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Linear Regression Minitutorial

*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, 23 Nov 2010 10:33:31 +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/23/t1290508356mn4zal2ap5paxzf.htm/, Retrieved Tue, 23 Nov 2010 11:32:37 +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/23/t1290508356mn4zal2ap5paxzf.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?

This computation is/was private until 2010-11-24

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

55 1 20 0 80 0 52 0 75 1 30 1 90 1 68 1 24 0 60 0 65 1 60 0 80 1 65 1 90 0 65 1 76 1 70 1 38 0 60 1 10 0 5 0 93 1 70 0 61 1 72 1 40 0 75 1 100 1 29 0 70 1 25 0 70 1 82 0 40 0 50 1 70 1 91 1 10 0 25 0 56 0 30 0 74 0 60 0 80 0 80 1 60 1 64 1 40 1 80 1 71 1 65 1 90 0 68 1 76 1 25 1 79 1 40 0 61 1 27 1 70 0 40 0 13 0 15 0 38 1 47 0 65 1 62 1 50 0 80 1 87 1 40 1 80 1 20 0 60 1 48 1 70 1 91 1 10 0 50 0 70 0 45 1 20 1 10 0 90 1 80 1 74 0 71 0 40 0 29 1 60 1 31 0 67 0 82 0 40 1 30 1 70 0 63 0 35 0 35 1 70 0 60 1 80 1 70 1 71 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	8 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Multiple Linear Regression - Estimated Regression Equation

Q1[t] = + 50.0313369097804 + 16.4922088057442gender[t] -0.0467799991133598t + 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)	50.0313369097804	4.91902	10.171	0	0
gender	16.4922088057442	4.303411	3.8324	0.00022	0.00011
t	-0.0467799991133598	0.070445	-0.6641	0.508147	0.254073

Multiple Linear Regression - Regression Statistics
Multiple R	0.358961497027954
R-squared	0.128853356348550
Adjusted R-squared	0.111772049610286
F-TEST (value)	7.54353038224565
F-TEST (DF numerator)	2
F-TEST (DF denominator)	102
p-value	0.000880348550419296
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	21.8780400356169
Sum Squared Residuals	48822.1608516056

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	55	66.476765716411	-11.4767657164110
2	20	49.9377769115537	-29.9377769115537
3	80	49.8909969124403	30.1090030875597
4	52	49.8442169133269	2.15578308667306
5	75	66.2896457199578	8.71035428004222
6	30	66.2428657208444	-36.2428657208444
7	90	66.196085721731	23.8039142782689
8	68	66.1493057226177	1.85069427738230
9	24	49.6103169177601	-25.6103169177601
10	60	49.5635369186468	10.4364630813532
11	65	66.0089657252776	-1.00896572527762
12	60	49.4699769204201	10.5300230795799
13	80	65.9154057270509	14.0845942729491
14	65	65.8686257279375	-0.868625727937538
15	90	49.32963692308	40.67036307692
16	65	65.7750657297108	-0.775065729710819
17	76	65.7282857305975	10.2717142694025
18	70	65.6815057314841	4.3184942685159
19	38	49.1425169266265	-11.1425169266265
20	60	65.5879457332574	-5.58794573325738
21	10	49.0489569283998	-39.0489569283998
22	5	49.0021769292865	-44.0021769292865
23	93	65.4476057359173	27.5523942640827
24	70	48.9086169310597	21.0913830689403
25	61	65.3540457376906	-4.35404573769058
26	72	65.3072657385772	6.69273426142278
27	40	48.7682769337197	-8.76827693371967
28	75	65.2137057403505	9.7862942596495
29	100	65.1669257412372	34.8330742587629
30	29	48.6279369363796	-19.6279369363796
31	70	65.0733657430104	4.92663425698958
32	25	48.5343769381529	-23.5343769381529
33	70	64.9798057447837	5.0201942552163
34	82	48.4408169399262	33.5591830600738
35	40	48.3940369408128	-8.39403694081279
36	50	64.8394657474436	-14.8394657474436
37	70	64.7926857483303	5.20731425166974
38	91	64.7459057492169	26.2540942507831
39	10	48.2069169443594	-38.2069169443594
40	25	48.160136945246	-23.160136945246
41	56	48.1133569461326	7.88664305386737
42	30	48.0665769470193	-18.0665769470193
43	74	48.0197969479059	25.9802030520941
44	60	47.9730169487925	12.0269830512074
45	80	47.9262369496792	32.0737630503208
46	80	64.37166575631	15.6283342436900
47	60	64.3248857571967	-4.32488575719667
48	64	64.2781057580833	-0.278105758083305
49	40	64.23132575897	-24.2313257589699
50	80	64.1845457598566	15.8154542401434
51	71	64.1377657607432	6.86223423925677
52	65	64.0909857616299	0.909014238370135
53	90	47.5519969567723	42.4480030432277
54	68	63.9974257634031	4.00257423659685
55	76	63.9506457642898	12.0493542357102
56	25	63.9038657651764	-38.9038657651764
57	79	63.8570857660631	15.1429142339369
58	40	47.3180969612055	-7.31809696120551
59	61	63.7635257678363	-2.76352576783635
60	27	63.716745768723	-36.716745768723
61	70	47.1777569638654	22.8222430361346
62	40	47.1309769647521	-7.13097696475207
63	13	47.0841969656387	-34.0841969656387
64	15	47.0374169665254	-32.0374169665254
65	38	63.4828457731562	-25.4828457731562
66	47	46.9438569682986	0.0561430317013662
67	65	63.3892857749295	1.61071422507053
68	62	63.3425057758161	-1.34250577581611
69	50	46.8035169709586	3.19648302904144
70	80	63.2489457775894	16.7510542224106
71	87	63.202165778476	23.7978342215240
72	40	63.1553857793627	-23.1553857793627
73	80	63.1086057802493	16.8913942197507
74	20	46.5696169753918	-26.5696169753918
75	60	63.0150457820226	-3.01504578202259
76	48	62.9682657829092	-14.9682657829092
77	70	62.9214857837959	7.07851421620413
78	91	62.8747057846825	28.1252942153175
79	10	46.335716979825	-36.3357169798250
80	50	46.2889369807116	3.7110630192884
81	70	46.2421569815982	23.7578430184018
82	45	62.6875857882291	-17.6875857882291
83	20	62.6408057891157	-42.6408057891157
84	10	46.1018169842582	-36.1018169842582
85	90	62.547245790889	27.452754209111
86	80	62.5004657917756	17.4995342082244
87	74	45.9614769869181	28.0385230130819
88	71	45.9146969878047	25.0853030121953
89	40	45.8679169886914	-5.86791698869136
90	29	62.3133457953222	-33.3133457953222
91	60	62.2665657962088	-2.26656579620883
92	31	45.7275769913513	-14.7275769913513
93	67	45.6807969922379	21.3192030077621
94	82	45.6340169931246	36.3659830068754
95	40	62.0794457997554	-22.0794457997554
96	30	62.032665800642	-32.032665800642
97	70	45.4936769957845	24.5063230042155
98	63	45.4468969966711	17.5531030033289
99	35	45.4001169975578	-10.4001169975578
100	35	61.8455458041886	-26.8455458041886
101	70	45.306556999331	24.6934430006690
102	60	61.7519858059619	-1.75198580596188
103	80	61.7052058068485	18.2947941931515
104	70	61.6584258077352	8.34157419226484
105	71	61.6116458086218	9.3883541913782

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
6	0.878795797461267	0.242408405077466	0.121204202538733
7	0.875782729908569	0.248434540182862	0.124217270091431
8	0.796726403328559	0.406547193342882	0.203273596671441
9	0.824622769974233	0.350754460051534	0.175377230025767
10	0.767583414941772	0.464833170116455	0.232416585058228
11	0.678079032650712	0.643841934698575	0.321920967349287
12	0.59211232429718	0.81577535140564	0.40788767570282
13	0.509920306697048	0.980159386605905	0.490079693302952
14	0.42527771164438	0.85055542328876	0.57472228835562
15	0.490835600938214	0.981671201876428	0.509164399061786
16	0.430328440704781	0.860656881409562	0.569671559295219
17	0.35085071094332	0.70170142188664	0.64914928905668
18	0.285278775161203	0.570557550322405	0.714721224838797
19	0.312481826224507	0.624963652449015	0.687518173775493
20	0.265721896929803	0.531443793859605	0.734278103070197
21	0.462045174021886	0.924090348043773	0.537954825978114
22	0.60905752550716	0.78188494898568	0.39094247449284
23	0.655884850625971	0.688230298748058	0.344115149374029
24	0.667618466833235	0.66476306633353	0.332381533166765
25	0.608402669071449	0.783194661857101	0.391597330928551
26	0.544792192894675	0.91041561421065	0.455207807105325
27	0.483875439411012	0.967750878822025	0.516124560588988
28	0.425878352901707	0.851756705803413	0.574121647098293
29	0.490135462442746	0.980270924885493	0.509864537557254
30	0.47202968002773	0.94405936005546	0.52797031997227
31	0.410905666672776	0.821811333345551	0.589094333327224
32	0.404823786977301	0.809647573954601	0.595176213022699
33	0.34676118612332	0.69352237224664	0.65323881387668
34	0.445141482218927	0.890282964437853	0.554858517781073
35	0.392778725036848	0.785557450073696	0.607221274963152
36	0.376737219185625	0.75347443837125	0.623262780814375
37	0.322715397010365	0.645430794020729	0.677284602989635
38	0.333555798241835	0.66711159648367	0.666444201758165
39	0.434731225052095	0.86946245010419	0.565268774947905
40	0.428580908599056	0.857161817198112	0.571419091400944
41	0.389018515953399	0.778037031906797	0.610981484046601
42	0.366713597814166	0.733427195628333	0.633286402185834
43	0.403737381570018	0.807474763140037	0.596262618429982
44	0.367281419743842	0.734562839487684	0.632718580256158
45	0.427705314676918	0.855410629353836	0.572294685323082
46	0.394309129634731	0.788618259269462	0.605690870365269
47	0.353019794111570	0.706039588223139	0.64698020588843
48	0.307317196269744	0.614634392539488	0.692682803730256
49	0.330193778873095	0.66038755774619	0.669806221126905
50	0.306109795930223	0.612219591860447	0.693890204069777
51	0.265649537702238	0.531299075404476	0.734350462297762
52	0.224953169987447	0.449906339974894	0.775046830012553
53	0.370088839276916	0.740177678553832	0.629911160723084
54	0.329958479874097	0.659916959748193	0.670041520125903
55	0.310907188537979	0.621814377075958	0.689092811462021
56	0.414263791601545	0.82852758320309	0.585736208398455
57	0.407179989640992	0.814359979281983	0.592820010359008
58	0.356558150249602	0.713116300499204	0.643441849750398
59	0.313152567529503	0.626305135059006	0.686847432470497
60	0.37768178379388	0.75536356758776	0.62231821620612
61	0.403580640386880	0.807161280773759	0.59641935961312
62	0.351317167894595	0.70263433578919	0.648682832105405
63	0.399403184302114	0.798806368604227	0.600596815697886
64	0.444121620900521	0.888243241801043	0.555878379099479
65	0.442510986949166	0.885021973898332	0.557489013050834
66	0.38680114044867	0.77360228089734	0.61319885955133
67	0.333916201015247	0.667832402030495	0.666083798984753
68	0.282032732163145	0.56406546432629	0.717967267836855
69	0.236274891682798	0.472549783365595	0.763725108317202
70	0.230178441308229	0.460356882616457	0.769821558691771
71	0.268134140892007	0.536268281784014	0.731865859107993
72	0.248405363302791	0.496810726605582	0.75159463669721
73	0.258892236623465	0.517784473246931	0.741107763376535
74	0.270913340773641	0.541826681547282	0.729086659226359
75	0.224821427264756	0.449642854529511	0.775178572735244
76	0.186426737307574	0.372853474615149	0.813573262692426
77	0.165058010132899	0.330116020265798	0.834941989867101
78	0.278688864376440	0.557377728752881	0.72131113562356
79	0.368641187591506	0.737282375183013	0.631358812408494
80	0.310225549329449	0.620451098658899	0.68977445067055
81	0.319887602198721	0.639775204397442	0.680112397801279
82	0.268697254134773	0.537394508269547	0.731302745865227
83	0.337506591688212	0.675013183376424	0.662493408311788
84	0.55660152813987	0.88679694372026	0.44339847186013
85	0.669441234005733	0.661117531988535	0.330558765994267
86	0.779972927989275	0.44005414402145	0.220027072010725
87	0.818388664119635	0.363222671760730	0.181611335880365
88	0.857600631240944	0.284798737518112	0.142399368759056
89	0.804608860722844	0.390782278554313	0.195391139277156
90	0.765825359077205	0.46834928184559	0.234174640922795
91	0.79041540846136	0.419169183077281	0.209584591538640
92	0.785015683939536	0.429968632120928	0.214984316060464
93	0.74679480080459	0.50641039839082	0.25320519919541
94	0.904290341620881	0.191419316758238	0.0957096583791188
95	0.865501549507816	0.268996900984369	0.134498450492185
96	0.789379545608882	0.421240908782237	0.210620454391118
97	0.845679402755769	0.308641194488463	0.154320597244231
98	0.89031048295367	0.219379034092660	0.109689517046330
99	0.85751899531626	0.284962009367482	0.142481004683741

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	0	0	OK
10% type I error level	0	0	OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290508356mn4zal2ap5paxzf/10qjv41290508399.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290508356mn4zal2ap5paxzf/10qjv41290508399.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290508356mn4zal2ap5paxzf/11igb1290508399.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290508356mn4zal2ap5paxzf/11igb1290508399.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290508356mn4zal2ap5paxzf/21igb1290508399.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290508356mn4zal2ap5paxzf/21igb1290508399.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290508356mn4zal2ap5paxzf/3uafe1290508399.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290508356mn4zal2ap5paxzf/3uafe1290508399.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290508356mn4zal2ap5paxzf/4uafe1290508399.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290508356mn4zal2ap5paxzf/4uafe1290508399.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290508356mn4zal2ap5paxzf/5uafe1290508399.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290508356mn4zal2ap5paxzf/5uafe1290508399.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290508356mn4zal2ap5paxzf/6mjfy1290508399.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290508356mn4zal2ap5paxzf/6mjfy1290508399.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290508356mn4zal2ap5paxzf/7xsw11290508399.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290508356mn4zal2ap5paxzf/7xsw11290508399.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290508356mn4zal2ap5paxzf/8xsw11290508399.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290508356mn4zal2ap5paxzf/8xsw11290508399.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290508356mn4zal2ap5paxzf/9xsw11290508399.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290508356mn4zal2ap5paxzf/9xsw11290508399.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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