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multiple regression

*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, 05 Dec 2009 08:21:45 -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/05/t1260027076a7umdhikxr4vno0.htm/, Retrieved Sat, 05 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/05/t1260027076a7umdhikxr4vno0.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 «

9051 0 8823 0 8776 0 8255 0 7969 0 8758 0 8693 0 8271 0 7790 0 7769 0 8170 0 8209 0 9395 0 9260 0 9018 0 8501 0 8500 0 9649 0 9319 0 8830 0 8436 0 8169 0 8269 0 7945 0 9144 0 8770 0 8834 0 7837 0 7792 0 8616 0 8518 0 7940 0 7545 0 7531 0 7665 0 7599 0 8444 0 8549 0 7986 0 7335 0 7287 0 7870 0 7839 0 7327 0 7259 0 6964 0 7271 0 6956 0 7608 0 7692 0 7255 0 6804 0 6655 0 7341 0 7602 0 7086 0 6625 0 6272 0 6576 0 6491 0 7649 0 7400 0 6913 0 6532 0 6486 0 7295 0 7556 0 7088 1 6952 1 6773 1 6917 1 7371 1 8221 1 7953 1 8027 1 7287 1 8076 1 8933 1 9433 1 9479 1 9199 1 9469 1 10015 1 10999 1 13009 1 13699 1 13895 1 13248 1 13973 1 15095 1 15201 1 14823 1 14538 1 14547 1 14407 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	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation

Y[t] = + 7888.67164179105 + 2776.57835820895X[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)	7888.67164179105	220.688658	35.7457	0	0
X	2776.57835820895	406.502107	6.8304	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.577988961847573
R-squared	0.334071240017635
Adjusted R-squared	0.326910715716750
F-TEST (value)	46.6545780699768
F-TEST (DF numerator)	1
F-TEST (DF denominator)	93
p-value	8.61620108594252e-10
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	1806.41452043425
Sum Squared Residuals	303471408.026119

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	9051	7888.67164179103	1162.32835820897
2	8823	7888.67164179104	934.328358208957
3	8776	7888.67164179104	887.328358208955
4	8255	7888.67164179104	366.328358208955
5	7969	7888.67164179104	80.328358208955
6	8758	7888.67164179104	869.328358208955
7	8693	7888.67164179104	804.328358208955
8	8271	7888.67164179104	382.328358208955
9	7790	7888.67164179104	-98.671641791045
10	7769	7888.67164179104	-119.671641791045
11	8170	7888.67164179104	281.328358208955
12	8209	7888.67164179104	320.328358208955
13	9395	7888.67164179104	1506.32835820896
14	9260	7888.67164179104	1371.32835820896
15	9018	7888.67164179104	1129.32835820896
16	8501	7888.67164179104	612.328358208955
17	8500	7888.67164179104	611.328358208955
18	9649	7888.67164179104	1760.32835820896
19	9319	7888.67164179104	1430.32835820896
20	8830	7888.67164179104	941.328358208955
21	8436	7888.67164179104	547.328358208955
22	8169	7888.67164179104	280.328358208955
23	8269	7888.67164179104	380.328358208955
24	7945	7888.67164179104	56.328358208955
25	9144	7888.67164179104	1255.32835820896
26	8770	7888.67164179104	881.328358208955
27	8834	7888.67164179104	945.328358208955
28	7837	7888.67164179104	-51.671641791045
29	7792	7888.67164179104	-96.671641791045
30	8616	7888.67164179104	727.328358208955
31	8518	7888.67164179104	629.328358208955
32	7940	7888.67164179104	51.328358208955
33	7545	7888.67164179104	-343.671641791045
34	7531	7888.67164179104	-357.671641791045
35	7665	7888.67164179104	-223.671641791045
36	7599	7888.67164179104	-289.671641791045
37	8444	7888.67164179104	555.328358208955
38	8549	7888.67164179104	660.328358208955
39	7986	7888.67164179104	97.328358208955
40	7335	7888.67164179104	-553.671641791045
41	7287	7888.67164179104	-601.671641791045
42	7870	7888.67164179104	-18.6716417910449
43	7839	7888.67164179104	-49.671641791045
44	7327	7888.67164179104	-561.671641791045
45	7259	7888.67164179104	-629.671641791045
46	6964	7888.67164179104	-924.671641791045
47	7271	7888.67164179104	-617.671641791045
48	6956	7888.67164179104	-932.671641791045
49	7608	7888.67164179104	-280.671641791045
50	7692	7888.67164179104	-196.671641791045
51	7255	7888.67164179104	-633.671641791045
52	6804	7888.67164179104	-1084.67164179104
53	6655	7888.67164179104	-1233.67164179104
54	7341	7888.67164179104	-547.671641791045
55	7602	7888.67164179104	-286.671641791045
56	7086	7888.67164179104	-802.671641791045
57	6625	7888.67164179104	-1263.67164179104
58	6272	7888.67164179104	-1616.67164179104
59	6576	7888.67164179104	-1312.67164179104
60	6491	7888.67164179104	-1397.67164179104
61	7649	7888.67164179104	-239.671641791045
62	7400	7888.67164179104	-488.671641791045
63	6913	7888.67164179104	-975.671641791045
64	6532	7888.67164179104	-1356.67164179104
65	6486	7888.67164179104	-1402.67164179104
66	7295	7888.67164179104	-593.671641791045
67	7556	7888.67164179104	-332.671641791045
68	7088	10665.25	-3577.25
69	6952	10665.25	-3713.25
70	6773	10665.25	-3892.25
71	6917	10665.25	-3748.25
72	7371	10665.25	-3294.25
73	8221	10665.25	-2444.25
74	7953	10665.25	-2712.25
75	8027	10665.25	-2638.25
76	7287	10665.25	-3378.25
77	8076	10665.25	-2589.25
78	8933	10665.25	-1732.25
79	9433	10665.25	-1232.25
80	9479	10665.25	-1186.25
81	9199	10665.25	-1466.25
82	9469	10665.25	-1196.25
83	10015	10665.25	-650.25
84	10999	10665.25	333.75
85	13009	10665.25	2343.75
86	13699	10665.25	3033.75
87	13895	10665.25	3229.75
88	13248	10665.25	2582.75
89	13973	10665.25	3307.75
90	15095	10665.25	4429.75
91	15201	10665.25	4535.75
92	14823	10665.25	4157.75
93	14538	10665.25	3872.75
94	14547	10665.25	3881.75
95	14407	10665.25	3741.75

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
5	0.0282534985603525	0.0565069971207049	0.971746501439648
6	0.00678630971856363	0.0135726194371273	0.993213690281436
7	0.00143040869264635	0.0028608173852927	0.998569591307354
8	0.000383222768787568	0.000766445537575136	0.999616777231212
9	0.000334097215063108	0.000668194430126216	0.999665902784937
10	0.000205012088418882	0.000410024176837765	0.999794987911581
11	5.43962744442585e-05	0.000108792548888517	0.999945603725556
12	1.32531381304222e-05	2.65062762608444e-05	0.99998674686187
13	2.20557365529464e-05	4.41114731058927e-05	0.999977944263447
14	1.60151474374326e-05	3.20302948748652e-05	0.999983984852563
15	6.42826746521932e-06	1.28565349304386e-05	0.999993571732535
16	1.71405999983858e-06	3.42811999967715e-06	0.99999828594
17	4.4080701235009e-07	8.8161402470018e-07	0.999999559192988
18	8.38234541824112e-07	1.67646908364822e-06	0.999999161765458
19	5.03167780658305e-07	1.00633556131661e-06	0.99999949683222
20	1.51835047873197e-07	3.03670095746394e-07	0.999999848164952
21	4.44359877803178e-08	8.88719755606357e-08	0.999999955564012
22	1.64939558617211e-08	3.29879117234422e-08	0.999999983506044
23	5.24274667484043e-09	1.04854933496809e-08	0.999999994757253
24	2.65436806618254e-09	5.30873613236509e-09	0.999999997345632
25	1.23952975945155e-09	2.47905951890310e-09	0.99999999876047
26	3.53248785525986e-10	7.06497571051972e-10	0.999999999646751
27	1.04020148541567e-10	2.08040297083133e-10	0.99999999989598
28	6.92311581986717e-11	1.38462316397343e-10	0.99999999993077
29	4.66177224697494e-11	9.32354449394987e-11	0.999999999953382
30	1.26624727267042e-11	2.53249454534084e-11	0.999999999987337
31	3.34193066304222e-12	6.68386132608444e-12	0.999999999996658
32	1.54423429299077e-12	3.08846858598153e-12	0.999999999998456
33	1.76614884829276e-12	3.53229769658551e-12	0.999999999998234
34	1.77132868694403e-12	3.54265737388805e-12	0.999999999998229
35	1.13786126165427e-12	2.27572252330853e-12	0.999999999998862
36	7.8273818467608e-13	1.56547636935216e-12	0.999999999999217
37	2.19916105246470e-13	4.39832210492940e-13	0.99999999999978
38	6.32964321121567e-14	1.26592864224313e-13	0.999999999999937
39	2.18030833929713e-14	4.36061667859426e-14	0.999999999999978
40	2.68539181132149e-14	5.37078362264299e-14	0.999999999999973
41	3.20491037141878e-14	6.40982074283756e-14	0.999999999999968
42	1.16270274262040e-14	2.32540548524079e-14	0.999999999999988
43	4.28230258633098e-15	8.56460517266196e-15	0.999999999999996
44	3.79049321380814e-15	7.58098642761629e-15	0.999999999999996
45	3.55098374850178e-15	7.10196749700357e-15	0.999999999999996
46	6.20132383366803e-15	1.24026476673361e-14	0.999999999999994
47	4.5191056946561e-15	9.0382113893122e-15	0.999999999999996
48	5.99659188757903e-15	1.19931837751581e-14	0.999999999999994
49	2.36245786956794e-15	4.72491573913589e-15	0.999999999999998
50	8.42022231659214e-16	1.68404446331843e-15	1
51	5.12545414536227e-16	1.02509082907245e-15	1
52	7.32646799047137e-16	1.46529359809427e-15	1
53	1.27657565865882e-15	2.55315131731763e-15	0.999999999999999
54	5.74837954563833e-16	1.14967590912767e-15	1
55	1.97910298104689e-16	3.95820596209379e-16	1
56	1.1980075782973e-16	2.3960151565946e-16	1
57	1.62369813479999e-16	3.24739626959997e-16	1
58	4.33284141600166e-16	8.66568283200332e-16	1
59	4.8440266399452e-16	9.6880532798904e-16	1
60	5.77014206560861e-16	1.15402841312172e-15	1
61	1.76138521656478e-16	3.52277043312956e-16	1
62	5.9496520018796e-17	1.18993040037592e-16	1
63	3.14666080510727e-17	6.29332161021454e-17	1
64	2.8592739854673e-17	5.7185479709346e-17	1
65	2.66571924079631e-17	5.33143848159263e-17	1
66	8.66741132170579e-18	1.73348226434116e-17	1
67	2.37182806182964e-18	4.74365612365929e-18	1
68	2.37273597438096e-18	4.74547194876192e-18	1
69	3.29913653892463e-18	6.59827307784926e-18	1
70	7.46380382025737e-18	1.49276076405147e-17	1
71	2.07898685346107e-17	4.15797370692214e-17	1
72	5.70462204037328e-17	1.14092440807466e-16	1
73	1.59559599635218e-16	3.19119199270436e-16	1
74	5.33706820432813e-16	1.06741364086563e-15	1
75	2.48234412083168e-15	4.96468824166336e-15	0.999999999999998
76	6.5450849624582e-14	1.30901699249164e-13	0.999999999999934
77	1.36499553033344e-12	2.72999106066688e-12	0.999999999998635
78	2.71229904723371e-11	5.42459809446742e-11	0.999999999972877
79	6.06851097136876e-10	1.21370219427375e-09	0.999999999393149
80	1.82873071695125e-08	3.65746143390251e-08	0.999999981712693
81	1.76583774099185e-06	3.53167548198369e-06	0.99999823416226
82	0.000354031881625109	0.000708063763250219	0.999645968118375
83	0.0530364891748082	0.106072978349616	0.946963510825192
84	0.722323331451597	0.555353337096805	0.277676668548403
85	0.909938223625944	0.180123552748113	0.0900617763740564
86	0.939628795914862	0.120742408170277	0.0603712040851383
87	0.941002694625346	0.117994610749307	0.0589973053746537
88	0.987657966741125	0.0246840665177505	0.0123420332588753
89	0.991855189746171	0.0162896205076581	0.00814481025382907
90	0.981644073542237	0.0367118529155251	0.0183559264577626

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	76	0.883720930232558	NOK
5% type I error level	80	0.930232558139535	NOK
10% type I error level	81	0.94186046511628	NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/05/t1260027076a7umdhikxr4vno0/10tln01260026500.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/05/t1260027076a7umdhikxr4vno0/10tln01260026500.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/05/t1260027076a7umdhikxr4vno0/1twjj1260026500.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/05/t1260027076a7umdhikxr4vno0/1twjj1260026500.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/05/t1260027076a7umdhikxr4vno0/2nem11260026500.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/05/t1260027076a7umdhikxr4vno0/2nem11260026500.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/05/t1260027076a7umdhikxr4vno0/3vh161260026500.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/05/t1260027076a7umdhikxr4vno0/3vh161260026500.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/05/t1260027076a7umdhikxr4vno0/49cbw1260026500.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/05/t1260027076a7umdhikxr4vno0/49cbw1260026500.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/05/t1260027076a7umdhikxr4vno0/5rmox1260026500.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/05/t1260027076a7umdhikxr4vno0/5rmox1260026500.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/05/t1260027076a7umdhikxr4vno0/6pt3l1260026500.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/05/t1260027076a7umdhikxr4vno0/6pt3l1260026500.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/05/t1260027076a7umdhikxr4vno0/712n31260026500.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/05/t1260027076a7umdhikxr4vno0/712n31260026500.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/05/t1260027076a7umdhikxr4vno0/8jasb1260026500.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/05/t1260027076a7umdhikxr4vno0/8jasb1260026500.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/05/t1260027076a7umdhikxr4vno0/9pjt61260026500.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/05/t1260027076a7umdhikxr4vno0/9pjt61260026500.ps (open in new window)

Parameters (Session):

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