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Multiple Linear Regression Minitutorial + Trend

*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: Sat, 20 Nov 2010 09:33:22 +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/Nov/20/t1290245609ey2rw3o69fi2ncf.htm/, Retrieved Sat, 20 Nov 2010 10:33:29 +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/Nov/20/t1290245609ey2rw3o69fi2ncf.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 «

44164 -9 -7.7 544686 2.2 40399 -13 -4.9 537034 2.2 36763 -8 -2.4 551531 2.2 37903 -13 -3.6 563250 1.6 35532 -15 -7 574761 1.6 35533 -15 -7 580112 1.6 32110 -15 -7.9 575093 -0.1 33374 -10 -8.8 557560 -0.1 35462 -12 -14.2 564478 -0.1 33508 -11 -17.8 580523 -2.7 36080 -11 -18.2 596594 -2.7 34560 -17 -22.8 586570 -2.7 38737 -18 -23.6 536214 -4.1 38144 -19 -27.6 523597 -4.1 37594 -22 -29.4 536535 -4.1 36424 -24 -31.8 536322 -3.7 36843 -24 -31.4 532638 -3.7 37246 -20 -27.6 528222 -3.7 38661 -25 -28.8 516141 -1.3 40454 -22 -21.9 501866 -1.3 44928 -17 -13.9 506174 -1.3 48441 -9 -8 517945 1.1 48140 -11 -2.8 533590 1.1 45998 -13 -3.3 528379 1.1 47369 -11 -1.3 477580 1.9 49554 -9 0.5 469357 1.9 47510 -7 -1.9 490243 1.9 44873 -3 2 492622 1.6 45344 -3 1.7 507561 1.6 42413 -6 1.9 516922 1.6 36912 -4 0.1 514258 1.8 43452 -8 2.4 509846 1.8 42142 -1 2.3 527070 1.8 44382 -2 4.7 541657 2.7 43636 -2 5 564591 2.7 44167 -1 7.2 555362 2.7 44423 1 8.5 498662 3.3 42868 2 6.8 511038 3.3 43908 2 5. 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	7 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Multiple Linear Regression - Estimated Regression Equation

Vacatures[t] = + 78260.7264072135 -122.646983408323Consumentenvertrouwen[t] + 589.77146339065producentenvertrouwen[t] -0.0547284462719926nietwerkendewerkzoekende[t] -1137.19034873606economischegroei[t] -214.228069954972t + 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)	78260.7264072135	5866.813195	13.3396	0	0
Consumentenvertrouwen	-122.646983408323	133.646004	-0.9177	0.361076	0.180538
producentenvertrouwen	589.77146339065	141.212379	4.1765	6.5e-05	3.3e-05
nietwerkendewerkzoekende	-0.0547284462719926	0.010685	-5.1221	2e-06	1e-06
economischegroei	-1137.19034873606	595.050893	-1.9111	0.058977	0.029489
t	-214.228069954972	21.154852	-10.1267	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.87691598966497
R-squared	0.768981652930093
Adjusted R-squared	0.756949447353535
F-TEST (value)	63.9102821205365
F-TEST (DF numerator)	5
F-TEST (DF denominator)	96
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	4186.97278306626
Sum Squared Residuals	1682951144.26921

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	44164	42297.4436664993	1866.55633350070
2	40399	44643.9456985449	-4244.94569854493
3	36763	44497.5130844199	-7734.5130844199
4	37903	44229.7457228179	-6326.74572281791
5	35532	41625.6094991145	-6093.60949911447
6	35533	41118.5295131581	-5585.52951315806
7	32110	42581.4127908419	-10471.4127908419
8	33374	42182.7093352806	-8808.70933528062
9	35462	38650.3979385231	-3188.39793852313
10	33508	38268.9226032331	-4760.92260323313
11	36080	36939.2450878847	-859.245087884708
12	34560	35296.5481322131	-736.548132213131
13	38737	39081.1220036569	-344.122003656902
14	38144	37320.9638701614	823.03612983862
15	37594	35705.0114784612	1888.98852153883
16	36424	33877.4068827468	2546.59311725321
17	36843	34100.7069942141	2742.2930057859
18	37246	35878.7033702474	1367.29662975257
19	38661	33501.9019837107	5159.09801628931
20	40454	37770.4046314589	2683.59536854107
21	44928	41425.3432050478	3502.65679495219
22	48441	40336.1255237969	8104.87447620308
23	48140	42577.7764883647	5562.22351163534
24	45998	42599.1465870544	3398.85341294564
25	47369	45189.5655402461	2179.43445975386
26	49554	46241.6641512723	3312.33584872771
27	47510	43223.6322735263	4286.36772647373
28	44873	45029.8831081013	-156.883108101299
29	45344	43821.1353402718	1522.86465972817
30	42413	43580.4895276678	-1167.48952766784
31	36912	41977.7373679144	-5065.73736791443
32	43452	43852.0335023433	-400.033502343274
33	42142	41777.6566436022	364.343356397822
34	44382	41279.7319095611	3102.26809043892
35	43636	39987.2930918214	3648.70690817858
36	44167	41453.0040885618	2713.99591143822
37	44423	44180.9736485784	242.026351421647
38	42868	42164.1678563888	703.83214361123
39	43908	40545.7543140696	3362.24568593037
40	42013	39032.3206064966	2980.67939350339
41	38846	38281.2577440556	564.7422559444
42	35087	38437.4996961248	-3350.49969612482
43	33026	40189.2071498252	-7163.20714982518
44	34646	37699.9899900953	-3053.98999009529
45	37135	36873.2181030308	261.781896969240
46	37985	35011.5377988877	2973.46220111232
47	43121	35064.5664584425	8056.4335415575
48	43722	35899.6791061861	7822.3208938139
49	43630	37638.9228646631	5991.07713533692
50	42234	37452.6052081563	4781.3947918437
51	39351	36796.8672005376	2554.1327994624
52	39327	34764.7161192697	4562.2838807303
53	35704	32971.5731608079	2732.42683919214
54	30466	31508.4896692562	-1042.48966925616
55	28155	31913.2348320129	-3758.2348320129
56	29257	31753.8636898141	-2496.86368981409
57	29998	29912.5406505163	85.459349483669
58	32529	28941.2978169249	3587.70218307514
59	34787	25900.6901591437	8886.30984085628
60	33855	25901.2283032332	7953.77169676685
61	34556	28702.2459592903	5853.75404070966
62	31348	28279.1652751796	3068.83472482038
63	30805	27668.9165637453	3136.0834362547
64	28353	28172.8856902246	180.114309775411
65	24514	28164.2069442197	-3650.2069442197
66	21106	29298.1819874327	-8192.18198743268
67	21346	26642.4966103054	-5296.49661030535
68	23335	27741.916814553	-4406.916814553
69	24379	27586.6315889434	-3207.63158894336
70	26290	26596.5383217769	-306.538321776861
71	30084	26011.7407067126	4072.25929328744
72	29429	28519.3477229952	909.652277004832
73	30632	29272.2658513077	1359.73414869227
74	27349	30361.4826515672	-3012.48265156723
75	27264	28755.6064805989	-1491.60648059895
76	27474	27283.6091073912	190.390892608775
77	24482	25991.0822732541	-1509.08227325408
78	21453	25410.8483085981	-3957.84830859807
79	18788	27859.7664505414	-9071.76645054135
80	19282	27581.1197639226	-8299.11976392257
81	19713	25886.6521470392	-6173.65214703925
82	21917	23562.2085400657	-1645.20854006571
83	23812	22102.3513032302	1709.64869676978
84	23785	20873.8089487932	2911.19105120685
85	24696	22646.7146342658	2049.28536573416
86	24562	24354.7865452424	207.213454757600
87	23580	22871.6595573315	708.340442668476
88	24939	23783.676006453	1155.32399354699
89	23899	24869.0632408593	-970.063240859339
90	21454	23751.4217038596	-2297.42170385961
91	19761	23663.2522662087	-3902.25226620871
92	19815	23594.3840437027	-3779.38404370267
93	20780	22215.2226144297	-1435.22261442975
94	23462	22868.5966723694	593.40332763061
95	25005	22533.0356370294	2471.96436297059
96	24725	23473.8568258226	1251.14317417739
97	26198	28395.6404906254	-2197.64049062540
98	27543	28226.0847884776	-683.084788477575
99	26471	26951.6110843667	-480.61108436672
100	26558	25858.5840171563	699.415982843666
101	25317	23474.8041015733	1842.19589842672
102	22896	23367.8649756791	-471.864975679136

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
9	0.0858266937520184	0.171653387504037	0.914173306247982
10	0.0304661556905826	0.0609323113811652	0.969533844309417
11	0.0483906660447092	0.0967813320894185	0.95160933395529
12	0.0202155247197181	0.0404310494394363	0.979784475280282
13	0.0315633075397167	0.0631266150794333	0.968436692460283
14	0.0160630437369281	0.0321260874738562	0.983936956263072
15	0.00702876428698979	0.0140575285739796	0.99297123571301
16	0.00341138123773872	0.00682276247547743	0.996588618762261
17	0.00168238717756481	0.00336477435512961	0.998317612822435
18	0.00359507344080350	0.00719014688160699	0.996404926559197
19	0.00233349099087638	0.00466698198175275	0.997666509009124
20	0.00534688712786349	0.0106937742557270	0.994653112872137
21	0.0334271612660670	0.0668543225321339	0.966572838733933
22	0.0346984863969409	0.0693969727938819	0.96530151360306
23	0.0377162496264081	0.0754324992528161	0.962283750373592
24	0.0236567942687182	0.0473135885374364	0.976343205731282
25	0.0305690670820603	0.0611381341641206	0.96943093291794
26	0.0243049793524897	0.0486099587049793	0.97569502064751
27	0.0238822163464664	0.0477644326929327	0.976117783653534
28	0.0405242434528046	0.0810484869056093	0.959475756547195
29	0.0337862650245897	0.0675725300491795	0.96621373497541
30	0.0380852244352141	0.0761704488704281	0.961914775564786
31	0.205261304540284	0.410522609080569	0.794738695459716
32	0.16897566427075	0.3379513285415	0.83102433572925
33	0.139973924835134	0.279947849670269	0.860026075164866
34	0.115348697350303	0.230697394700606	0.884651302649697
35	0.0990143296859027	0.198028659371805	0.900985670314097
36	0.0770961488908347	0.154192297781669	0.922903851109165
37	0.0705147921716739	0.141029584343348	0.929485207828326
38	0.0636701084857684	0.127340216971537	0.936329891514232
39	0.0471442001962569	0.0942884003925138	0.952855799803743
40	0.037107554797767	0.074215109595534	0.962892445202233
41	0.0325877139647937	0.0651754279295875	0.967412286035206
42	0.0501376289960257	0.100275257992051	0.949862371003974
43	0.115463711865514	0.230927423731029	0.884536288134486
44	0.140871310610995	0.28174262122199	0.859128689389005
45	0.12600945175806	0.25201890351612	0.87399054824194
46	0.151688665262756	0.303377330525513	0.848311334737244
47	0.343552659467058	0.687105318934116	0.656447340532942
48	0.515858748061756	0.968282503876488	0.484141251938244
49	0.534266654171628	0.931466691656745	0.465733345828372
50	0.554645359703255	0.89070928059349	0.445354640296745
51	0.549586042861775	0.90082791427645	0.450413957138225
52	0.586898897332337	0.826202205335325	0.413101102667663
53	0.577564272037735	0.84487145592453	0.422435727962265
54	0.612413633289242	0.775172733421516	0.387586366710758
55	0.70220743380092	0.59558513239816	0.29779256619908
56	0.718346604317007	0.563306791365985	0.281653395682993
57	0.678833986029128	0.642332027941744	0.321166013970872
58	0.710609210352995	0.578781579294011	0.289390789647005
59	0.828428721357428	0.343142557285145	0.171571278642572
60	0.911793414142432	0.176413171715137	0.0882065858575685
61	0.94595300015713	0.108093999685739	0.0540469998428696
62	0.957582427366182	0.0848351452676362	0.0424175726338181
63	0.96451648449614	0.070967031007719	0.0354835155038595
64	0.967435657835493	0.0651286843290138	0.0325643421645069
65	0.972533897602128	0.0549322047957435	0.0274661023978718
66	0.990506190253594	0.0189876194928124	0.00949380974640622
67	0.995152947704328	0.00969410459134455	0.00484705229567228
68	0.995472616634094	0.00905476673181111	0.00452738336590556
69	0.993857647379972	0.0122847052400552	0.00614235262002759
70	0.990161018036907	0.0196779639261868	0.00983898196309342
71	0.992932206103958	0.0141355877920846	0.00706779389604229
72	0.995946243910198	0.00810751217960404	0.00405375608980202
73	0.996917153488513	0.00616569302297349	0.00308284651148675
74	0.997030542970505	0.00593891405899063	0.00296945702949531
75	0.997782838362767	0.0044343232744656	0.0022171616372328
76	0.999526876750251	0.00094624649949705	0.000473123249748525
77	0.999831633542305	0.000336732915389663	0.000168366457694831
78	0.99991352209223	0.000172955815538786	8.64779077693932e-05
79	0.99991882450748	0.000162350985041432	8.11754925207159e-05
80	0.999931001319406	0.000137997361187621	6.89986805938107e-05
81	0.999956976810938	8.6046378123254e-05	4.3023189061627e-05
82	0.999954026972784	9.19460544320242e-05	4.59730272160121e-05
83	0.999894183289605	0.000211633420790813	0.000105816710395406
84	0.999739531700566	0.000520936598869045	0.000260468299434523
85	0.99952882208046	0.000942355839080833	0.000471177919540417
86	0.998844098893342	0.00231180221331584	0.00115590110665792
87	0.99862103395551	0.00275793208898162	0.00137896604449081
88	0.999890392516844	0.000219214966312324	0.000109607483156162
89	0.999836412653611	0.000327174692777891	0.000163587346388946
90	0.999273559609755	0.00145288078048953	0.000726440390244763
91	0.997156512673882	0.00568697465223706	0.00284348732611853
92	0.99173103200526	0.0165379359894786	0.00826896799473929
93	0.982711595128439	0.0345768097431221	0.0172884048715611

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	26	0.305882352941176	NOK
5% type I error level	39	0.458823529411765	NOK
10% type I error level	56	0.658823529411765	NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/20/t1290245609ey2rw3o69fi2ncf/100vvz1290245591.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/20/t1290245609ey2rw3o69fi2ncf/100vvz1290245591.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/20/t1290245609ey2rw3o69fi2ncf/1tcg51290245591.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/20/t1290245609ey2rw3o69fi2ncf/1tcg51290245591.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/20/t1290245609ey2rw3o69fi2ncf/2mmg81290245591.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/20/t1290245609ey2rw3o69fi2ncf/2mmg81290245591.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/20/t1290245609ey2rw3o69fi2ncf/3mmg81290245591.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/20/t1290245609ey2rw3o69fi2ncf/3mmg81290245591.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/20/t1290245609ey2rw3o69fi2ncf/4mmg81290245591.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/20/t1290245609ey2rw3o69fi2ncf/4mmg81290245591.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/20/t1290245609ey2rw3o69fi2ncf/5wvxb1290245591.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/20/t1290245609ey2rw3o69fi2ncf/5wvxb1290245591.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/20/t1290245609ey2rw3o69fi2ncf/6wvxb1290245591.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/20/t1290245609ey2rw3o69fi2ncf/6wvxb1290245591.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/20/t1290245609ey2rw3o69fi2ncf/774we1290245591.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/20/t1290245609ey2rw3o69fi2ncf/774we1290245591.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/20/t1290245609ey2rw3o69fi2ncf/874we1290245591.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/20/t1290245609ey2rw3o69fi2ncf/874we1290245591.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/20/t1290245609ey2rw3o69fi2ncf/90vvz1290245591.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/20/t1290245609ey2rw3o69fi2ncf/90vvz1290245591.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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