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*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: Thu, 11 Dec 2008 14:57:33 -0700
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/11/t1229032752tla7fpf4rk7mf9x.htm/, Retrieved Thu, 11 Dec 2008 21:59:12 +0000
 
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/2008/Dec/11/t1229032752tla7fpf4rk7mf9x.htm/},
    year = {2008},
}
@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 = {2008},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}
 
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
 
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Original text written by user:
 
IsPrivate?
No (this computation is public)
 
User-defined keywords:
 
Dataseries X:
» Textbox « » Textfile « » CSV «
103.3 0 101.2 0 107.7 0 110.4 0 101.9 0 115.9 0 89.9 0 88.6 0 117.2 0 123.9 0 100 0 103.6 0 94.1 0 98.7 0 119.5 0 112.7 0 104.4 0 124.7 0 89.1 0 97 0 121.6 0 118.8 0 114 0 111.5 0 97.2 0 102.5 0 113.4 0 109.8 0 104.9 0 126.1 0 80 0 96.8 0 117.2 1 112.3 1 117.3 1 111.1 1 102.2 1 104.3 1 122.9 1 107.6 1 121.3 1 131.5 1 89 1 104.4 1 128.9 1 135.9 1 133.3 1 121.3 1 120.5 1 120.4 1 137.9 1 126.1 1 133.2 1 151.1 1 105 1 119 1 140.4 1 156.6 1 137.1 1 122.7 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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time8 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001


Multiple Linear Regression - Estimated Regression Equation
metaal[t] = + 96.0083333333333 -0.997222222222228conjunctuur[t] -5.08694444444447M1[t] -3.64444444444444M2[t] + 10.6980555555556M3[t] + 3.22055555555556M4[t] + 2.52305555555556M5[t] + 18.7255555555556M6[t] -21.0519444444444M7[t] -11.0094444444444M8[t] + 12.5725M9[t] + 16.495M10[t] + 6.8175M11[t] + 0.5175t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)96.00833333333333.87639524.767400
conjunctuur-0.9972222222222283.730063-0.26730.7903970.395198
M1-5.086944444444474.523743-1.12450.2666350.133318
M2-3.644444444444444.512194-0.80770.4234270.211714
M310.69805555555564.5031922.37570.021740.01087
M43.220555555555564.496750.71620.4774910.238745
M52.523055555555564.4928810.56160.5771370.288568
M618.72555555555564.491594.1690.0001346.7e-05
M7-21.05194444444444.492881-4.68562.5e-051.3e-05
M8-11.00944444444444.49675-2.44830.0182260.009113
M912.57254.4877172.80150.0074160.003708
M1016.4954.4812533.68090.0006090.000304
M116.81754.477371.52270.134690.067345
t0.51750.1076784.8061.7e-058e-06


Multiple Linear Regression - Regression Statistics
Multiple R0.916870594178745
R-squared0.840651686469685
Adjusted R-squared0.795618467428509
F-TEST (value)18.6673683198404
F-TEST (DF numerator)13
F-TEST (DF denominator)46
p-value3.98570065840431e-14
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation7.07729666040103
Sum Squared Residuals2304.05388888889


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
1103.391.43888888888911.861111111111
2101.293.39888888888897.80111111111112
3107.7108.258888888889-0.558888888888885
4110.4101.2988888888899.10111111111113
5101.9101.1188888888890.781111111111119
6115.9117.838888888889-1.93888888888887
789.978.578888888888911.3211111111111
888.689.1388888888889-0.53888888888889
9117.2113.2383333333333.96166666666667
10123.9117.6783333333336.22166666666668
11100108.518333333333-8.51833333333334
12103.6102.2183333333331.38166666666666
1394.197.6488888888889-3.54888888888887
1498.799.6088888888889-0.908888888888883
15119.5114.4688888888895.03111111111111
16112.7107.5088888888895.19111111111111
17104.4107.328888888889-2.92888888888888
18124.7124.0488888888890.651111111111116
1989.184.78888888888894.31111111111111
209795.34888888888891.65111111111111
21121.6119.4483333333332.15166666666666
22118.8123.888333333333-5.08833333333333
23114114.728333333333-0.72833333333333
24111.5108.4283333333333.07166666666667
2597.2103.858888888889-6.65888888888886
26102.5105.818888888889-3.31888888888889
27113.4120.678888888889-7.27888888888889
28109.8113.718888888889-3.91888888888889
29104.9113.538888888889-8.63888888888889
30126.1130.258888888889-4.15888888888890
318090.9988888888889-10.9988888888889
3296.8101.558888888889-4.7588888888889
33117.2124.661111111111-7.46111111111111
34112.3129.101111111111-16.8011111111111
35117.3119.941111111111-2.64111111111111
36111.1113.641111111111-2.54111111111111
37102.2109.071666666667-6.87166666666663
38104.3111.031666666667-6.73166666666667
39122.9125.891666666667-2.99166666666666
40107.6118.931666666667-11.3316666666667
41121.3118.7516666666672.54833333333333
42131.5135.471666666667-3.97166666666667
438996.2116666666667-7.21166666666667
44104.4106.771666666667-2.37166666666666
45128.9130.871111111111-1.97111111111111
46135.9135.3111111111110.588888888888891
47133.3126.1511111111117.1488888888889
48121.3119.8511111111111.44888888888889
49120.5115.2816666666675.21833333333336
50120.4117.2416666666673.15833333333333
51137.9132.1016666666675.79833333333333
52126.1125.1416666666670.958333333333324
53133.2124.9616666666678.23833333333332
54151.1141.6816666666679.41833333333332
55105102.4216666666672.57833333333333
56119112.9816666666676.01833333333333
57140.4137.0811111111113.31888888888889
58156.6141.52111111111115.0788888888889
59137.1132.3611111111114.73888888888888
60122.7126.061111111111-3.36111111111111


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.628974126225040.7420517475499210.371025873774960
180.5676008337260230.8647983325479530.432399166273977
190.5507881099708930.8984237800582140.449211890029107
200.5394916059842220.9210167880315550.460508394015778
210.4942792676213120.9885585352426240.505720732378688
220.4786481835191380.9572963670382760.521351816480862
230.570813299397590.858373401204820.42918670060241
240.663513220411110.672973559177780.33648677958889
250.6234482127234130.7531035745531750.376551787276587
260.5510267400984540.8979465198030920.448973259901546
270.4708769882764130.9417539765528270.529123011723587
280.5006126266736140.9987747466527710.499387373326386
290.4414024192403380.8828048384806750.558597580759662
300.3584561922237810.7169123844475610.641543807776219
310.4494758769458590.8989517538917190.550524123054141
320.3560687985023480.7121375970046960.643931201497652
330.2768267550793960.5536535101587930.723173244920604
340.5107318269731090.9785363460537820.489268173026891
350.5755145194886990.8489709610226030.424485480511301
360.643229787481980.7135404250360410.356770212518020
370.5740160029449340.8519679941101330.425983997055066
380.4715240775112270.9430481550224540.528475922488773
390.394035872738330.788071745476660.60596412726167
400.3580764045093710.7161528090187420.641923595490629
410.3539006150222030.7078012300444070.646099384977797
420.3271412263130130.6542824526260260.672858773686987
430.2323456299444710.4646912598889430.767654370055529


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level00OK
10% type I error level00OK
 
Charts produced by software:
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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/11/t1229032752tla7fpf4rk7mf9x/2gncz1229032639.ps (open in new window)


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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/11/t1229032752tla7fpf4rk7mf9x/3bp1h1229032639.ps (open in new window)


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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/11/t1229032752tla7fpf4rk7mf9x/5ijr41229032639.ps (open in new window)


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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/11/t1229032752tla7fpf4rk7mf9x/6nk4e1229032639.ps (open in new window)


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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/11/t1229032752tla7fpf4rk7mf9x/7bxq61229032639.ps (open in new window)


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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/11/t1229032752tla7fpf4rk7mf9x/84lfi1229032639.ps (open in new window)


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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/11/t1229032752tla7fpf4rk7mf9x/942061229032639.ps (open in new window)


 
Parameters (Session):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;
 
Parameters (R input):
par1 = 1 ; par2 = Include Monthly 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')
}
 





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