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Multiple Regression

*Unverified author*

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

Title produced by software: Multiple Regression

Date of computation: Sat, 20 Dec 2008 09:33:49 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/20/t12297912306qz6c913bxzscy8.htm/, Retrieved Sat, 20 Dec 2008 17:40:40 +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/2008/Dec/20/t12297912306qz6c913bxzscy8.htm/},
    year = {2008},
}
@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 = {2008},
    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 0 604 0 584 0 574 0 555 0 545 0 599 0 620 0 608 0 590 0 579 0 580 0 579 0 572 0 560 0 551 0 537 0 541 0 588 0 607 0 599 0 578 0 563 0 566 0 561 0 554 0 540 0 526 0 512 0 505 0 554 0 584 0 569 0 540 0 522 0 526 0 527 0 516 0 503 0 489 0 479 0 475 0 524 0 552 0 532 0 511 0 492 0 492 0 493 0 481 0 462 0 457 0 442 0 439 0 488 0 521 0 501 0 485 0 464 0 460 0 467 0 460 0 448 0 443 0 436 0 431 0 484 0 510 0 513 0 503 0 471 0 471 0 476 0 475 0 470 0 461 0 455 0 456 0 517 0 525 0 523 0 519 1 509 1 512 1 519 1 517 1 510 1 509 1 501 1 507 1 569 1 580 1 578 1 565 1 547 1 555 1 562 1 561 1 555 1 544 1 537 1 543 1 594 1 611 1 613 1 611 1 594 1 595 1 591 1 589 1 584 1 573 1 567 1 569 1 621 1 629 1 628 1 612 1 595 1 597 1 593 1 590 1 580 1 574 1 573 1 573 1 620 1 626 1 620 1 588 1 566 1 557 1 561 1 549 1 532 1 526 1 511 1 499 1 555 1 565 1 542 1 527 1 510 1 514 1 517 1 508 1 493 1 490 1 469 1 478 1 528 1 534 1 518 1 506 1 502 1

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	5 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation

X[t] = + 566.656504065041 + 129.841027874565Y[t] + 7.02847855058232M1[t] + 1.26130356770599M2[t] -9.4289483382472M3[t] -16.1961233211234M4[t] -25.9632983039996M5[t] -25.7304732868758M6[t] + 27.8100440379404M7[t] + 46.1967152089103M8[t] + 38.1987709952649M9[t] + 13.3669015604991M10[t] -2.40027342237711M11[t] -1.2328250171238t + 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)	566.656504065041	10.49703	53.9826	0	0
Y	129.841027874565	10.20842	12.719	0	0
M1	7.02847855058232	12.68771	0.554	0.580484	0.290242
M2	1.26130356770599	12.686154	0.0994	0.920943	0.460472
M3	-9.4289483382472	12.685623	-0.7433	0.45855	0.229275
M4	-16.1961233211234	12.686117	-1.2767	0.203814	0.101907
M5	-25.9632983039996	12.687636	-2.0463	0.04258	0.02129
M6	-25.7304732868758	12.69018	-2.0276	0.044486	0.022243
M7	27.8100440379404	12.693747	2.1908	0.030106	0.015053
M8	46.1967152089103	12.698337	3.638	0.000385	0.000192
M9	38.1987709952649	12.703949	3.0068	0.003126	0.001563
M10	13.3669015604991	12.686154	1.0537	0.293841	0.14692
M11	-2.40027342237711	12.68771	-0.1892	0.850223	0.425112
t	-1.2328250171238	0.114028	-10.8116	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.788247462298977
R-squared	0.621334061820778
Adjusted R-squared	0.58642159943546
F-TEST (value)	17.7969131756821
F-TEST (DF numerator)	13
F-TEST (DF denominator)	141
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	31.6848820233807
Sum Squared Residuals	141554.376585813

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	621	572.452157598497	48.5478424015029
2	604	565.452157598499	38.5478424015009
3	584	553.529080675422	30.4709193245779
4	574	545.529080675422	28.4709193245776
5	555	534.529080675422	20.4709193245778
6	545	533.529080675422	11.4709193245778
7	599	585.836772983114	13.1632270168857
8	620	602.99061913696	17.0093808630394
9	608	593.759849906191	14.2401500938085
10	590	567.695155454302	22.3048445456982
11	579	550.695155454302	28.3048445456981
12	580	551.862603859555	28.1373961404449
13	579	557.658257393014	21.3417426069863
14	572	550.658257393014	21.3417426069864
15	560	538.735180469937	21.2648195300634
16	551	530.735180469937	20.2648195300634
17	537	519.735180469937	17.2648195300634
18	541	518.735180469937	22.2648195300634
19	588	571.042872777629	16.9571272223711
20	607	588.196718931475	18.8032810685249
21	599	578.965949700706	20.0340502992942
22	578	552.901255248816	25.0987447511837
23	563	535.901255248816	27.0987447511837
24	566	537.068703654070	28.9312963459304
25	561	542.864357187528	18.1356428124719
26	554	535.864357187528	18.1356428124721
27	540	523.941280264451	16.058719735549
28	526	515.941280264451	10.058719735549
29	512	504.941280264451	7.05871973554897
30	505	503.941280264451	1.05871973554898
31	554	556.248972572143	-2.24897257214335
32	584	573.402818725990	10.5971812740105
33	569	564.17204949522	4.82795050477976
34	540	538.107355043331	1.89264495666931
35	522	521.107355043331	0.892644956669311
36	526	522.274803448584	3.72519655141602
37	527	528.070456982043	-1.07045698204253
38	516	521.070456982042	-5.07045698204234
39	503	509.147380058965	-6.14738005896543
40	489	501.147380058965	-12.1473800589654
41	479	490.147380058965	-11.1473800589654
42	475	489.147380058965	-14.1473800589654
43	524	541.455072366658	-17.4550723666577
44	552	558.608918520504	-6.60891852050391
45	532	549.378149289735	-17.3781492897347
46	511	523.313454837845	-12.3134548378451
47	492	506.313454837845	-14.3134548378451
48	492	507.480903243098	-15.4809032430984
49	493	513.276556776557	-20.2765567765569
50	481	506.276556776557	-25.2765567765567
51	462	494.35347985348	-32.3534798534798
52	457	486.35347985348	-29.3534798534798
53	442	475.35347985348	-33.3534798534799
54	439	474.35347985348	-35.3534798534799
55	488	526.661172161172	-38.6611721611722
56	521	543.815018315018	-22.8150183150183
57	501	534.584249084249	-33.5842490842491
58	485	508.51955463236	-23.5195546323595
59	464	491.519554632360	-27.5195546323595
60	460	492.687003037613	-32.6870030376128
61	467	498.482656571071	-31.4826565710714
62	460	491.482656571071	-31.4826565710711
63	448	479.559579647994	-31.5595796479943
64	443	471.559579647994	-28.5595796479942
65	436	460.559579647994	-24.5595796479943
66	431	459.559579647994	-28.5595796479943
67	484	511.867271955687	-27.8672719556866
68	510	529.021118109533	-19.0211181095327
69	513	519.790348878764	-6.7903488787635
70	503	493.725654426874	9.27434557312606
71	471	476.725654426874	-5.72565442687393
72	471	477.893102832127	-6.89310283212723
73	476	483.688756365586	-7.68875636558575
74	475	476.688756365586	-1.68875636558556
75	470	464.765679442509	5.23432055749134
76	461	456.765679442509	4.23432055749133
77	455	445.765679442509	9.23432055749131
78	456	444.765679442509	11.2343205574913
79	517	497.073371750201	19.926628249799
80	525	514.227217904047	10.7727820959528
81	523	504.996448673278	18.0035513267221
82	519	608.772782095953	-89.7727820959529
83	509	591.772782095953	-82.7727820959529
84	512	592.940230501206	-80.9402305012062
85	519	598.735884034665	-79.7358840346647
86	517	591.735884034665	-74.7358840346645
87	510	579.812807111588	-69.8128071115876
88	509	571.812807111588	-62.8128071115876
89	501	560.812807111588	-59.8128071115876
90	507	559.812807111588	-52.8128071115876
91	569	612.12049941928	-43.1204994192800
92	580	629.274345573126	-49.2743455731261
93	578	620.043576342357	-42.0435763423569
94	565	593.978881890467	-28.9788818904673
95	547	576.978881890467	-29.9788818904673
96	555	578.146330295721	-23.1463302957206
97	562	583.941983829179	-21.9419838291791
98	561	576.941983829179	-15.9419838291789
99	555	565.018906906102	-10.0189069061020
100	544	557.018906906102	-13.018906906102
101	537	546.018906906102	-9.01890690610207
102	543	545.018906906102	-2.01890690610205
103	594	597.326599213794	-3.32659921379437
104	611	614.480445367641	-3.48044536764051
105	613	605.249676136871	7.75032386312873
106	611	579.184981684982	31.8150183150183
107	594	562.184981684982	31.8150183150183
108	595	563.352430090235	31.647569909765
109	591	569.148083623694	21.8519163763065
110	589	562.148083623693	26.8519163763067
111	584	550.225006700616	33.7749932993836
112	573	542.225006700616	30.7749932993836
113	567	531.225006700616	35.7749932993835
114	569	530.225006700616	38.7749932993835
115	621	582.532699008309	38.4673009916912
116	629	599.686545162155	29.3134548378451
117	628	590.455775931386	37.5442240686143
118	612	564.391081479496	47.6089185205039
119	595	547.391081479496	47.6089185205039
120	597	548.558529884749	48.4414701152506
121	593	554.354183418208	38.6458165817920
122	590	547.354183418208	42.6458165817922
123	580	535.431106495131	44.5688935048691
124	574	527.431106495131	46.5688935048692
125	573	516.431106495131	56.5688935048691
126	573	515.431106495131	57.5688935048691
127	620	567.738798802823	52.2612011971768
128	626	584.892644956669	41.1073550433306
129	620	575.6618757259	44.3381242740999
130	588	549.597181274010	38.4028187259895
131	566	532.59718127401	33.4028187259895
132	557	533.764629679264	23.2353703207362
133	561	539.560283212722	21.4397167872776
134	549	532.560283212722	16.4397167872778
135	532	520.637206289645	11.3627937103547
136	526	512.637206289645	13.3627937103547
137	511	501.637206289645	9.36279371035469
138	499	500.637206289645	-1.63720628964529
139	555	552.944898597338	2.05510140266239
140	565	570.098744751184	-5.09874475118376
141	542	560.867975520414	-18.8679755204145
142	527	534.803281068525	-7.80328106852495
143	510	517.803281068525	-7.80328106852495
144	514	518.970729473778	-4.97072947377825
145	517	524.766383007237	-7.7663830072368
146	508	517.766383007237	-9.7663830072366
147	493	505.84330608416	-12.8433060841597
148	490	497.84330608416	-7.84330608415967
149	469	486.84330608416	-17.8433060841597
150	478	485.84330608416	-7.84330608415972
151	528	538.150998391852	-10.1509983918520
152	534	555.304844545698	-21.3048445456982
153	518	546.074075314929	-28.0740753149289
154	506	520.009380863039	-14.0093808630394
155	502	503.009380863039	-1.00938086303938

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
17	0.0190809807343247	0.0381619614686493	0.980919019265675
18	0.0192904225802337	0.0385808451604675	0.980709577419766
19	0.00771895510078658	0.0154379102015732	0.992281044899213
20	0.0026251980974191	0.0052503961948382	0.99737480190258
21	0.00104006377306810	0.00208012754613619	0.998959936226932
22	0.000340051266697294	0.000680102533394588	0.999659948733303
23	9.63957957329703e-05	0.000192791591465941	0.999903604204267
24	2.8060660014031e-05	5.6121320028062e-05	0.999971939339986
25	1.29939485075426e-05	2.59878970150851e-05	0.999987006051492
26	3.77898644219506e-06	7.55797288439012e-06	0.999996221013558
27	9.96877818441493e-07	1.99375563688299e-06	0.999999003122181
28	2.98741653610171e-07	5.97483307220342e-07	0.999999701258346
29	7.52903704183283e-08	1.50580740836657e-07	0.99999992470963
30	2.22893707441682e-08	4.45787414883363e-08	0.99999997771063
31	7.01204539059853e-09	1.40240907811971e-08	0.999999992987955
32	1.84012333404186e-09	3.68024666808372e-09	0.999999998159877
33	4.38748045967440e-10	8.77496091934879e-10	0.999999999561252
34	2.39430569120931e-10	4.78861138241862e-10	0.99999999976057
35	2.62438096591543e-10	5.24876193183087e-10	0.999999999737562
36	1.65120758746045e-10	3.30241517492089e-10	0.99999999983488
37	1.15028668960566e-10	2.30057337921132e-10	0.999999999884971
38	6.92608710272117e-11	1.38521742054423e-10	0.99999999993074
39	2.72730124089226e-11	5.45460248178451e-11	0.999999999972727
40	1.33184414288370e-11	2.66368828576741e-11	0.999999999986682
41	3.68749115874959e-12	7.37498231749918e-12	0.999999999996313
42	9.6145563472652e-13	1.92291126945304e-12	0.999999999999039
43	2.52856888986096e-13	5.05713777972191e-13	0.999999999999747
44	6.2986784252851e-14	1.25973568505702e-13	0.999999999999937
45	2.15223759446316e-14	4.30447518892632e-14	0.999999999999978
46	6.17958481469962e-15	1.23591696293992e-14	0.999999999999994
47	2.67386613406426e-15	5.34773226812851e-15	0.999999999999997
48	1.54059722871203e-15	3.08119445742406e-15	0.999999999999998
49	8.34188603489296e-16	1.66837720697859e-15	1
50	4.83386985633041e-16	9.66773971266082e-16	1
51	4.92147745928162e-16	9.84295491856324e-16	1
52	1.62576381493857e-16	3.25152762987713e-16	1
53	5.57604260152468e-17	1.11520852030494e-16	1
54	1.6701113144847e-17	3.3402226289694e-17	1
55	5.32907309271629e-18	1.06581461854326e-17	1
56	1.2296917972602e-18	2.4593835945204e-18	1
57	3.11765117438682e-19	6.23530234877363e-19	1
58	7.02807457174604e-20	1.40561491434921e-19	1
59	1.61279931557583e-20	3.22559863115165e-20	1
60	6.3303200161202e-21	1.26606400322404e-20	1
61	1.43117471224090e-21	2.86234942448181e-21	1
62	3.23090451751574e-22	6.46180903503147e-22	1
63	8.98441728791089e-23	1.79688345758218e-22	1
64	4.56565189256116e-23	9.13130378512231e-23	1
65	9.02332165597748e-23	1.80466433119550e-22	1
66	1.16774619689209e-22	2.33549239378419e-22	1
67	2.62806317911439e-22	5.25612635822877e-22	1
68	3.65205754717838e-22	7.30411509435675e-22	1
69	3.97293901126147e-20	7.94587802252293e-20	1
70	1.98648253666234e-17	3.97296507332468e-17	1
71	5.97898015257913e-17	1.19579603051583e-16	1
72	1.21351215411415e-16	2.42702430822831e-16	1
73	2.46733182148956e-16	4.93466364297912e-16	1
74	1.43000668144550e-15	2.86001336289099e-15	0.999999999999999
75	2.36698484184752e-14	4.73396968369505e-14	0.999999999999976
76	1.93750610564518e-13	3.87501221129035e-13	0.999999999999806
77	2.28534108264910e-12	4.57068216529821e-12	0.999999999997715
78	2.60529518264041e-11	5.21059036528081e-11	0.999999999973947
79	5.1433630772657e-10	1.02867261545314e-09	0.999999999485664
80	9.49420386755708e-10	1.89884077351142e-09	0.99999999905058
81	3.05136168191135e-09	6.1027233638227e-09	0.999999996948638
82	4.22428784123323e-09	8.44857568246646e-09	0.999999995775712
83	5.98148402479127e-09	1.19629680495825e-08	0.999999994018516
84	1.12733248728723e-08	2.25466497457446e-08	0.999999988726675
85	2.07443651001808e-08	4.14887302003616e-08	0.999999979255635
86	4.34866948933640e-08	8.69733897867279e-08	0.999999956513305
87	1.05287377238076e-07	2.10574754476152e-07	0.999999894712623
88	2.80465421640188e-07	5.60930843280377e-07	0.999999719534578
89	8.6310207731261e-07	1.72620415462522e-06	0.999999136897923
90	3.25812578888216e-06	6.51625157776431e-06	0.99999674187421
91	1.21171861953919e-05	2.42343723907837e-05	0.999987882813805
92	2.85411206028041e-05	5.70822412056083e-05	0.999971458879397
93	7.18225860828422e-05	0.000143645172165684	0.999928177413917
94	0.000307444264807862	0.000614888529615724	0.999692555735192
95	0.00141277133934836	0.00282554267869673	0.998587228660652
96	0.00591651664880521	0.0118330332976104	0.994083483351195
97	0.0179630032932648	0.0359260065865296	0.982036996706735
98	0.0488287701476242	0.0976575402952483	0.951171229852376
99	0.113683976251279	0.227367952502557	0.886316023748721
100	0.246570240768988	0.493140481537976	0.753429759231012
101	0.452373949381086	0.904747898762172	0.547626050618914
102	0.682162314576994	0.635675370846013	0.317837685423006
103	0.875675607170485	0.24864878565903	0.124324392829515
104	0.957153702676804	0.0856925946463925	0.0428462973231962
105	0.984503002990652	0.0309939940186952	0.0154969970093476
106	0.9944330627154	0.0111338745691983	0.00556693728459916
107	0.998308633793043	0.00338273241391453	0.00169136620695726
108	0.999346524895114	0.00130695020977118	0.000653475104885589
109	0.999792752276716	0.000414495446567769	0.000207247723283884
110	0.999923437893083	0.000153124213834567	7.65621069172837e-05
111	0.999958255500245	8.34889995098125e-05	4.17444997549063e-05
112	0.999986104380729	2.77912385418954e-05	1.38956192709477e-05
113	0.999993935903118	1.21281937645322e-05	6.0640968822661e-06
114	0.999997187328604	5.62534279134788e-06	2.81267139567394e-06
115	0.99999879607517	2.40784966106446e-06	1.20392483053223e-06
116	0.999999524402484	9.5119503307383e-07	4.75597516536915e-07
117	0.999999448134738	1.10373052400566e-06	5.5186526200283e-07
118	0.999999324744982	1.35051003664539e-06	6.75255018322695e-07
119	0.999999363676638	1.27264672308890e-06	6.36323361544452e-07
120	0.99999874952542	2.50094916108164e-06	1.25047458054082e-06
121	0.999997857468564	4.28506287260259e-06	2.14253143630129e-06
122	0.999995315841436	9.36831712857371e-06	4.68415856428685e-06
123	0.999989210111172	2.15797776558450e-05	1.07898888279225e-05
124	0.99997538964261	4.92207147783472e-05	2.46103573891736e-05
125	0.999968473700979	6.30525980423011e-05	3.15262990211506e-05
126	0.99996758114439	6.48377112197536e-05	3.24188556098768e-05
127	0.999953123375887	9.37532482253167e-05	4.68766241126584e-05
128	0.999927234467232	0.000145531065536563	7.27655327682814e-05
129	0.999989619812412	2.07603751754419e-05	1.03801875877210e-05
130	0.9999915323763	1.69352474007217e-05	8.46762370036083e-06
131	0.99998057122035	3.88575593010375e-05	1.94287796505188e-05
132	0.99994948711054	0.000101025778918594	5.05128894592972e-05
133	0.999891935414767	0.000216129170465154	0.000108064585232577
134	0.99972909602262	0.000541807954761121	0.000270903977380561
135	0.999277074117008	0.00144585176598436	0.000722925882992179
136	0.997777858430463	0.00444428313907455	0.00222214156953728
137	0.99768868414771	0.00462263170458157	0.00231131585229079
138	0.986760708815708	0.0264785823685845	0.0132392911842923

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	107	0.877049180327869	NOK
5% type I error level	115	0.942622950819672	NOK
10% type I error level	117	0.959016393442623	NOK

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/20/t12297912306qz6c913bxzscy8/10s6kg1229790821.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/20/t12297912306qz6c913bxzscy8/10s6kg1229790821.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/20/t12297912306qz6c913bxzscy8/1kabz1229790821.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/20/t12297912306qz6c913bxzscy8/1kabz1229790821.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/20/t12297912306qz6c913bxzscy8/2bta81229790821.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/20/t12297912306qz6c913bxzscy8/2bta81229790821.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/20/t12297912306qz6c913bxzscy8/3s9mz1229790821.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/20/t12297912306qz6c913bxzscy8/3s9mz1229790821.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/20/t12297912306qz6c913bxzscy8/4m6621229790821.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/20/t12297912306qz6c913bxzscy8/4m6621229790821.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/20/t12297912306qz6c913bxzscy8/5m3l11229790821.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/20/t12297912306qz6c913bxzscy8/5m3l11229790821.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/20/t12297912306qz6c913bxzscy8/6rxxb1229790821.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/20/t12297912306qz6c913bxzscy8/6rxxb1229790821.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/20/t12297912306qz6c913bxzscy8/7etqw1229790821.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/20/t12297912306qz6c913bxzscy8/7etqw1229790821.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/20/t12297912306qz6c913bxzscy8/87hu31229790821.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/20/t12297912306qz6c913bxzscy8/87hu31229790821.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/20/t12297912306qz6c913bxzscy8/96r8p1229790821.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/20/t12297912306qz6c913bxzscy8/96r8p1229790821.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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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