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Paper Dummy Variables

*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, 16 Dec 2008 12:45:52 -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/16/t12294568213j6yoygckibd5kc.htm/, Retrieved Tue, 16 Dec 2008 20:47:01 +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/2008/Dec/16/t12294568213j6yoygckibd5kc.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},
}
 
Original text written by user:
 
IsPrivate?
No (this computation is public)
 
User-defined keywords:
 
Dataseries X:
» Textbox « » Textfile « » CSV «
94.7 0 101.8 0 102.5 0 105.3 0 110.3 0 109.8 0 117.3 0 118.8 0 131.3 0 125.9 0 133.1 0 147 0 145.8 0 164.4 0 149.8 0 137.7 0 151.7 0 156.8 0 180 0 180.4 0 170.4 0 191.6 0 199.5 0 218.2 1 217.5 1 205 1 194 0 199.3 0 219.3 1 211.1 1 215.2 1 240.2 1 242.2 1 240.7 1 255.4 1 253 1 218.2 1 203.7 1 205.6 1 215.6 1 188.5 1 202.9 1 214 1 230.3 1 230 1 241 1 259.6 1 247.8 1 270.3 1 289.7 1 322.7 1 315 1 320.2 1 329.5 1 360.6 1 382.2 1 435.4 1 464 1 468.8 1 403 1 351.6 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 time6 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24


Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 144.768 + 129.898666666667D[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)144.76812.79734211.312300
D129.89866666666716.6584067.797800


Multiple Linear Regression - Regression Statistics
Multiple R0.712414843906071
R-squared0.507534909817711
Adjusted R-squared0.499188043882418
F-TEST (value)60.8054464696387
F-TEST (DF numerator)1
F-TEST (DF denominator)59
p-value1.20324861185850e-10
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation63.9867113322653
Sum Squared Residuals241563.6544


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
194.7144.768-50.0679999999999
2101.8144.768-42.9680000000001
3102.5144.768-42.268
4105.3144.768-39.468
5110.3144.768-34.468
6109.8144.768-34.968
7117.3144.768-27.468
8118.8144.768-25.968
9131.3144.768-13.468
10125.9144.768-18.868
11133.1144.768-11.6680000000000
12147144.7682.232
13145.8144.7681.03200000000001
14164.4144.76819.632
15149.8144.7685.03200000000001
16137.7144.768-7.06800000000002
17151.7144.7686.93199999999999
18156.8144.76812.0320000000000
19180144.76835.232
20180.4144.76835.632
21170.4144.76825.632
22191.6144.76846.832
23199.5144.76854.732
24218.2274.666666666667-56.4666666666667
25217.5274.666666666667-57.1666666666667
26205274.666666666667-69.6666666666667
27194144.76849.232
28199.3144.76854.532
29219.3274.666666666667-55.3666666666667
30211.1274.666666666667-63.5666666666667
31215.2274.666666666667-59.4666666666667
32240.2274.666666666667-34.4666666666667
33242.2274.666666666667-32.4666666666667
34240.7274.666666666667-33.9666666666667
35255.4274.666666666667-19.2666666666667
36253274.666666666667-21.6666666666667
37218.2274.666666666667-56.4666666666667
38203.7274.666666666667-70.9666666666667
39205.6274.666666666667-69.0666666666667
40215.6274.666666666667-59.0666666666667
41188.5274.666666666667-86.1666666666667
42202.9274.666666666667-71.7666666666667
43214274.666666666667-60.6666666666667
44230.3274.666666666667-44.3666666666667
45230274.666666666667-44.6666666666667
46241274.666666666667-33.6666666666667
47259.6274.666666666667-15.0666666666666
48247.8274.666666666667-26.8666666666667
49270.3274.666666666667-4.36666666666665
50289.7274.66666666666715.0333333333333
51322.7274.66666666666748.0333333333333
52315274.66666666666740.3333333333333
53320.2274.66666666666745.5333333333333
54329.5274.66666666666754.8333333333333
55360.6274.66666666666785.9333333333334
56382.2274.666666666667107.533333333333
57435.4274.666666666667160.733333333333
58464274.666666666667189.333333333333
59468.8274.666666666667194.133333333333
60403274.666666666667128.333333333333
61351.6274.66666666666776.9333333333334


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
50.001405292625403860.002810585250807720.998594707374596
60.0001958689924987850.0003917379849975710.999804131007501
78.02075444807798e-050.0001604150889615600.99991979245552
82.58913485624334e-055.17826971248669e-050.999974108651438
93.7892565574932e-057.5785131149864e-050.999962107434425
101.36201601058841e-052.72403202117682e-050.999986379839894
118.36022136617385e-061.67204427323477e-050.999991639778634
121.58338237394955e-053.16676474789911e-050.99998416617626
131.36772237625704e-052.73544475251408e-050.999986322776237
143.86081388609191e-057.72162777218382e-050.99996139186114
152.29771657379327e-054.59543314758653e-050.999977022834262
168.19707425877212e-061.63941485175442e-050.999991802925741
174.70098357439579e-069.40196714879158e-060.999995299016426
183.16811807288251e-066.33623614576502e-060.999996831881927
197.53975382511244e-061.50795076502249e-050.999992460246175
201.14283789648216e-052.28567579296431e-050.999988571621035
218.56642897985676e-061.71328579597135e-050.99999143357102
221.48189633721079e-052.96379267442158e-050.999985181036628
232.73764049054581e-055.47528098109163e-050.999972623595095
241.19112283377746e-052.38224566755492e-050.999988088771662
255.14901647224441e-061.02980329444888e-050.999994850983528
262.52299810194725e-065.04599620389451e-060.999997477001898
273.06809110942965e-066.1361822188593e-060.99999693190889
283.86442241994174e-067.72884483988348e-060.99999613557758
291.77195621072267e-063.54391242144533e-060.99999822804379
308.62602671645233e-071.72520534329047e-060.999999137397328
314.10824798166279e-078.21649596332559e-070.999999589175202
322.10197696377074e-074.20395392754148e-070.999999789802304
331.03539886231574e-072.07079772463149e-070.999999896460114
344.79131042462929e-089.58262084925858e-080.999999952086896
352.62308511152649e-085.24617022305298e-080.999999973769149
361.27434052842484e-082.54868105684967e-080.999999987256595
376.76909337667732e-091.35381867533546e-080.999999993230907
385.81388340566969e-091.16277668113394e-080.999999994186117
395.13422990538869e-091.02684598107774e-080.99999999486577
403.77753325955153e-097.55506651910307e-090.999999996222467
411.04301252358051e-082.08602504716102e-080.999999989569875
421.90951249321186e-083.81902498642372e-080.999999980904875
433.22458150132755e-086.4491630026551e-080.999999967754185
444.90465370159535e-089.8093074031907e-080.999999950953463
451.10539094573963e-072.21078189147926e-070.999999889460905
463.04736994623648e-076.09473989247297e-070.999999695263005
479.53542945107505e-071.90708589021501e-060.999999046457055
486.43280447507626e-061.28656089501525e-050.999993567195525
494.6265267915978e-059.2530535831956e-050.999953734732084
500.0003343274777811720.0006686549555623430.999665672522219
510.001711324535679620.003422649071359250.99828867546432
520.007047255446319680.01409451089263940.99295274455368
530.02680326522684350.05360653045368710.973196734773156
540.0899045743247570.1798091486495140.910095425675243
550.1579032625575520.3158065251151040.842096737442448
560.1849219487301330.3698438974602660.815078051269867


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level470.903846153846154NOK
5% type I error level480.923076923076923NOK
10% type I error level490.942307692307692NOK
 
Charts produced by software:
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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')
}
 





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Software written by Ed van Stee & Patrick Wessa


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