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Verbetering Workshop 7

*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: Fri, 27 Nov 2009 06:21:09 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Nov/27/t1259328140f3buq1891lum2xe.htm/, Retrieved Fri, 27 Nov 2009 14:22:32 +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/2009/Nov/27/t1259328140f3buq1891lum2xe.htm/},
    year = {2009},
}
@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 = {2009},
    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 «

384 257,9 367,6 275,8 457,1 319,4 429,4 299,8 442,2 331,1 507,5 339,3 348,5 209,6 393,2 280,9 426,8 285,5 403 247,6 454,8 275,1 413 262,3 388,9 267,8 406,5 448,2 447,4 563,4 474,4 346,6 428,5 455,1 472,8 424,4 411 381,2 463,9 382,9 497,3 466,6 474 400,2 518,1 493,6 566 367,5 509,4 307,1 445,1 316,7 466,6 314,2 600,5 403,7 538,7 370,6 548 343,7 591,9 383 547,3 365,4 610,2 417,2 621,6 411 582,4 420,8 635,8 493 663,9 471,8 624,2 452,4 654,1 464,8 723,5 541,5 641,2 484 565,5 449,4 698,6 436,8 651 490 721,6 475,4 643,5 393,6 604 486,8 618,2 536,7 783,5 467 672,9 475,5 726,7 532,8 738,6 554,1 692,2 507,3 669,5 455,2 546,2 465,3 715 563,2 789,8 680,1 684 518,2 639 426,6 768,5 612,4 643,8 518,1 623 540 692,8 541,7 936,5 627,6 795,9 637 695,7 564,2 648,3 665 675,2 703,2 826,5 824,4 742,4 700,3 793,9 1219,6 685,3 764,7 756,1 479,9 704 543,4 860,6 593,3 795,9 584,3 816,7 645,9 777,9 548,9 746,4 421,8 694,7 460,3 909,2 553,4 783,6 424,4 730 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	4 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation

yt[t] = + 196.193390381622 + 0.97222446927995xt[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)	196.193390381622	30.883563	6.3527	0	0
xt	0.97222446927995	0.054574	17.8148	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.853794014428263
R-squared	0.728964219073528
Adjusted R-squared	0.726667305675846
F-TEST (value)	317.366871475954
F-TEST (DF numerator)	1
F-TEST (DF denominator)	118
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	117.144117054869
Sum Squared Residuals	1619283.81094664

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	384	446.930081008918	-62.9300810089183
2	367.6	464.332899009031	-96.732899009031
3	457.1	506.721885869637	-49.6218858696371
4	429.4	487.66628627175	-58.2662862717502
5	442.2	518.096912160213	-75.8969121602126
6	507.5	526.069152808308	-18.5691528083082
7	348.5	399.971639142699	-51.4716391426987
8	393.2	469.291243802359	-76.0912438023591
9	426.8	473.763476361047	-46.9634763610469
10	403	436.916168975337	-33.9161689753368
11	454.8	463.652341880535	-8.85234188053544
12	413	451.207868673752	-38.2078686737521
13	388.9	456.555103254792	-67.6551032547918
14	406.5	631.944397512895	-225.444397512895
15	447.4	743.944656373945	-296.544656373945
16	474.4	533.166391434052	-58.7663914340519
17	428.5	638.652746350926	-210.152746350926
18	472.8	608.805455144032	-136.005455144032
19	411	566.805358071138	-155.805358071138
20	463.9	568.458139668914	-104.558139668914
21	497.3	649.833327747646	-152.533327747646
22	474	585.277622987457	-111.277622987457
23	518.1	676.083388418204	-157.983388418204
24	566	553.485882842003	12.5141171579973
25	509.4	494.763524897494	14.6364751025061
26	445.1	504.096879802581	-58.9968798025813
27	466.6	501.666318629381	-35.0663186293814
28	600.5	588.680408629937	11.8195913700631
29	538.7	556.49977869677	-17.7997786967706
30	548	530.34694047314	17.6530595268601
31	591.9	568.555362115842	23.3446378841580
32	547.3	551.444211456515	-4.14421145651486
33	610.2	601.805438965216	8.39456103478386
34	621.6	595.77764725568	25.8223527443195
35	582.4	605.305447054624	-22.9054470546241
36	635.8	675.500053736636	-39.7000537366364
37	663.9	654.888894987901	9.01110501209853
38	624.2	636.02774028387	-11.8277402838704
39	654.1	648.083323702942	6.01667629705822
40	723.5	722.652940496714	0.847059503286108
41	641.2	666.750033513117	-25.5500335131168
42	565.5	633.111066876031	-67.6110668760305
43	698.6	620.861038563103	77.7389614368968
44	651	672.583380328796	-21.5833803287965
45	721.6	658.38890307731	63.2110969226908
46	643.5	578.86094149021	64.6390585097906
47	604	669.4722620271	-65.4722620271007
48	618.2	717.98626304417	-99.7862630441701
49	783.5	650.222217535358	133.277782464642
50	672.9	658.486125524237	14.4138744757627
51	726.7	714.194587613978	12.5054123860218
52	738.6	734.902968809641	3.69703119035875
53	692.2	689.40286364734	2.79713635266041
54	669.5	638.749968797854	30.7500312021457
55	546.2	648.569435937582	-102.369435937582
56	715	743.750211480089	-28.7502114800888
57	789.8	857.403251938915	-67.6032519389149
58	684	700.000110362491	-16.0001103624911
59	639	610.944348976448	28.0556510235522
60	768.5	791.583655368662	-23.0836553686623
61	643.8	699.902887915563	-56.1028879155631
62	623	721.194603792794	-98.194603792794
63	692.8	722.84738539057	-30.0473853905700
64	936.5	806.361467301718	130.138532698282
65	795.9	815.500377312949	-19.6003773129491
66	695.7	744.722435949369	-49.0224359493687
67	648.3	842.722662452788	-194.422662452788
68	675.2	879.861637179282	-204.661637179282
69	826.5	997.695242856011	-171.195242856011
70	742.4	877.04218621837	-134.642186218370
71	793.9	1381.91835311545	-588.018353115447
72	685.3	939.653442039999	-254.353442039999
73	756.1	662.763913189069	93.336086810931
74	704	724.500166988346	-20.5001669883458
75	860.6	773.014168005415	87.5858319945848
76	795.9	764.264147781896	31.6358522181043
77	816.7	824.15317508954	-7.4531750895405
78	777.9	729.847401569386	48.0525984306145
79	746.4	606.277671523904	140.122328476096
80	694.7	643.708313591182	50.991686408818
81	909.2	734.222411681145	174.977588318855
82	783.6	608.805455144032	174.794544855968
83	730.4	653.333335837053	77.0666641629465
84	847.7	728.19461997161	119.505380028390
85	758.7	628.638834317343	130.061165682657
86	839.2	708.26401835137	130.935981648629
87	784.8	777.875290351815	6.92470964818499
88	906.1	724.597389435274	181.502610564726
89	838.2	819.583720083925	18.6162799160752
90	729	706.611236753595	22.3887632464053
91	768.1	703.208451111115	64.8915488888851
92	710.5	732.666852530297	-22.1668525302973
93	863	724.79183432913	138.208165670870
94	778.3	655.180562328685	123.119437671315
95	827.7	670.638931390237	157.061068609763
96	853.1	821.139279234773	31.9607207652273
97	859.3	781.180853547367	78.1191464526331
98	779.2	734.708523915785	44.4914760842148
99	724.6	704.180675580395	20.4193244196052
100	829.2	748.805778720345	80.3942212796555
101	862.9	852.833796933299	10.0662030667009
102	601.6	681.430622999244	-79.830622999244
103	964.9	730.333513804025	234.566486195975
104	766.3	712.63902846313	53.6609715368695
105	847.8	763.291923312616	84.5080766873842
106	992.7	708.069573457515	284.630426542485
107	865.3	695.138988016091	170.161011983909
108	1054.1	905.042250933632	149.057749066368
109	972.5	928.958972877919	43.5410271220809
110	857.4	752.014119468968	105.385880531032
111	1043.3	858.181031514339	185.118968485661
112	1061	932.750648308111	128.249351691889
113	989.4	979.222977939692	10.1770220603075
114	963.2	864.792157905443	98.4078420945576
115	1181.9	1120.58441577300	61.315584227003
116	1256.4	1228.69577675693	27.7042232430727
117	1492.7	1275.94588596393	216.754114036067
118	1360.8	1264.57085967336	96.2291403266424
119	1342.8	1233.55689910333	109.243100896673
120	1464	1518.51589104928	-54.5158910492802

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
5	0.0069008378850938	0.0138016757701876	0.993099162114906
6	0.00332074252517141	0.00664148505034282	0.996679257474829
7	0.00128648483488638	0.00257296966977276	0.998713515165114
8	0.000292038866978543	0.000584077733957085	0.999707961133022
9	6.30250238829106e-05	0.000126050047765821	0.999936974976117
10	2.29752418172646e-05	4.59504836345291e-05	0.999977024758183
11	2.22934397131453e-05	4.45868794262906e-05	0.999977706560287
12	5.32167234897169e-06	1.06433446979434e-05	0.999994678327651
13	1.29627255788566e-06	2.59254511577132e-06	0.999998703727442
14	5.28566396782272e-05	0.000105713279356454	0.999947143360322
15	3.29380999791753e-05	6.58761999583505e-05	0.99996706190002
16	2.11362448747642e-05	4.22724897495284e-05	0.999978863755125
17	9.694879920924e-06	1.9389759841848e-05	0.99999030512008
18	4.57679316648509e-06	9.15358633297017e-06	0.999995423206834
19	2.09473314408442e-06	4.18946628816885e-06	0.999997905266856
20	9.51763227453465e-07	1.90352645490693e-06	0.999999048236773
21	6.26005774531525e-07	1.25201154906305e-06	0.999999373994225
22	3.015893181375e-07	6.03178636275e-07	0.999999698410682
23	2.39369811241985e-07	4.78739622483969e-07	0.999999760630189
24	4.37997448119579e-06	8.75994896239159e-06	0.999995620025519
25	6.14952583534122e-06	1.22990516706824e-05	0.999993850474165
26	2.76217839002568e-06	5.52435678005137e-06	0.99999723782161
27	1.41947041766316e-06	2.83894083532633e-06	0.999998580529582
28	1.4162209032819e-05	2.8324418065638e-05	0.999985837790967
29	1.61330242499726e-05	3.22660484999452e-05	0.99998386697575
30	2.39175356140545e-05	4.7835071228109e-05	0.999976082464386
31	6.14066360631152e-05	0.000122813272126230	0.999938593363937
32	6.01181968719802e-05	0.000120236393743960	0.999939881803128
33	0.000117586561034347	0.000235173122068694	0.999882413438966
34	0.000233459057525668	0.000466918115051336	0.999766540942474
35	0.000213479083364675	0.000426958166729349	0.999786520916635
36	0.00023027068568042	0.00046054137136084	0.99976972931432
37	0.000348571458122545	0.00069714291624509	0.999651428541877
38	0.000324824982034744	0.000649649964069488	0.999675175017965
39	0.000354855140560897	0.000709710281121794	0.99964514485944
40	0.000421558119079243	0.000843116238158486	0.99957844188092
41	0.000317392426927100	0.000634784853854201	0.999682607573073
42	0.000216402568524278	0.000432805137048555	0.999783597431476
43	0.000413399148274553	0.000826798296549106	0.999586600851725
44	0.000300923349061675	0.000601846698123351	0.999699076650938
45	0.000423276310001115	0.000846552620002231	0.99957672369
46	0.000478075484047462	0.000956150968094925	0.999521924515953
47	0.000336483672100497	0.000672967344200994	0.9996635163279
48	0.000266949515076312	0.000533899030152623	0.999733050484924
49	0.000852969186321463	0.00170593837264293	0.999147030813679
50	0.000654918453248795	0.00130983690649759	0.999345081546751
51	0.000495347790598667	0.000990695581197333	0.999504652209401
52	0.000351863926967962	0.000703727853935925	0.999648136073032
53	0.000244155113951282	0.000488310227902565	0.999755844886049
54	0.000186950198538119	0.000373900397076237	0.999813049801462
55	0.000190087549652508	0.000380175099305015	0.999809912450347
56	0.000124844950835703	0.000249689901671406	0.999875155049164
57	8.38847381307245e-05	0.000167769476261449	0.99991611526187
58	5.56139618157054e-05	0.000111227923631411	0.999944386038184
59	4.19491024582443e-05	8.38982049164886e-05	0.999958050897542
60	2.62535315791874e-05	5.25070631583747e-05	0.999973746468421
61	1.92158431404067e-05	3.84316862808134e-05	0.99998078415686
62	1.95525080778254e-05	3.91050161556507e-05	0.999980447491922
63	1.31632964088945e-05	2.63265928177891e-05	0.999986836703591
64	3.12088274396559e-05	6.24176548793118e-05	0.99996879117256
65	1.92526240074891e-05	3.85052480149782e-05	0.999980747375993
66	1.38864902569803e-05	2.77729805139607e-05	0.999986113509743
67	6.17164784883315e-05	0.000123432956976663	0.999938283521512
68	0.000251577050364403	0.000503154100728806	0.999748422949636
69	0.000391719476891106	0.000783438953782212	0.999608280523109
70	0.000522210361770449	0.00104442072354090	0.99947778963823
71	0.477312018929955	0.95462403785991	0.522687981070045
72	0.868049103099581	0.263901793800837	0.131950896900419
73	0.871902251088728	0.256195497822543	0.128097748911272
74	0.884449679478885	0.231100641042231	0.115550320521115
75	0.896398798031264	0.207202403937471	0.103601201968736
76	0.895727481547384	0.208545036905233	0.104272518452616
77	0.904471731958085	0.191056536083830	0.0955282680419152
78	0.900286717107315	0.199426565785370	0.0997132828926848
79	0.905309974101657	0.189380051796685	0.0946900258983427
80	0.895250208097561	0.209499583804878	0.104749791902439
81	0.929903184370668	0.140193631258665	0.0700968156293325
82	0.94287927170443	0.114241456591139	0.0571207282955696
83	0.932436124362724	0.135127751274553	0.0675638756372764
84	0.930778561436835	0.138442877126330	0.0692214385631649
85	0.924920103167805	0.150159793664389	0.0750798968321947
86	0.92297510005185	0.154049799896301	0.0770248999481506
87	0.91808769413211	0.163824611735782	0.0819123058678908
88	0.937198560349047	0.125602879301906	0.0628014396509532
89	0.929487361679105	0.141025276641791	0.0705126383208954
90	0.920268421836468	0.159463156327064	0.0797315781635319
91	0.902521859176762	0.194956281646477	0.0974781408232385
92	0.915199069618946	0.169601860762107	0.0848009303810537
93	0.906565542061613	0.186868915876774	0.0934344579383868
94	0.887492962169585	0.22501407566083	0.112507037830415
95	0.87999099888671	0.24001800222658	0.12000900111329
96	0.861012053673431	0.277975892653137	0.138987946326569
97	0.830210065633226	0.339579868733547	0.169789934366774
98	0.801815579272483	0.396368841455035	0.198184420727517
99	0.791075164423762	0.417849671152475	0.208924835576238
100	0.750071913135521	0.499856173728958	0.249928086864479
101	0.745138618197829	0.509722763604343	0.254861381802171
102	0.928659942158043	0.142680115683913	0.0713400578419567
103	0.942025207992126	0.115949584015748	0.0579747920078739
104	0.9445855388509	0.110828922298198	0.0554144611490991
105	0.934769173961351	0.130461652077297	0.0652308260386486
106	0.970458201543941	0.0590835969121182	0.0295417984560591
107	0.95598242432029	0.0880351513594212	0.0440175756797106
108	0.93877939811843	0.122441203763138	0.061220601881569
109	0.919519676117799	0.160960647764403	0.0804803238822014
110	0.87788673985379	0.24422652029242	0.12211326014621
111	0.851483337697007	0.297033324605987	0.148516662302993
112	0.780536151853306	0.438927696293388	0.219463848146694
113	0.756484465620842	0.487031068758317	0.243515534379158
114	0.677444419896127	0.645111160207747	0.322555580103873
115	0.623656352641125	0.75268729471775	0.376343647358875

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	65	0.585585585585586	NOK
5% type I error level	66	0.594594594594595	NOK
10% type I error level	68	0.612612612612613	NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259328140f3buq1891lum2xe/101ilo1259328064.png (open in new window)

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http://www.freestatistics.org/blog/date/2009/Nov/27/t1259328140f3buq1891lum2xe/9syoc1259328064.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259328140f3buq1891lum2xe/9syoc1259328064.ps (open in new window)

Parameters (Session):

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

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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