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Multiple regressie- OPJ en 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: Sun, 26 Dec 2010 17:01:47 +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/26/t1293382867v81xe0q2k2oxs5c.htm/, Retrieved Sun, 26 Dec 2010 18:01:18 +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/26/t1293382867v81xe0q2k2oxs5c.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 «

20503 206010 22885 198112 26217 194519 26583 185705 27751 180173 28158 176142 27373 203401 28367 221902 26851 197378 26733 185001 26849 176356 26733 180449 27951 180144 29781 173666 32914 165688 33488 161570 35652 156145 36488 153730 35387 182698 35676 200765 34844 176512 32447 166618 31068 158644 29010 159585 29812 163095 30951 159044 32974 155511 32936 153745 34012 150569 32946 150605 31948 179612 30599 194690 27691 189917 25073 184128 23406 175335 22248 179566 22896 181140 25317 177876 26558 175041 26471 169292 27543 166070 26198 166972 24725 206348 25005 215706 23462 202108 20780 195411 19815 193111 19761 195198 21454 198770 23899 194163 24939 190420 23580 189733 24562 186029 24696 191531 23785 232571 23812 243477 21917 227247 19713 217859 19282 208679 18788 213188 21453 216234 24482 213586 27474 209465 27264 204045 27349 200237 30632 203666 29429 241476 30084 260307 26290 243324 24379 244460 23335 233575 21346 237217 21106 235243 24 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	13 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

OPJV[t] = + 45978.6315862238 -0.119988854669597`NWWZ `[t] + 144.461975506960t + 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)	45978.6315862238	3235.605082	14.2102	0	0
`NWWZ `	-0.119988854669597	0.016739	-7.1683	0	0
t	144.461975506960	10.633327	13.5858	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.768201032787013
R-squared	0.590132826775033
Adjusted R-squared	0.584277581443248
F-TEST (value)	100.787036808089
F-TEST (DF numerator)	2
F-TEST (DF denominator)	140
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	5105.16763955805
Sum Squared Residuals	3648783127.91870

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	20503	21404.1896112472	-901.18961124715
2	22885	22496.3235609346	388.676439065388
3	26217	23071.9054912695	3145.09450873052
4	26583	24273.9492318342	2309.05076816578
5	27751	25082.1895513734	2668.81044862661
6	28158	25710.3266000535	2447.67339994651
7	27373	22584.0123861219	4788.98761387808
8	28367	20508.5605613867	7858.43943861333
9	26851	23595.6292088108	3255.37079118918
10	26733	25225.1932385634	1507.80676143663
11	26849	26406.958862689	442.041137311004
12	26733	26060.3064560333	672.693543966703
13	27951	26241.3650322145	1709.63496778552
14	29781	27163.1148082711	2617.88519172891
15	32914	28264.8478663321	4649.15213366791
16	33488	28903.4239453684	4584.57605463155
17	35652	29698.8254574580	5953.17454254203
18	36488	30133.060516992	6354.939483008
19	35387	26801.6853504301	8585.31464956991
20	35676	24778.3086886214	10897.6913113786
21	34844	27832.8603564301	7011.13964356987
22	32447	29164.4920600381	3282.50793996192
23	31068	30265.7451626804	802.254837319595
24	29010	30297.2976259433	-1287.29762594327
25	29812	30020.5987215599	-208.59872155995
26	30951	30651.1355473334	299.864452666555
27	32974	31219.5181463881	1754.48185361191
28	32936	31575.8804392416	1360.11956075844
29	34012	32101.4270171792	1910.57298282084
30	32946	32241.569393918	704.43060608199
31	31948	28905.514662024	3042.48533797602
32	30599	27240.7846868228	3358.21531317724
33	27691	27957.9534656677	-266.953465667705
34	25073	28797.0309208570	-3724.03092085696
35	23406	29996.5548954737	-6590.55489547368
36	22248	29633.3440268736	-7385.34402687358
37	22896	29588.9435451306	-6692.94354513059
38	25317	30125.0491422791	-4808.04914227912
39	26558	30609.6795207744	-4051.67952077438
40	26471	31443.9574217769	-4972.95742177685
41	27543	31975.0234870293	-4432.02348702925
42	26198	32011.2555156242	-5813.25551562424
43	24725	27431.0363496612	-2706.03634966116
44	25005	26452.6426231700	-1447.64262317003
45	23462	28228.7130444742	-4766.71304447417
46	20780	29176.7403797034	-8396.74037970342
47	19815	29597.1767209504	-9782.17672095045
48	19761	29491.2219567620	-9730.22195676196
49	21454	29207.0837433891	-7753.08374338912
50	23899	29904.3343723589	-6005.33437235891
51	24939	30497.9146308942	-5558.91463089417
52	23580	30724.8089495591	-7144.80894955914
53	24562	31313.7096427623	-6751.70964276229
54	24696	30797.9929398771	-6101.99293987713
55	23785	26018.1123197438	-2233.11231974384
56	23812	24853.9758462242	-1041.97584622418
57	21917	26945.8569330187	-5028.85693301869
58	19713	28216.7742761638	-8503.77427616383
59	19282	29462.7339375377	-10180.7339375377
60	18788	29066.1661673394	-10278.1661673394
61	21453	28845.1420915228	-7392.1420915228
62	24482	29307.3345541949	-4825.33455419485
63	27474	29946.2705997952	-2472.27059979522
64	27264	30741.0721676114	-3477.07216761139
65	27349	31342.4517017002	-3993.45170170017
66	30632	31075.4718945451	-443.471894545086
67	29429	26683.1552749946	2745.84472500540
68	30084	24568.1071282184	5515.89287178162
69	26290	26750.3398225791	-460.339822579101
70	24379	26758.4944591814	-2379.4944591814
71	23335	28209.0351177669	-4874.03511776692
72	21346	27916.4976845672	-6570.4976845672
73	21106	28297.8176591919	-7191.81765919195
74	24514	29028.9051451786	-4514.90514517857
75	28353	29553.7317899881	-1200.73178998815
76	30805	30358.8523993059	446.147600694093
77	31348	31047.5838195942	300.416180405844
78	34556	30914.8715408143	3641.12845918565
79	33855	26620.4658266742	7234.53417332575
80	34787	25637.1525571417	9149.84744285833
81	32529	27847.9425989138	4681.05740108625
82	29998	28893.5208729894	1104.47912701062
83	29257	30462.1305645698	-1205.13056456979
84	28155	30299.4210721226	-2144.42107212258
85	30466	31947.1034189302	-1481.10341893024
86	35704	32087.2457956691	3616.7542043309
87	39327	33035.9930640264	6291.00693597364
88	39351	32921.1591245923	6429.84087540768
89	42234	33501.0606536953	8732.93934630475
90	43630	33607.7261399813	10022.2738600187
91	43722	30321.5867716298	13400.4132283702
92	43121	30395.4953005910	12725.5046994090
93	37985	31746.5651986555	6238.43480134453
94	37135	34504.9843731396	2630.01562686041
95	34646	35954.0851654691	-1308.08516546908
96	33026	36497.6300716071	-3471.63007160711
97	35087	36643.8918799341	-1556.89187993412
98	38846	37855.6547177271	990.345282272862
99	42013	38909.6322116296	3103.36778837036
100	43908	39713.7929101100	4194.20708988996
101	42868	40494.9157484939	2373.08425150612
102	44423	40549.266094144	3873.73390585603
103	44167	36584.4697637813	7582.53023621874
104	43636	36718.3727200773	6917.62727992271
105	44382	39247.2532155785	5134.74678442152
106	42142	40476.4144372986	1665.58556270141
107	43452	41464.6380388422	1987.36196115785
108	36912	41026.7941026376	-4114.79410263756
109	42413	41362.7582901972	1050.24170980280
110	45344	42169.4387546257	3174.56124537434
111	44873	42586.0354525233	2286.96454747674
112	47510	43006.7117714796	4503.28822852037
113	49554	44184.3977745465	5369.60222545351
114	47369	43475.3790267886	3893.62097321139
115	45998	40210.2377080043	5787.76229199569
116	48140	40290.0256908444	7849.97430915564
117	48441	41963.0256859873	6477.97431401269
118	44928	42703.5922914928	2224.40770850717
119	40454	43152.2260135872	-2698.22601358721
120	38661	41951.612928248	-3290.61292824799
121	37246	41091.0482570424	-3845.04825704241
122	36843	40897.9815843638	-4054.98158436379
123	36424	40762.0296065079	-4338.02960650791
124	37594	41225.301968872	-3631.30196887198
125	38144	41717.8516117754	-3573.85161177544
126	38737	40745.9372834365	-2008.93728343648
127	34560	37503.9538136034	-2943.95381360341
128	36080	37244.4133154378	-1164.41331543784
129	33508	38921.4929316396	-5413.49293163955
130	35462	39932.634404425	-4470.63440442501
131	33374	40372.3889512738	-6998.38895127385
132	32110	38605.0685053301	-6495.06850533012
133	35533	39476.0629958615	-3943.06299586149
134	35532	39828.3456676562	-4296.34566765619
135	37903	40785.3721669857	-2882.37216698566
136	36763	41364.1937963966	-4601.19379639656
137	40399	42285.4636170345	-1886.46361703449
138	44164	42089.0372564251	2074.96274357488
139	44496	38564.7200115545	5931.2799884455
140	43110	38662.6263114497	4447.37368855035
141	43880	40925.971471567	2954.02852843298
142	43930	42067.9007959423	1862.09920405767
143	44327	43146.4760050521	1180.52399494790

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
6	0.0201020699785137	0.0402041399570275	0.979897930021486
7	0.00411696833262132	0.00823393666524265	0.995883031667379
8	0.00111667902065158	0.00223335804130315	0.998883320979348
9	0.00303115038170803	0.00606230076341606	0.996968849618292
10	0.00430608130732657	0.00861216261465315	0.995693918692673
11	0.00320151077705976	0.00640302155411951	0.99679848922294
12	0.00181722246185436	0.00363444492370872	0.998182777538146
13	0.000679280195220995	0.00135856039044199	0.999320719804779
14	0.000245117914805707	0.000490235829611415	0.999754882085194
15	0.000222376721110299	0.000444753442220598	0.99977762327889
16	0.000132292772335143	0.000264585544670286	0.999867707227665
17	0.000125363935875477	0.000250727871750955	0.999874636064125
18	9.29297883642812e-05	0.000185859576728562	0.999907070211636
19	6.1439004325789e-05	0.000122878008651578	0.999938560995674
20	4.43199583300636e-05	8.86399166601272e-05	0.99995568004167
21	2.36550004415454e-05	4.73100008830909e-05	0.999976344999558
22	4.5789567851917e-05	9.1579135703834e-05	0.999954210432148
23	0.000181031621967575	0.000362063243935149	0.999818968378032
24	0.00117563318662306	0.00235126637324611	0.998824366813377
25	0.00217350966416116	0.00434701932832233	0.997826490335839
26	0.00226181212259598	0.00452362424519197	0.997738187877404
27	0.00157755447522451	0.00315510895044902	0.998422445524775
28	0.00112216588746951	0.00224433177493901	0.99887783411253
29	0.000744097886138097	0.00148819577227619	0.999255902113862
30	0.00056176249314812	0.00112352498629624	0.999438237506852
31	0.000490870296163281	0.000981740592326562	0.999509129703837
32	0.000458033243048578	0.000916066486097155	0.999541966756951
33	0.000728295960536249	0.00145659192107250	0.999271704039464
34	0.00213007175501904	0.00426014351003807	0.997869928244981
35	0.0080915119329674	0.0161830238659348	0.991908488067033
36	0.0193546352840969	0.0387092705681939	0.980645364715903
37	0.0254179587166885	0.050835917433377	0.974582041283311
38	0.0215593834441851	0.0431187668883702	0.978440616555815
39	0.0163063111133154	0.0326126222266309	0.983693688886685
40	0.0128149629414075	0.0256299258828149	0.987185037058593
41	0.00931049882878952	0.0186209976575790	0.99068950117121
42	0.00724440508662023	0.0144888101732405	0.99275559491338
43	0.00504395212690356	0.0100879042538071	0.994956047873096
44	0.00382146093809115	0.0076429218761823	0.996178539061909
45	0.00255168264914144	0.00510336529828288	0.997448317350859
46	0.00257074674963801	0.00514149349927602	0.997429253250362
47	0.00316267384614634	0.00632534769229268	0.996837326153854
48	0.00346795172242251	0.00693590344484502	0.996532048277577
49	0.00269193578668493	0.00538387157336987	0.997308064213315
50	0.00188301104539643	0.00376602209079286	0.998116988954604
51	0.00131407072628343	0.00262814145256686	0.998685929273717
52	0.00096977830044946	0.00193955660089892	0.99903022169955
53	0.000709802682417361	0.00141960536483472	0.999290197317583
54	0.000528559550765495	0.00105711910153099	0.999471440449235
55	0.000686744832180596	0.00137348966436119	0.99931325516782
56	0.000907735149980512	0.00181547029996102	0.99909226485002
57	0.000693967880448228	0.00138793576089646	0.999306032119552
58	0.000711989888766513	0.00142397977753303	0.999288010111233
59	0.00105832882479435	0.00211665764958871	0.998941671175206
60	0.00173659944783391	0.00347319889566783	0.998263400552166
61	0.00194613694866253	0.00389227389732507	0.998053863051337
62	0.00216076580130378	0.00432153160260756	0.997839234198696
63	0.00296313347405968	0.00592626694811936	0.99703686652594
64	0.00363516431043497	0.00727032862086995	0.996364835689565
65	0.00446100596401694	0.00892201192803388	0.995538994035983
66	0.00768524228379942	0.0153704845675988	0.9923147577162
67	0.0180678492370577	0.0361356984741153	0.981932150762942
68	0.0452462860416908	0.0904925720833817	0.95475371395831
69	0.0440166705002314	0.0880333410004628	0.95598332949977
70	0.0410471141885868	0.0820942283771736	0.958952885811413
71	0.0450077482602525	0.090015496520505	0.954992251739748
72	0.0626858651192243	0.125371730238449	0.937314134880776
73	0.103297491659598	0.206594983319196	0.896702508340402
74	0.137131335501145	0.274262671002291	0.862868664498855
75	0.166869168859396	0.333738337718791	0.833130831140604
76	0.208288643845081	0.416577287690162	0.791711356154919
77	0.254760737679703	0.509521475359406	0.745239262320297
78	0.333715936160316	0.667431872320632	0.666284063839684
79	0.43709339400859	0.87418678801718	0.56290660599141
80	0.559219621028206	0.881560757943588	0.440780378971794
81	0.574480898342695	0.85103820331461	0.425519101657305
82	0.571727091049807	0.856545817900386	0.428272908950193
83	0.600257592520796	0.799484814958408	0.399742407479204
84	0.662552305307299	0.674895389385401	0.337447694692701
85	0.727686809017243	0.544626381965513	0.272313190982757
86	0.761174541848349	0.477650916303303	0.238825458151651
87	0.809134765946524	0.381730468106952	0.190865234053476
88	0.839399145122065	0.321201709755869	0.160600854877935
89	0.884909685127977	0.230180629744045	0.115090314872023
90	0.927025039007677	0.145949921984647	0.0729749609923235
91	0.97326088452481	0.0534782309503781	0.0267391154751891
92	0.99313442288934	0.0137311542213196	0.00686557711065982
93	0.994017441773178	0.0119651164536445	0.00598255822682224
94	0.992082178233182	0.0158356435336367	0.00791782176681836
95	0.989887085720284	0.0202258285594321	0.0101129142797160
96	0.990873516691963	0.0182529666160747	0.00912648330803737
97	0.990263732463165	0.0194725350736705	0.00973626753683527
98	0.987741829653991	0.0245163406920175	0.0122581703460088
99	0.984185474545531	0.0316290509089378	0.0158145254544689
100	0.980228869220837	0.0395422615583266	0.0197711307791633
101	0.9739159780409	0.0521680439182015	0.0260840219591007
102	0.96651440027446	0.0669711994510808	0.0334855997255404
103	0.971158440285357	0.0576831194292863	0.0288415597146431
104	0.977964551257724	0.0440708974845513	0.0220354487422756
105	0.978411089063322	0.0431778218733567	0.0215889109366784
106	0.970170741107757	0.0596585177844858	0.0298292588922429
107	0.959329563871027	0.081340872257946	0.040670436128973
108	0.960453760111941	0.0790924797761177	0.0395462398880588
109	0.94569020692599	0.108619586148021	0.0543097930740106
110	0.929729770055731	0.140540459888538	0.0702702299442692
111	0.90733188680261	0.185336226394782	0.0926681131973912
112	0.891605021959847	0.216789956080307	0.108394978040153
113	0.882814517354155	0.234370965291691	0.117185482645846
114	0.867747988314436	0.264504023371129	0.132252011685564
115	0.904788970362977	0.190422059274047	0.0952110296370235
116	0.977831778543842	0.0443364429123151	0.0221682214561576
117	0.997505504980812	0.00498899003837655	0.00249449501918827
118	0.999318668387878	0.00136266322424481	0.000681331612122404
119	0.99915888537596	0.00168222924807792	0.000841114624038959
120	0.998918887103034	0.00216222579393107	0.00108111289696553
121	0.998467409148758	0.00306518170248386	0.00153259085124193
122	0.99776680672829	0.00446638654342146	0.00223319327171073
123	0.996600495380002	0.00679900923999676	0.00339950461999838
124	0.99589140097716	0.00821719804568105	0.00410859902284052
125	0.99674433799793	0.00651132400414082	0.00325566200207041
126	0.999698325167557	0.000603349664885533	0.000301674832442766
127	0.999550672215271	0.000898655569458054	0.000449327784729027
128	0.99974476010149	0.000510479797020546	0.000255239898510273
129	0.999462076526754	0.00107584694649269	0.000537923473246347
130	0.999548899085512	0.000902201828976162	0.000451100914488081
131	0.998782114505666	0.00243577098866762	0.00121788549433381
132	0.998435925642865	0.00312814871427018	0.00156407435713509
133	0.995467645730074	0.00906470853985257	0.00453235426992628
134	0.991708873221513	0.0165822535569744	0.0082911267784872
135	0.977676855158092	0.0446462896838167	0.0223231448419083
136	0.991873854753413	0.0162522904931734	0.00812614524658668
137	0.998142923253459	0.00371415349308229	0.00185707674654114

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	68	0.515151515151515	NOK
5% type I error level	94	0.712121212121212	NOK
10% type I error level	106	0.803030303030303	NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293382867v81xe0q2k2oxs5c/10ltl31293382893.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293382867v81xe0q2k2oxs5c/10ltl31293382893.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293382867v81xe0q2k2oxs5c/1wao91293382893.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293382867v81xe0q2k2oxs5c/1wao91293382893.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293382867v81xe0q2k2oxs5c/2wao91293382893.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293382867v81xe0q2k2oxs5c/2wao91293382893.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293382867v81xe0q2k2oxs5c/3p1nu1293382893.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293382867v81xe0q2k2oxs5c/3p1nu1293382893.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293382867v81xe0q2k2oxs5c/4p1nu1293382893.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293382867v81xe0q2k2oxs5c/4p1nu1293382893.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293382867v81xe0q2k2oxs5c/5p1nu1293382893.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293382867v81xe0q2k2oxs5c/5p1nu1293382893.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293382867v81xe0q2k2oxs5c/60bmf1293382893.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293382867v81xe0q2k2oxs5c/60bmf1293382893.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293382867v81xe0q2k2oxs5c/7sklh1293382893.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293382867v81xe0q2k2oxs5c/7sklh1293382893.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293382867v81xe0q2k2oxs5c/8sklh1293382893.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293382867v81xe0q2k2oxs5c/8sklh1293382893.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293382867v81xe0q2k2oxs5c/9sklh1293382893.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293382867v81xe0q2k2oxs5c/9sklh1293382893.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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