801694	0.970801703509915
66	0.0246700755068033	0.0493401510136066	0.975329924493197
67	0.0322009229273765	0.064401845854753	0.967799077072623
68	0.0754904255846083	0.150980851169217	0.924509574415392
69	0.0853288976688794	0.170657795337759	0.91467110233112
70	0.0954887737709104	0.190977547541821	0.90451122622909
71	0.0857268330418035	0.171453666083607	0.914273166958196
72	0.0804694982195402	0.160938996439080	0.91953050178046
73	0.0727198097829153	0.145439619565831	0.927280190217085
74	0.0614333253507152	0.122866650701430	0.938566674649285
75	0.0501218034610469	0.100243606922094	0.949878196538953
76	0.0394405023193261	0.0788810046386522	0.960559497680674
77	0.030724685283826	0.061449370567652	0.969275314716174
78	0.0237212554610944	0.0474425109221887	0.976278744538906
79	0.0401557166289328	0.0803114332578655	0.959844283371067
80	0.099325290587089	0.198650581174178	0.90067470941291
81	0.134164780565649	0.268329561131297	0.865835219434351
82	0.159506014795637	0.319012029591273	0.840493985204363
83	0.163833591295395	0.32766718259079	0.836166408704605
84	0.181279104131323	0.362558208262646	0.818720895868677
85	0.182701358669821	0.365402717339643	0.817298641330178
86	0.188711184859528	0.377422369719055	0.811288815140472
87	0.192632485034569	0.385264970069137	0.807367514965431
88	0.201771274439937	0.403542548879875	0.798228725560063
89	0.211784982538785	0.423569965077570	0.788215017461215
90	0.226312113347533	0.452624226695067	0.773687886652467
91	0.391334695393913	0.782669390787826	0.608665304606087
92	0.662440897149997	0.675118205700006	0.337559102850003
93	0.864014902214024	0.271970195571953	0.135985097785976
94	0.928147926194483	0.143704147611035	0.0718520738055173
95	0.958437417853986	0.0831251642920288	0.0415625821460144
96	0.97675316817565	0.0464936636487014	0.0232468318243507
97	0.98843432069422	0.023131358611561	0.0115656793057805
98	0.993275956875397	0.0134480862492050	0.00672404312460252
99	0.995568505506898	0.00886298898620354	0.00443149449310177
100	0.996826748255746	0.00634650348850764	0.00317325174425382
101	0.997635460758308	0.00472907848338446	0.00236453924169223
102	0.998022563799406	0.00395487240118692	0.00197743620059346
103	0.999436391422168	0.00112721715566413	0.000563608577832067
104	0.99992177040971	0.000156459180577778	7.82295902888888e-05
105	0.999955848893535	8.8302212930286e-05	4.4151106465143e-05
106	0.99996112101767	7.77579646611738e-05	3.88789823305869e-05
107	0.999958551155626	8.28976887484403e-05	4.14488443742201e-05
108	0.99995335472527	9.32905494604138e-05	4.66452747302069e-05
109	0.999942328324607	0.000115343350786265	5.76716753931327e-05
110	0.999926564373588	0.000146871252824267	7.34356264121333e-05
111	0.999909460003344	0.000181079993311992	9.05399966559961e-05
112	0.999900898165418	0.000198203669163463	9.91018345817316e-05
113	0.999952678712574	9.46425748528749e-05	4.73212874264374e-05
114	0.999968273487871	6.345302425709e-05	3.1726512128545e-05
115	0.999941556002515	0.000116887994970617	5.84439974853086e-05
116	0.999892851138677	0.000214297722646731	0.000107148861323366
117	0.99982740373157	0.000345192536860037	0.000172596268430018
118	0.999815328097929	0.000369343804142392	0.000184671902071196
119	0.99989015066228	0.000219698675441486	0.000109849337720743
120	0.999877060732127	0.000245878535745364	0.000122939267872682
121	0.99980314338786	0.00039371322427901	0.000196856612139505
122	0.999681374322649	0.000637251354702104	0.000318625677351052
123	0.999492514199533	0.00101497160093467	0.000507485800467336
124	0.999454685331568	0.00109062933686497	0.000545314668432486
125	0.999757948167308	0.000484103665384173	0.000242051832692086
126	0.999840269185505	0.000319461628991011	0.000159730814495505
127	0.999664693619323	0.000670612761354741	0.000335306380677370
128	0.999552885669145	0.000894228661709843	0.000447114330854922
129	0.998913105103281	0.00217378979343742	0.00108689489671871
130	0.99747642041538	0.00504715916923981	0.00252357958461990
131	0.995019705381825	0.00996058923635044	0.00498029461817522
132	0.990611718721732	0.0187765625565362	0.00938828127826809
133	0.98040545444214	0.0391890911157208	0.0195945455578604
134	0.96083048654713	0.0783390269057394	0.0391695134528697
135	0.920701158842177	0.158597682315647	0.0792988411578235
136	0.857118534086778	0.285762931826444	0.142881465913222
137	0.845000065470258	0.309999869059485	0.154999934529742
138	0.993649900297682	0.0127001994046353	0.00635009970231765

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	65	0.485074626865672	NOK
5% type I error level	86	0.641791044776119	NOK
10% type I error level	100	0.746268656716418	NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293461163n6mtrcko4y55n8g/1026mk1293461203.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293461163n6mtrcko4y55n8g/1026mk1293461203.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293461163n6mtrcko4y55n8g/16eou1293461203.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293461163n6mtrcko4y55n8g/16eou1293461203.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293461163n6mtrcko4y55n8g/26eou1293461203.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293461163n6mtrcko4y55n8g/26eou1293461203.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293461163n6mtrcko4y55n8g/36eou1293461203.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293461163n6mtrcko4y55n8g/36eou1293461203.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293461163n6mtrcko4y55n8g/4y5ne1293461203.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293461163n6mtrcko4y55n8g/4y5ne1293461203.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293461163n6mtrcko4y55n8g/5y5ne1293461203.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293461163n6mtrcko4y55n8g/5y5ne1293461203.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293461163n6mtrcko4y55n8g/6y5ne1293461203.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293461163n6mtrcko4y55n8g/6y5ne1293461203.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293461163n6mtrcko4y55n8g/79wnh1293461203.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293461163n6mtrcko4y55n8g/79wnh1293461203.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293461163n6mtrcko4y55n8g/826mk1293461203.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293461163n6mtrcko4y55n8g/826mk1293461203.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293461163n6mtrcko4y55n8g/926mk1293461203.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293461163n6mtrcko4y55n8g/926mk1293461203.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

R code (references can be found in the software module):

library(lattice)

library(lmtest)

n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test

par1 <- as.numeric(par1)

x <- t(y)

k <- length(x[1,])

n <- length(x[,1])

x1 <- cbind(x[,par1], x[,1:k!=par1])

mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1])

colnames(x1) <- mycolnames #colnames(x)[par1]

x <- x1

if (par3 == 'First Differences'){

x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep='')))

for (i in 1:n-1) {

for (j in 1:k) {

x2[i,j] <- x[i+1,j] - x[i,j]

}

}

x <- x2

}

if (par2 == 'Include Monthly Dummies'){

x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep ='')))

for (i in 1:11){

x2[seq(i,n,12),i] <- 1

}

x <- cbind(x, x2)

}

if (par2 == 'Include Quarterly Dummies'){

x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep ='')))

for (i in 1:3){

x2[seq(i,n,4),i] <- 1

}

x <- cbind(x, x2)

}

k <- length(x[1,])

if (par3 == 'Linear Trend'){

x <- cbind(x, c(1:n))

colnames(x)[k+1] <- 't'

}

x

k <- length(x[1,])

df <- as.data.frame(x)

(mylm <- lm(df))

(mysum <- summary(mylm))

if (n > n25) {

kp3 <- k + 3

nmkm3 <- n - k - 3

gqarr <- array(NA, dim=c(nmkm3-kp3+1,3))

numgqtests <- 0

numsignificant1 <- 0

numsignificant5 <- 0

numsignificant10 <- 0

for (mypoint in kp3:nmkm3) {

j <- 0

numgqtests <- numgqtests + 1

for (myalt in c('greater', 'two.sided', 'less')) {

j <- j + 1

gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value

}

if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1

if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1

if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1

}

gqarr

}

bitmap(file='test0.png')

plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')

points(x[,1]-mysum$resid)

grid()

dev.off()

bitmap(file='test1.png')

plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')

grid()

dev.off()

bitmap(file='test2.png')

hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')

grid()

dev.off()

bitmap(file='test3.png')

densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')

dev.off()

bitmap(file='test4.png')

qqnorm(mysum$resid, main='Residual Normal Q-Q Plot')

qqline(mysum$resid)

grid()

dev.off()

(myerror <- as.ts(mysum$resid))

bitmap(file='test5.png')

dum <- cbind(lag(myerror,k=1),myerror)

dum

dum1 <- dum[2:length(myerror),]

dum1

z <- as.data.frame(dum1)

z

plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals')

lines(lowess(z))

abline(lm(z))

grid()

dev.off()

bitmap(file='test6.png')

acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')

grid()

dev.off()

bitmap(file='test7.png')

pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')

grid()

dev.off()

bitmap(file='test8.png')

opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))

plot(mylm, las = 1, sub='Residual Diagnostics')

par(opar)

dev.off()

if (n > n25) {

bitmap(file='test9.png')

plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')

grid()

dev.off()

}

load(file='createtable')

a<-table.start()

a<-table.row.start(a)

a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)

a<-table.row.end(a)

myeq <- colnames(x)[1]

myeq <- paste(myeq, '[t] = ', sep='')

for (i in 1:k){

if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')

myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ')

if (rownames(mysum$coefficients)[i] != '(Intercept)') {

myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')

if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')

}

}

myeq <- paste(myeq, ' + e[t]')

a<-table.row.start(a)

a<-table.element(a, myeq)

a<-table.row.end(a)

a<-table.end(a)

table.save(a,file='mytable1.tab')

a<-table.start()

a<-table.row.start(a)

a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'Variable',header=TRUE)

a<-table.element(a,'Parameter',header=TRUE)

a<-table.element(a,'S.D.',header=TRUE)

a<-table.element(a,'T-STAT<br />H0: parameter = 0',header=TRUE)

a<-table.element(a,'2-tail p-value',header=TRUE)

a<-table.element(a,'1-tail p-value',header=TRUE)

a<-table.row.end(a)

for (i in 1:k){

a<-table.row.start(a)

a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)

a<-table.element(a,mysum$coefficients[i,1])

a<-table.element(a, round(mysum$coefficients[i,2],6))

a<-table.element(a, round(mysum$coefficients[i,3],4))

a<-table.element(a, round(mysum$coefficients[i,4],6))

a<-table.element(a, round(mysum$coefficients[i,4]/2,6))

a<-table.row.end(a)

}

a<-table.end(a)

table.save(a,file='mytable2.tab')

a<-table.start()

a<-table.row.start(a)

a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'Multiple R',1,TRUE)

a<-table.element(a, sqrt(mysum$r.squared))

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'R-squared',1,TRUE)

a<-table.element(a, mysum$r.squared)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'Adjusted R-squared',1,TRUE)

a<-table.element(a, mysum$adj.r.squared)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'F-TEST (value)',1,TRUE)

a<-table.element(a, mysum$fstatistic[1])

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)

a<-table.element(a, mysum$fstatistic[2])

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)

a<-table.element(a, mysum$fstatistic[3])

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'p-value',1,TRUE)

a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]))

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'Residual Standard Deviation',1,TRUE)

a<-table.element(a, mysum$sigma)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'Sum Squared Residuals',1,TRUE)

a<-table.element(a, sum(myerror*myerror))

a<-table.row.end(a)

a<-table.end(a)

table.save(a,file='mytable3.tab')

a<-table.start()

a<-table.row.start(a)

a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'Time or Index', 1, TRUE)

a<-table.element(a, 'Actuals', 1, TRUE)

a<-table.element(a, 'Interpolation<br />Forecast', 1, TRUE)

a<-table.element(a, 'Residuals<br />Prediction Error', 1, TRUE)

a<-table.row.end(a)

for (i in 1:n) {

a<-table.row.start(a)

a<-table.element(a,i, 1, TRUE)

a<-table.element(a,x[i])

a<-table.element(a,x[i]-mysum$resid[i])

a<-table.element(a,mysum$resid[i])

a<-table.row.end(a)

}

a<-table.end(a)

table.save(a,file='mytable4.tab')

if (n > n25) {

a<-table.start()

a<-table.row.start(a)

a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'p-values',header=TRUE)

a<-table.element(a,'Alternative Hypothesis',3,header=TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'breakpoint index',header=TRUE)

a<-table.element(a,'greater',header=TRUE)

a<-table.element(a,'2-sided',header=TRUE)

a<-table.element(a,'less',header=TRUE)

a<-table.row.end(a)

for (mypoint in kp3:nmkm3) {

a<-table.row.start(a)

a<-table.element(a,mypoint,header=TRUE)

a<-table.element(a,gqarr[mypoint-kp3+1,1])

a<-table.element(a,gqarr[mypoint-kp3+1,2])

a<-table.element(a,gqarr[mypoint-kp3+1,3])

a<-table.row.end(a)

}

a<-table.end(a)

table.save(a,file='mytable5.tab')

a<-table.start()

a<-table.row.start(a)

a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'Description',header=TRUE)

a<-table.element(a,'# significant tests',header=TRUE)

a<-table.element(a,'% significant tests',header=TRUE)

a<-table.element(a,'OK/NOK',header=TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'1% type I error level',header=TRUE)

a<-table.element(a,numsignificant1)

a<-table.element(a,numsignificant1/numgqtests)

if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK'

a<-table.element(a,dum)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'5% type I error level',header=TRUE)

a<-table.element(a,numsignificant5)

a<-table.element(a,numsignificant5/numgqtests)

if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK'

a<-table.element(a,dum)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'10% type I error level',header=TRUE)

a<-table.element(a,numsignificant10)

a<-table.element(a,numsignificant10/numgqtests)

if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK'

a<-table.element(a,dum)

a<-table.row.end(a)

a<-table.end(a)

table.save(a,file='mytable6.tab')

}

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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