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Multiple Regression X1 & X2

*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: Tue, 28 Dec 2010 18:45:22 +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/28/t1293561889c6hlvu9560z7mrr.htm/, Retrieved Tue, 28 Dec 2010 19:45:01 +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/28/t1293561889c6hlvu9560z7mrr.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 «

621 0 0 587 0 0 655 0 0 517 0 0 646 0 0 657 0 0 382 0 0 345 0 0 625 0 0 654 0 0 606 0 0 510 0 0 614 0 0 647 0 0 580 0 0 614 0 0 636 0 0 388 0 0 356 0 0 639 0 0 753 0 0 611 0 0 639 0 0 630 0 0 586 0 0 695 0 0 552 0 0 619 0 0 681 0 0 421 0 0 307 0 0 754 0 0 690 0 0 644 0 0 643 0 0 608 0 0 651 0 0 691 0 0 627 0 0 634 0 0 731 0 0 475 0 0 337 0 0 803 0 0 722 0 0 590 0 0 724 0 0 627 0 0 696 0 0 825 0 0 677 0 0 656 0 0 785 0 0 412 0 0 352 0 0 839 0 0 729 0 0 696 0 0 641 0 0 695 0 0 638 0 0 762 0 0 635 0 0 721 0 0 854 0 0 418 0 0 367 0 0 824 0 0 687 0 0 601 0 0 676 0 0 740 0 0 691 0 0 683 0 0 594 0 0 729 0 0 731 0 0 386 0 0 331 0 0 706 0 0 715 0 0 657 0 0 653 0 0 642 0 0 643 0 0 718 0 0 654 0 0 632 0 0 731 0 0 392 0 0 344 0 0 792 0 0 852 0 0 649 0 0 629 0 0 685 0 0 617 0 0 715 0 0 715 0 0 629 0 0 916 0 0 531 1 0 357 1 0 917 1 0 828 1 0 708 1 0 858 1 0 775 1 0 785 1 0 1006 1 0 789 1 0 734 1 0 906 1 0 532 1 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	10 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Multiple Linear Regression - Estimated Regression Equation

Y[t] = + 628.524752475248 + 93.8323903818953X1[t] + 99.3095238095238X2[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)	628.524752475248	14.07734	44.648	0	0
X1	93.8323903818953	40.346465	2.3257	0.021622	0.010811
X2	99.3095238095238	52.573953	1.8889	0.061179	0.03059

Multiple Linear Regression - Regression Statistics
Multiple R	0.420632001624795
R-squared	0.176931280790882
Adjusted R-squared	0.163969568677353
F-TEST (value)	13.6503016917187
F-TEST (DF numerator)	2
F-TEST (DF denominator)	127
p-value	4.26768281913681e-06
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	141.475512912452
Sum Squared Residuals	2541945.73573786

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	621	628.524752475242	-7.52475247524237
2	587	628.524752475247	-41.5247524752473
3	655	628.524752475248	26.4752475247524
4	517	628.524752475248	-111.524752475248
5	646	628.524752475248	17.4752475247524
6	657	628.524752475248	28.4752475247524
7	382	628.524752475248	-246.524752475248
8	345	628.524752475248	-283.524752475248
9	625	628.524752475248	-3.52475247524757
10	654	628.524752475248	25.4752475247524
11	606	628.524752475248	-22.5247524752476
12	510	628.524752475248	-118.524752475248
13	614	628.524752475248	-14.5247524752476
14	647	628.524752475248	18.4752475247524
15	580	628.524752475248	-48.5247524752476
16	614	628.524752475248	-14.5247524752476
17	636	628.524752475248	7.47524752475243
18	388	628.524752475248	-240.524752475248
19	356	628.524752475248	-272.524752475248
20	639	628.524752475248	10.4752475247524
21	753	628.524752475248	124.475247524752
22	611	628.524752475248	-17.5247524752476
23	639	628.524752475248	10.4752475247524
24	630	628.524752475248	1.47524752475243
25	586	628.524752475248	-42.5247524752476
26	695	628.524752475248	66.4752475247524
27	552	628.524752475248	-76.5247524752476
28	619	628.524752475248	-9.52475247524757
29	681	628.524752475248	52.4752475247524
30	421	628.524752475248	-207.524752475248
31	307	628.524752475248	-321.524752475248
32	754	628.524752475248	125.475247524752
33	690	628.524752475248	61.4752475247524
34	644	628.524752475248	15.4752475247524
35	643	628.524752475248	14.4752475247524
36	608	628.524752475248	-20.5247524752476
37	651	628.524752475248	22.4752475247524
38	691	628.524752475248	62.4752475247524
39	627	628.524752475248	-1.52475247524757
40	634	628.524752475248	5.47524752475243
41	731	628.524752475248	102.475247524752
42	475	628.524752475248	-153.524752475248
43	337	628.524752475248	-291.524752475248
44	803	628.524752475248	174.475247524752
45	722	628.524752475248	93.4752475247524
46	590	628.524752475248	-38.5247524752476
47	724	628.524752475248	95.4752475247524
48	627	628.524752475248	-1.52475247524757
49	696	628.524752475248	67.4752475247524
50	825	628.524752475248	196.475247524752
51	677	628.524752475248	48.4752475247524
52	656	628.524752475248	27.4752475247524
53	785	628.524752475248	156.475247524752
54	412	628.524752475248	-216.524752475248
55	352	628.524752475248	-276.524752475248
56	839	628.524752475248	210.475247524752
57	729	628.524752475248	100.475247524752
58	696	628.524752475248	67.4752475247524
59	641	628.524752475248	12.4752475247524
60	695	628.524752475248	66.4752475247524
61	638	628.524752475248	9.47524752475243
62	762	628.524752475248	133.475247524752
63	635	628.524752475248	6.47524752475243
64	721	628.524752475248	92.4752475247524
65	854	628.524752475248	225.475247524752
66	418	628.524752475248	-210.524752475248
67	367	628.524752475248	-261.524752475248
68	824	628.524752475248	195.475247524752
69	687	628.524752475248	58.4752475247524
70	601	628.524752475248	-27.5247524752476
71	676	628.524752475248	47.4752475247524
72	740	628.524752475248	111.475247524752
73	691	628.524752475248	62.4752475247524
74	683	628.524752475248	54.4752475247524
75	594	628.524752475248	-34.5247524752476
76	729	628.524752475248	100.475247524752
77	731	628.524752475248	102.475247524752
78	386	628.524752475248	-242.524752475248
79	331	628.524752475248	-297.524752475248
80	706	628.524752475248	77.4752475247524
81	715	628.524752475248	86.4752475247524
82	657	628.524752475248	28.4752475247524
83	653	628.524752475248	24.4752475247524
84	642	628.524752475248	13.4752475247524
85	643	628.524752475248	14.4752475247524
86	718	628.524752475248	89.4752475247524
87	654	628.524752475248	25.4752475247524
88	632	628.524752475248	3.47524752475243
89	731	628.524752475248	102.475247524752
90	392	628.524752475248	-236.524752475248
91	344	628.524752475248	-284.524752475248
92	792	628.524752475248	163.475247524752
93	852	628.524752475248	223.475247524752
94	649	628.524752475248	20.4752475247524
95	629	628.524752475248	0.47524752475243
96	685	628.524752475248	56.4752475247524
97	617	628.524752475248	-11.5247524752476
98	715	628.524752475248	86.4752475247524
99	715	628.524752475248	86.4752475247524
100	629	628.524752475248	0.47524752475243
101	916	628.524752475248	287.475247524752
102	531	722.357142857143	-191.357142857143
103	357	722.357142857143	-365.357142857143
104	917	722.357142857143	194.642857142857
105	828	722.357142857143	105.642857142857
106	708	722.357142857143	-14.3571428571429
107	858	722.357142857143	135.642857142857
108	775	722.357142857143	52.6428571428571
109	785	722.357142857143	62.6428571428571
110	1006	722.357142857143	283.642857142857
111	789	722.357142857143	66.6428571428571
112	734	722.357142857143	11.6428571428571
113	906	722.357142857143	183.642857142857
114	532	722.357142857143	-190.357142857143
115	387	722.357142857143	-335.357142857143
116	991	821.666666666667	169.333333333333
117	841	821.666666666667	19.3333333333333
118	892	821.666666666667	70.3333333333333
119	782	821.666666666667	-39.6666666666667
120	813	821.666666666667	-8.66666666666666
121	793	821.666666666667	-28.6666666666667
122	978	821.666666666667	156.333333333333
123	775	821.666666666667	-46.6666666666667
124	797	821.666666666667	-24.6666666666667
125	946	821.666666666667	124.333333333333
126	594	821.666666666667	-227.666666666667
127	438	821.666666666667	-383.666666666667
128	1022	821.666666666667	200.333333333333
129	868	821.666666666667	46.3333333333333
130	795	821.666666666667	-26.6666666666667

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
6	0.128445242038449	0.256890484076897	0.871554757961551
7	0.433745738881041	0.867491477762081	0.566254261118959
8	0.63260442623209	0.73479114753582	0.36739557376791
9	0.533506434016585	0.932987131966829	0.466493565983415
10	0.45869676197915	0.9173935239583	0.54130323802085
11	0.355327419048959	0.710654838097919	0.644672580951041
12	0.280825171747814	0.561650343495628	0.719174828252186
13	0.208477013003656	0.416954026007311	0.791522986996344
14	0.162296334101193	0.324592668202387	0.837703665898807
15	0.110324064412485	0.220648128824970	0.889675935587515
16	0.0748426229387198	0.149685245877440	0.92515737706128
17	0.052122565517573	0.104245131035146	0.947877434482427
18	0.0957861538374302	0.191572307674860	0.90421384616257
19	0.179033838216698	0.358067676433396	0.820966161783302
20	0.145591906689222	0.291183813378443	0.854408093310778
21	0.187093661417943	0.374187322835886	0.812906338582057
22	0.14373789592405	0.2874757918481	0.85626210407595
23	0.112873114366506	0.225746228733013	0.887126885633494
24	0.0855396993218817	0.171079398643763	0.914460300678118
25	0.0611659175581432	0.122331835116286	0.938834082441857
26	0.0552568836560181	0.110513767312036	0.944743116343982
27	0.0399978416482404	0.0799956832964809	0.96000215835176
28	0.0280236452317653	0.0560472904635306	0.971976354768235
29	0.0231202667987072	0.0462405335974145	0.976879733201293
30	0.0324181559806722	0.0648363119613444	0.967581844019328
31	0.109023600700924	0.218047201401849	0.890976399299076
32	0.127973207772816	0.255946415545632	0.872026792227184
33	0.114514284247623	0.229028568495245	0.885485715752377
34	0.0916551894310482	0.183310378862096	0.908344810568952
35	0.0722268348184431	0.144453669636886	0.927773165181557
36	0.0542749300961385	0.108549860192277	0.945725069903862
37	0.0421562421095561	0.0843124842191122	0.957843757890444
38	0.0359520385734665	0.071904077146933	0.964047961426533
39	0.0263183341317739	0.0526366682635478	0.973681665868226
40	0.0191233155489172	0.0382466310978345	0.980876684451083
41	0.018868020632179	0.037736041264358	0.98113197936782
42	0.0191379688828721	0.0382759377657441	0.980862031117128
43	0.052690304099798	0.105380608199596	0.947309695900202
44	0.0737790831671842	0.147558166334368	0.926220916832816
45	0.0688422830508	0.1376845661016	0.9311577169492
46	0.0532282451577711	0.106456490315542	0.946771754842229
47	0.0493697315553027	0.0987394631106054	0.950630268444697
48	0.0374026892224644	0.0748053784449287	0.962597310777536
49	0.0312511919034090	0.0625023838068179	0.96874880809659
50	0.047142797439941	0.094285594879882	0.952857202560059
51	0.0375513698251226	0.0751027396502452	0.962448630174877
52	0.0286353131221008	0.0572706262442017	0.9713646868779
53	0.0329758105693446	0.0659516211386892	0.967024189430655
54	0.0484546448322974	0.0969092896645948	0.951545355167703
55	0.0992953935248132	0.198590787049626	0.900704606475187
56	0.136316482768868	0.272632965537736	0.863683517231132
57	0.124762884282088	0.249525768564176	0.875237115717912
58	0.106459869409371	0.212919738818741	0.89354013059063
59	0.085196535974282	0.170393071948564	0.914803464025718
60	0.0712009014206415	0.142401802841283	0.928799098579358
61	0.0555957504608759	0.111191500921752	0.944404249539124
62	0.0546445141662437	0.109289028332487	0.945355485833756
63	0.0419921719112153	0.0839843438224307	0.958007828088785
64	0.0359786021573772	0.0719572043147544	0.964021397842623
65	0.0547123897927708	0.109424779585542	0.94528761020723
66	0.0747883503704704	0.149576700740941	0.92521164962953
67	0.131076991559043	0.262153983118085	0.868923008440957
68	0.154455776489055	0.30891155297811	0.845544223510945
69	0.130186128271966	0.260372256543933	0.869813871728034
70	0.106578203111826	0.213156406223651	0.893421796888174
71	0.0869021309109954	0.173804261821991	0.913097869089005
72	0.0783280343117673	0.156656068623535	0.921671965688233
73	0.063883763732837	0.127767527465674	0.936116236267163
74	0.0510156826791751	0.102031365358350	0.948984317320825
75	0.0398311231221342	0.0796622462442685	0.960168876877866
76	0.0340577596646461	0.0681155193292922	0.965942240335354
77	0.0291654843526436	0.0583309687052871	0.970834515647356
78	0.050653436807857	0.101306873615714	0.949346563192143
79	0.121162216548365	0.242324433096729	0.878837783451635
80	0.101672132748360	0.203344265496720	0.89832786725164
81	0.0856596592670118	0.171319318534024	0.914340340732988
82	0.067468418322295	0.13493683664459	0.932531581677705
83	0.052313461627083	0.104626923254166	0.947686538372917
84	0.0399321010635484	0.0798642021270967	0.960067898936452
85	0.0300273624997596	0.0600547249995191	0.96997263750024
86	0.0239868781366593	0.0479737562733186	0.97601312186334
87	0.0175355337345934	0.0350710674691868	0.982464466265407
88	0.0126414564206427	0.0252829128412855	0.987358543579357
89	0.0100631508836236	0.0201263017672472	0.989936849116376
90	0.0206697163733947	0.0413394327467894	0.979330283626605
91	0.067487300934888	0.134974601869776	0.932512699065112
92	0.0621013164432492	0.124202632886498	0.937898683556751
93	0.0718218576996432	0.143643715399286	0.928178142300357
94	0.0557676165333717	0.111535233066743	0.944232383466628
95	0.0438562300451685	0.087712460090337	0.956143769954832
96	0.0330942405442547	0.0661884810885094	0.966905759455745
97	0.0269846275819114	0.0539692551638228	0.973015372418089
98	0.0202755868272539	0.0405511736545078	0.979724413172746
99	0.0151474694750862	0.0302949389501725	0.984852530524914
100	0.0161922733460518	0.0323845466921037	0.983807726653948
101	0.0174268668740188	0.0348537337480375	0.982573133125981
102	0.0183183605483528	0.0366367210967057	0.981681639451647
103	0.0721762044820118	0.144352408964024	0.927823795517988
104	0.112156665318327	0.224313330636653	0.887843334681673
105	0.100521487456934	0.201042974913869	0.899478512543066
106	0.0765759628711882	0.153151925742376	0.923424037128812
107	0.0698542506512763	0.139708501302553	0.930145749348724
108	0.0516786067934658	0.103357213586932	0.948321393206534
109	0.0379517603397906	0.0759035206795812	0.96204823966021
110	0.0960094186993362	0.192018837398672	0.903990581300664
111	0.0846208578266544	0.169241715653309	0.915379142173346
112	0.0687785145628532	0.137557029125706	0.931221485437147
113	0.236375210145297	0.472750420290594	0.763624789854703
114	0.219983501200701	0.439967002401403	0.780016498799299
115	0.201073052767731	0.402146105535462	0.798926947232269
116	0.210015822198575	0.42003164439715	0.789984177801425
117	0.156508047667036	0.313016095334071	0.843491952332964
118	0.119868952807705	0.239737905615410	0.880131047192295
119	0.0806547225430924	0.161309445086185	0.919345277456908
120	0.0498213721610169	0.0996427443220338	0.950178627838983
121	0.028434673828391	0.056869347656782	0.97156532617161
122	0.0294808187239754	0.0589616374479507	0.970519181276025
123	0.0144324008005118	0.0288648016010236	0.985567599199488
124	0.00599815760403521	0.0119963152080704	0.994001842395965

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	0	0	OK
5% type I error level	16	0.134453781512605	NOK
10% type I error level	44	0.369747899159664	NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293561889c6hlvu9560z7mrr/10o2521293561911.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293561889c6hlvu9560z7mrr/10o2521293561911.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293561889c6hlvu9560z7mrr/1z17q1293561911.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293561889c6hlvu9560z7mrr/1z17q1293561911.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293561889c6hlvu9560z7mrr/2z17q1293561911.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293561889c6hlvu9560z7mrr/2z17q1293561911.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293561889c6hlvu9560z7mrr/3abpt1293561911.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293561889c6hlvu9560z7mrr/3abpt1293561911.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293561889c6hlvu9560z7mrr/4abpt1293561911.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293561889c6hlvu9560z7mrr/4abpt1293561911.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293561889c6hlvu9560z7mrr/5abpt1293561911.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293561889c6hlvu9560z7mrr/5abpt1293561911.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293561889c6hlvu9560z7mrr/63koe1293561911.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293561889c6hlvu9560z7mrr/63koe1293561911.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293561889c6hlvu9560z7mrr/7dt5h1293561911.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293561889c6hlvu9560z7mrr/7dt5h1293561911.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293561889c6hlvu9560z7mrr/8dt5h1293561911.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293561889c6hlvu9560z7mrr/8dt5h1293561911.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293561889c6hlvu9560z7mrr/9dt5h1293561911.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293561889c6hlvu9560z7mrr/9dt5h1293561911.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No 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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