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Paper: Multiple regression analysis

*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, 19 Dec 2009 08:30:06 -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/Dec/19/t1261236675h1gbx7eh7qrcq1z.htm/, Retrieved Sat, 19 Dec 2009 16:31:28 +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/Dec/19/t1261236675h1gbx7eh7qrcq1z.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 «

128,7 0 136,9 0 156,9 0 109,1 0 122,3 0 123,9 0 90,9 0 77,9 0 120,3 0 118,9 0 125,5 0 98,9 0 102,9 0 105,9 0 117,6 0 113,6 0 115,9 0 118,9 0 77,6 0 81,2 0 123,1 0 136,6 0 112,1 0 95,1 0 96,3 0 105,7 0 115,8 0 105,7 0 105,7 0 111,1 0 82,4 0 60 0 107,3 0 99,3 0 113,5 0 108,9 0 100,2 0 103,9 0 138,7 0 120,2 0 100,2 0 143,2 0 70,9 0 85,2 0 133 0 136,6 0 117,9 0 106,3 0 122,3 0 125,5 0 148,4 0 126,3 0 99,6 0 140,4 0 80,3 0 92,6 0 138,5 0 110,9 0 119,6 0 105 0 109 0 129,4 0 148,6 0 101,4 0 134,8 0 143,7 0 81,6 0 90,3 0 141,5 0 140,7 0 140,2 0 100,2 0 125,7 0 119,6 0 134,7 0 109 0 116,3 0 146,9 0 97,4 0 89,4 0 132,1 1 139,8 1 129 1 112,5 1 121,9 1 121,7 1 123,1 1 131,6 1 119,3 1 132,5 1 98,3 1 85,1 1 131,7 1 129,3 1 90,7 1 78,6 1 68,9 1 79,1 1 83,5 1 74,1 1 59,7 1 93,3 1 61,3 1 56,6 1 98,5 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	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation

Y[t] = + 113.60625 -11.51825X[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)	113.60625	2.479003	45.8274	0	0
X	-11.51825	5.080444	-2.2672	0.025469	0.012734

Multiple Linear Regression - Regression Statistics
Multiple R	0.218017562086058
R-squared	0.0475316573779481
Adjusted R-squared	0.0382843919155982
F-TEST (value)	5.14007709321982
F-TEST (DF numerator)	1
F-TEST (DF denominator)	103
p-value	0.0254685118302665
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	22.1728762131372
Sum Squared Residuals	50638.553275

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	128.7	113.606250000000	15.0937500000002
2	136.9	113.60625	23.2937500000000
3	156.9	113.60625	43.29375
4	109.1	113.60625	-4.50625000000001
5	122.3	113.60625	8.69375
6	123.9	113.60625	10.29375
7	90.9	113.60625	-22.70625
8	77.9	113.60625	-35.70625
9	120.3	113.60625	6.69375
10	118.9	113.60625	5.29375000000001
11	125.5	113.60625	11.89375
12	98.9	113.60625	-14.70625
13	102.9	113.60625	-10.70625
14	105.9	113.60625	-7.70625
15	117.6	113.60625	3.99374999999999
16	113.6	113.60625	-0.00625000000000564
17	115.9	113.60625	2.29375000000001
18	118.9	113.60625	5.29375000000001
19	77.6	113.60625	-36.00625
20	81.2	113.60625	-32.40625
21	123.1	113.60625	9.49375
22	136.6	113.60625	22.99375
23	112.1	113.60625	-1.50625000000001
24	95.1	113.60625	-18.50625
25	96.3	113.60625	-17.30625
26	105.7	113.60625	-7.90625
27	115.8	113.60625	2.19375000000000
28	105.7	113.60625	-7.90625
29	105.7	113.60625	-7.90625
30	111.1	113.60625	-2.50625000000001
31	82.4	113.60625	-31.20625
32	60	113.60625	-53.60625
33	107.3	113.60625	-6.30625
34	99.3	113.60625	-14.30625
35	113.5	113.60625	-0.10625
36	108.9	113.60625	-4.70624999999999
37	100.2	113.60625	-13.40625
38	103.9	113.60625	-9.70625
39	138.7	113.60625	25.09375
40	120.2	113.60625	6.59375
41	100.2	113.60625	-13.40625
42	143.2	113.60625	29.59375
43	70.9	113.60625	-42.70625
44	85.2	113.60625	-28.40625
45	133	113.60625	19.39375
46	136.6	113.60625	22.99375
47	117.9	113.60625	4.29375000000001
48	106.3	113.60625	-7.30625
49	122.3	113.60625	8.69375
50	125.5	113.60625	11.89375
51	148.4	113.60625	34.79375
52	126.3	113.60625	12.69375
53	99.6	113.60625	-14.00625
54	140.4	113.60625	26.79375
55	80.3	113.60625	-33.30625
56	92.6	113.60625	-21.00625
57	138.5	113.60625	24.89375
58	110.9	113.60625	-2.70624999999999
59	119.6	113.60625	5.99375
60	105	113.60625	-8.60625
61	109	113.60625	-4.60625
62	129.4	113.60625	15.79375
63	148.6	113.60625	34.99375
64	101.4	113.60625	-12.20625
65	134.8	113.60625	21.19375
66	143.7	113.60625	30.09375
67	81.6	113.60625	-32.00625
68	90.3	113.60625	-23.30625
69	141.5	113.60625	27.89375
70	140.7	113.60625	27.09375
71	140.2	113.60625	26.59375
72	100.2	113.60625	-13.40625
73	125.7	113.60625	12.09375
74	119.6	113.60625	5.99375
75	134.7	113.60625	21.09375
76	109	113.60625	-4.60625
77	116.3	113.60625	2.69375000000000
78	146.9	113.60625	33.29375
79	97.4	113.60625	-16.20625
80	89.4	113.60625	-24.20625
81	132.1	102.088	30.012
82	139.8	102.088	37.712
83	129	102.088	26.912
84	112.5	102.088	10.412
85	121.9	102.088	19.812
86	121.7	102.088	19.612
87	123.1	102.088	21.012
88	131.6	102.088	29.512
89	119.3	102.088	17.212
90	132.5	102.088	30.412
91	98.3	102.088	-3.788
92	85.1	102.088	-16.988
93	131.7	102.088	29.612
94	129.3	102.088	27.212
95	90.7	102.088	-11.388
96	78.6	102.088	-23.488
97	68.9	102.088	-33.188
98	79.1	102.088	-22.988
99	83.5	102.088	-18.588
100	74.1	102.088	-27.988
101	59.7	102.088	-42.388
102	93.3	102.088	-8.788
103	61.3	102.088	-40.788
104	56.6	102.088	-45.488
105	98.5	102.088	-3.588

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
5	0.538063448004671	0.923873103990659	0.461936551995329
6	0.381576334737799	0.763152669475598	0.618423665262201
7	0.609211690874291	0.781576618251419	0.390788309125709
8	0.825018308698839	0.349963382602321	0.174981691301161
9	0.743328145493518	0.513343709012965	0.256671854506482
10	0.649529921286236	0.700940157427527	0.350470078713764
11	0.559852018505186	0.880295962989629	0.440147981494814
12	0.530198835178118	0.939602329643764	0.469801164821882
13	0.470370998805343	0.940741997610685	0.529629001194657
14	0.397599903273297	0.795199806546595	0.602400096726702
15	0.315050328073017	0.630100656146035	0.684949671926983
16	0.242347750223172	0.484695500446343	0.757652249776828
17	0.180728074545295	0.361456149090590	0.819271925454705
18	0.132146390391085	0.264292780782171	0.867853609608915
19	0.245268228184057	0.490536456368115	0.754731771815943
20	0.322180104476987	0.644360208953975	0.677819895523013
21	0.271756198343596	0.543512396687192	0.728243801656404
22	0.280956625390115	0.56191325078023	0.719043374609885
23	0.223234141176673	0.446468282353347	0.776765858823327
24	0.208635635039526	0.417271270079051	0.791364364960474
25	0.188678914673008	0.377357829346016	0.811321085326992
26	0.149400298370861	0.298800596741723	0.850599701629138
27	0.113739544023745	0.227479088047490	0.886260455976255
28	0.0870002354784018	0.174000470956804	0.912999764521598
29	0.0654050280574022	0.130810056114804	0.934594971942598
30	0.0467614473498598	0.0935228946997197	0.95323855265014
31	0.0656494358156743	0.131298871631349	0.934350564184326
32	0.230147007481715	0.460294014963431	0.769852992518285
33	0.187288460945684	0.374576921891368	0.812711539054316
34	0.160007188059099	0.320014376118199	0.8399928119409
35	0.126437203891133	0.252874407782265	0.873562796108867
36	0.0982014843921265	0.196402968784253	0.901798515607873
37	0.0807346011787396	0.161469202357479	0.91926539882126
38	0.063051742412409	0.126103484824818	0.936948257587591
39	0.0773772614468502	0.154754522893700	0.92262273855315
40	0.0611647076879258	0.122329415375852	0.938835292312074
41	0.0499378749928025	0.099875749985605	0.950062125007197
42	0.070277208842048	0.140554417684096	0.929722791157952
43	0.14147915716859	0.28295831433718	0.85852084283141
44	0.163229036983448	0.326458073966895	0.836770963016553
45	0.160845012794499	0.321690025588997	0.839154987205502
46	0.168653251470136	0.337306502940272	0.831346748529864
47	0.137529008346973	0.275058016693946	0.862470991653027
48	0.112191877312903	0.224383754625806	0.887808122687097
49	0.0919344945453808	0.183868989090762	0.908065505454619
50	0.0772068814053523	0.154413762810705	0.922793118594648
51	0.113532231671363	0.227064463342725	0.886467768328637
52	0.0963094847531495	0.192618969506299	0.90369051524685
53	0.0834747003291493	0.166949400658299	0.91652529967085
54	0.0931406938110968	0.186281387622194	0.906859306188903
55	0.129680695680346	0.259361391360692	0.870319304319654
56	0.130580063328907	0.261160126657814	0.869419936671093
57	0.135209035845733	0.270418071691466	0.864790964154267
58	0.108387614577355	0.21677522915471	0.891612385422645
59	0.0857380446947852	0.171476089389570	0.914261955305215
60	0.0701551350567664	0.140310270113533	0.929844864943234
61	0.0548979872913263	0.109795974582653	0.945102012708674
62	0.0461676340829663	0.0923352681659326	0.953832365917034
63	0.0650260953786302	0.130052190757260	0.93497390462137
64	0.0550558814802481	0.110111762960496	0.944944118519752
65	0.0509032181610687	0.101806436322137	0.949096781838931
66	0.0601887125327898	0.120377425065580	0.93981128746721
67	0.0846735635729279	0.169347127145856	0.915326436427072
68	0.094092302597771	0.188184605195542	0.905907697402229
69	0.0982240903397094	0.196448180679419	0.90177590966029
70	0.101855552569304	0.203711105138608	0.898144447430696
71	0.106565356697243	0.213130713394487	0.893434643302757
72	0.091494126229723	0.182988252459446	0.908505873770277
73	0.073231640419031	0.146463280838062	0.926768359580969
74	0.0550597230095784	0.110119446019157	0.944940276990422
75	0.0518330382366269	0.103666076473254	0.948166961763373
76	0.037731074578261	0.075462149156522	0.962268925421739
77	0.0268609783358812	0.0537219566717625	0.973139021664119
78	0.0515350464711942	0.103070092942388	0.948464953528806
79	0.0395604141668958	0.0791208283337916	0.960439585833104
80	0.0315712673280729	0.0631425346561459	0.968428732671927
81	0.0326703219683390	0.0653406439366779	0.96732967803166
82	0.0459672206284862	0.0919344412569724	0.954032779371514
83	0.0495145937709292	0.0990291875418584	0.950485406229071
84	0.0409567174607528	0.0819134349215056	0.959043282539247
85	0.0388505725860461	0.0777011451720923	0.961149427413954
86	0.0380400078687497	0.0760800157374993	0.96195999213125
87	0.0408001744857374	0.0816003489714748	0.959199825514263
88	0.0666608824373679	0.133321764874736	0.933339117562632
89	0.0757153169564178	0.151430633912836	0.924284683043582
90	0.168870685815514	0.337741371631029	0.831129314184486
91	0.145900190666660	0.291800381333320	0.85409980933334
92	0.120589234685003	0.241178469370006	0.879410765314997
93	0.337613249115416	0.675226498230832	0.662386750884584
94	0.820442833476827	0.359114333046346	0.179557166523173
95	0.806341810315515	0.387316379368969	0.193658189684485
96	0.739632792923978	0.520734414152044	0.260367207076022
97	0.671523598380301	0.656952803239398	0.328476401619699
98	0.561190956565698	0.877618086868604	0.438809043434302
99	0.44911625377153	0.89823250754306	0.55088374622847
100	0.307382446760291	0.614764893520581	0.69261755323971

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	14	0.145833333333333	NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/19/t1261236675h1gbx7eh7qrcq1z/10q3cq1261236596.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/19/t1261236675h1gbx7eh7qrcq1z/10q3cq1261236596.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/19/t1261236675h1gbx7eh7qrcq1z/1br2i1261236596.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/19/t1261236675h1gbx7eh7qrcq1z/1br2i1261236596.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/19/t1261236675h1gbx7eh7qrcq1z/2bpw31261236596.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/19/t1261236675h1gbx7eh7qrcq1z/2bpw31261236596.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/19/t1261236675h1gbx7eh7qrcq1z/3aaal1261236596.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/19/t1261236675h1gbx7eh7qrcq1z/3aaal1261236596.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/19/t1261236675h1gbx7eh7qrcq1z/4o24s1261236596.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/19/t1261236675h1gbx7eh7qrcq1z/4o24s1261236596.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/19/t1261236675h1gbx7eh7qrcq1z/5aakw1261236596.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/19/t1261236675h1gbx7eh7qrcq1z/5aakw1261236596.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/19/t1261236675h1gbx7eh7qrcq1z/6dzgs1261236596.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/19/t1261236675h1gbx7eh7qrcq1z/6dzgs1261236596.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/19/t1261236675h1gbx7eh7qrcq1z/7rvcu1261236596.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/19/t1261236675h1gbx7eh7qrcq1z/7rvcu1261236596.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/19/t1261236675h1gbx7eh7qrcq1z/89g4p1261236596.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/19/t1261236675h1gbx7eh7qrcq1z/89g4p1261236596.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/19/t1261236675h1gbx7eh7qrcq1z/9twl31261236596.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/19/t1261236675h1gbx7eh7qrcq1z/9twl31261236596.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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