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workshop 7 data 2

*Unverified author*
R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)
Title produced by software: Multiple Regression
Date of computation: Fri, 20 Nov 2009 11:14:50 -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/Nov/20/t1258741016sykxmfxq11fztdq.htm/, Retrieved Fri, 20 Nov 2009 19:17:08 +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/Nov/20/t1258741016sykxmfxq11fztdq.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 «
543 0 594 0 611 0 613 0 611 0 594 0 595 0 591 0 589 0 584 0 573 0 567 0 569 0 621 0 629 0 628 0 612 0 595 0 597 0 593 0 590 0 580 0 574 0 573 0 573 0 620 0 626 0 620 0 588 0 566 0 557 0 561 0 549 0 532 0 526 0 511 0 499 0 555 0 565 0 542 0 527 0 510 0 514 0 517 0 508 0 493 0 490 0 469 1 478 1 528 1 534 1 518 1 506 1 502 1 516 1 528 1 533 1 536 1 537 1 524 1 536 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 time4 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
Yt[t] = + 616.551900582166 + 7.38444103238997X[t] -1.95296039659737t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)616.5519005821668.11310475.994600
X7.3844410323899712.2828560.60120.550050.275025
t-1.952960396597370.29336-6.657200


Multiple Linear Regression - Regression Statistics
Multiple R0.766800045961603
R-squared0.587982310486717
Adjusted R-squared0.573774803951776
F-TEST (value)41.3853274704243
F-TEST (DF numerator)2
F-TEST (DF denominator)58
p-value6.80078215964386e-12
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation27.6374538885241
Sum Squared Residuals44302.0737315372


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
1543614.598940185571-71.5989401855713
2594612.645979788972-18.6459797889719
3611610.6930193923750.306980607625428
4613608.7400589957774.25994100422288
5611606.787098599184.21290140082024
6594604.834138202582-10.8341382025824
7595602.881177805985-7.88117780598502
8591600.928217409388-9.92821740938765
9589598.97525701279-9.97525701279028
10584597.022296616193-13.0222966161929
11573595.069336219596-22.0693362195955
12567593.116375822998-26.1163758229982
13569591.1634154264-22.1634154264008
14621589.21045502980331.7895449701966
15629587.25749463320641.7425053667939
16628585.30453423660942.6954657633913
17612583.35157384001128.6484261599887
18595581.39861344341413.6013865565860
19597579.44565304681717.5543469531834
20593577.49269265021915.5073073497808
21590575.53973225362214.4602677463782
22580573.5867718570246.41322814297552
23574571.6338114604272.36618853957289
24573569.680851063833.31914893617026
25573567.7278906672325.27210933276763
26620565.77493027063554.225069729365
27626563.82196987403862.1780301259624
28620561.8690094774458.1309905225597
29588559.91604908084328.0839509191571
30566557.9630886842468.03691131575447
31557556.0101282876480.989871712351839
32561554.0571678910516.94283210894921
33549552.104207494453-3.10420749445342
34532550.151247097856-18.1512470978561
35526548.198286701259-22.1982867012587
36511546.245326304661-35.2453263046613
37499544.292365908064-45.2923659080639
38555542.33940551146712.6605944885334
39565540.38644511486924.6135548851308
40542538.4334847182723.56651528172816
41527536.480524321674-9.48052432167447
42510534.527563925077-24.5275639250771
43514532.57460352848-18.5746035284797
44517530.621643131882-13.6216431318824
45508528.668682735285-20.668682735285
46493526.715722338688-33.7157223386876
47490524.76276194209-34.7627619420903
48469530.194242577883-61.1942425778829
49478528.241282181286-50.2412821812855
50528526.2883217846881.71167821531184
51534524.3353613880919.6646386119092
52518522.382400991493-4.38240099149343
53506520.429440594896-14.4294405948961
54502518.476480198299-16.4764801982987
55516516.523519801701-0.523519801701317
56528514.57055940510413.4294405948960
57533512.61759900850720.3824009914934
58536510.66463861190925.3353613880908
59537508.71167821531228.2883217846882
60524506.75871781871417.2412821812855
61536504.80575742211731.1942425778829


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
60.6035617709783990.7928764580432020.396438229021601
70.5380781115901270.9238437768197460.461921888409873
80.4677993727459830.9355987454919650.532200627254017
90.3880824495150540.7761648990301080.611917550484946
100.3246655999146990.6493311998293990.6753344000853
110.3110134584195980.6220269168391950.688986541580402
120.3105101718131400.6210203436262810.68948982818686
130.2866245176613770.5732490353227530.713375482338623
140.3877568371339480.7755136742678960.612243162866052
150.4542024991140230.9084049982280470.545797500885977
160.4466267705869960.8932535411739920.553373229413004
170.3622712343638140.7245424687276280.637728765636186
180.2985735062415710.5971470124831430.701426493758429
190.2347333471706280.4694666943412550.765266652829372
200.1846498424914730.3692996849829450.815350157508527
210.1445057397259260.2890114794518510.855494260274074
220.1258939867500050.2517879735000110.874106013249994
230.1154390462648390.2308780925296790.884560953735161
240.09978365458784860.1995673091756970.900216345412151
250.08057012812332010.1611402562466400.91942987187668
260.1043062720875600.2086125441751210.89569372791244
270.1830484833267680.3660969666535360.816951516673232
280.3158553832360490.6317107664720970.684144616763951
290.3632375279035430.7264750558070850.636762472096457
300.4214246211928120.8428492423856240.578575378807188
310.4875334819401950.975066963880390.512466518059805
320.558242535112510.883514929774980.44175746488749
330.628954527745440.7420909445091210.371045472254561
340.6931750445704130.6136499108591740.306824955429587
350.730130660730950.5397386785381010.269869339269050
360.7734512418170270.4530975163659460.226548758182973
370.8292382374116740.3415235251766510.170761762588325
380.8590213928466210.2819572143067580.140978607153379
390.9580182865657890.08396342686842220.0419817134342111
400.9811893633111850.03762127337763060.0188106366888153
410.9874072711587730.02518545768245370.0125927288412268
420.984983106912230.03003378617553800.0150168930877690
430.9831429984189130.03371400316217440.0168570015810872
440.9848420096768130.03031598064637320.0151579903231866
450.982819391877370.03436121624525770.0171806081226288
460.9734163331287930.05316733374241490.0265836668712074
470.9574155859121930.08516882817561370.0425844140878068
480.9738671111754510.05226577764909780.0261328888245489
490.9934012098039740.01319758039205180.00659879019602592
500.991646213848790.01670757230242080.00835378615121039
510.997296524249070.005406951501857960.00270347575092898
520.9953270724892650.009345855021470.004672927510735
530.985498006193530.02900398761294070.0145019938064704
540.9867908487246580.02641830255068300.0132091512753415
550.9803209167184750.03935816656305020.0196790832815251


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level20.04NOK
5% type I error level130.26NOK
10% type I error level170.34NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258741016sykxmfxq11fztdq/10zn5u1258740885.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258741016sykxmfxq11fztdq/10zn5u1258740885.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258741016sykxmfxq11fztdq/1snmy1258740885.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258741016sykxmfxq11fztdq/1snmy1258740885.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258741016sykxmfxq11fztdq/2axol1258740885.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258741016sykxmfxq11fztdq/2axol1258740885.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258741016sykxmfxq11fztdq/3u0ab1258740885.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258741016sykxmfxq11fztdq/3u0ab1258740885.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258741016sykxmfxq11fztdq/48slz1258740885.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258741016sykxmfxq11fztdq/48slz1258740885.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258741016sykxmfxq11fztdq/5hr961258740885.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258741016sykxmfxq11fztdq/5hr961258740885.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258741016sykxmfxq11fztdq/6dk901258740885.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258741016sykxmfxq11fztdq/6dk901258740885.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258741016sykxmfxq11fztdq/7n3a51258740885.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258741016sykxmfxq11fztdq/7n3a51258740885.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258741016sykxmfxq11fztdq/8pkrj1258740885.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258741016sykxmfxq11fztdq/8pkrj1258740885.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258741016sykxmfxq11fztdq/9813w1258740885.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258741016sykxmfxq11fztdq/9813w1258740885.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')
}
 





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