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WS 7 Multiple regression 5

*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, 19 Nov 2009 13:16:00 -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/19/t12586619214nij0dxde3padqy.htm/, Retrieved Thu, 19 Nov 2009 21:18:54 +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/19/t12586619214nij0dxde3padqy.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 «
119,93 111,4 101,21 108,01 94,76 87,4 119,93 101,21 95,26 96,8 94,76 119,93 117,96 114,1 95,26 94,76 115,86 110,3 117,96 95,26 111,44 103,9 115,86 117,96 108,16 101,6 111,44 115,86 108,77 94,6 108,16 111,44 109,45 95,9 108,77 108,16 124,83 104,7 109,45 108,77 115,31 102,8 124,83 109,45 109,49 98,1 115,31 124,83 124,24 113,9 109,49 115,31 92,85 80,9 124,24 109,49 98,42 95,7 92,85 124,24 120,88 113,2 98,42 92,85 111,72 105,9 120,88 98,42 116,1 108,8 111,72 120,88 109,37 102,3 116,1 111,72 111,65 99 109,37 116,1 114,29 100,7 111,65 109,37 133,68 115,5 114,29 111,65 114,27 100,7 133,68 114,29 126,49 109,9 114,27 133,68 131 114,6 126,49 114,27 104 85,4 131 126,49 108,88 100,5 104 131 128,48 114,8 108,88 104 132,44 116,5 128,48 108,88 128,04 112,9 132,44 128,48 116,35 102 128,04 132,44 120,93 106 116,35 128,04 118,59 105,3 120,93 116,35 133,1 118,8 118,59 120,93 121,05 106,1 133,1 118,59 127,62 109,3 121,05 133,1 135,44 117,2 127,62 121,05 114,88 92,5 135,44 127,62 114,34 104,2 etc...
 
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 time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
Y[t] = -50.9640522907201 + 1.07016114979443X[t] + 0.173985757105798Y1[t] + 0.293977711131534Y2[t] + 1.59007716465838M1[t] + 4.34909964071228M2[t] -6.16808657058887M3[t] + 5.25575586956772M4[t] + 2.64205857405578M5[t] -3.92509865437882M6[t] -2.86912893355579M7[t] + 2.20031881493963M8[t] + 3.4871885785655M9[t] + 5.68632854743579M10[t] + 1.38569107000666M11[t] + 0.0128020945805415t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)-50.96405229072019.03349-5.64171e-061e-06
X1.070161149794430.07956513.450200
Y10.1739857571057980.0615562.82650.0071770.003588
Y20.2939777111315340.0688684.26870.000115.5e-05
M11.590077164658382.0571630.77290.4438820.221941
M24.349099640712282.4661781.76350.0850910.042545
M3-6.168086570588872.035795-3.02980.0041760.002088
M45.255755869567722.6180432.00750.0511580.025579
M52.642058574055782.6556490.99490.3254910.162745
M6-3.925098654378821.846348-2.12590.0394360.019718
M7-2.869128933555791.846323-1.5540.1276960.063848
M82.200318814939631.9296781.14030.2606420.130321
M93.48718857856552.1218851.64340.1077590.053879
M105.686328547435792.2033472.58080.0134420.006721
M111.385691070006662.1984150.63030.5319040.265952
t0.01280209458054150.0320640.39930.6917170.345859


Multiple Linear Regression - Regression Statistics
Multiple R0.980850670429848
R-squared0.962068037682683
Adjusted R-squared0.948520908283641
F-TEST (value)71.0163761889459
F-TEST (DF numerator)15
F-TEST (DF denominator)42
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation2.65910913178632
Sum Squared Residuals296.976177739476


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
1119.93119.2164101116130.713589888387024
294.7697.5623320245071-2.80233202450712
395.2698.2415039618835-2.98150396188351
4117.96120.879510277436-2.91951027743645
5115.86118.308468249154-2.4484682491536
6111.44111.2130057093790.226994290621141
7108.16108.434036640471-0.274036640471373
8108.77104.1551036684784.61489633152204
9109.45105.9878694407403.46213055925976
10124.83117.9148663410046.91513365899579
11115.31114.4695305614030.840469438597184
12109.49110.931916971499-1.44191697149868
13124.24125.632077481162-1.39207748116161
1492.8593.943923747105-1.09392374710498
1598.4298.1526829709810.267317029019022
16120.88120.0582879417810.821712058218956
17111.72115.190392302949-3.47039230294921
18116.1116.748534360424-0.648534360424116
19109.37108.9304804843220.43951951567756
20111.65110.5978967625111.05210323748911
21114.29112.1350601056542.15493989434616
22133.68131.3149787662012.36502123379860
23114.27115.338443354064-1.06844335406398
24126.49126.1342012301630.355798769836524
25131129.1868364722061.81316352779402
26104105.087038863418-1.08703886341766
27108.88107.3703121439401.50968785606044
28128.48127.0219134148621.45808658513812
29132.44131.0850242381771.35497576182347
30128.04127.1290357013800.91096429862042
31116.35116.931665388839-0.581665388839237
32120.93122.967164401547-2.03716440154736
33118.59120.877978779315-2.28797877931461
34133.1138.476387610345-5.37638761034508
35121.05122.434131116665-1.38413111666460
36127.62126.6548460359740.965153964025679
37135.44134.3126533836391.12734661636065
38114.88113.9434997370530.936500262947035
39114.34114.681759607881-0.341759607880524
40128.85128.86260763621-0.0126076362099425
41138.9139.222093189837-0.32209318983747
42129.44128.9434450402860.496554959714038
43114.96117.087644298075-2.12764429807471
44127.98128.320275533755-0.340275533754762
45127.03129.875783106862-2.84578310686236
46128.75132.539545050612-3.78954505061198
47137.91136.2978949678691.61210503213140
48128.37128.2490357623640.120964237636472
49135.9138.16202255138-2.26202255138009
50122.19118.1432056279174.04679437208273
51113.08111.5337413153151.54625868468456
52136.2135.5476807297110.652319270289317
53138133.1140220198834.88597798011681
54115.24116.225979188531-0.985979188531487
55110.95108.4061731882922.54382681170776
5699.23102.519559633709-3.28955963370902
57102.39102.873308567429-0.483308567428939
58112.67112.784222231837-0.114222231837341


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
190.4517427237684340.9034854475368690.548257276231566
200.3871567936930910.7743135873861810.612843206306909
210.31715034372780.63430068745560.6828496562722
220.3768086832416540.7536173664833070.623191316758346
230.2851609558182190.5703219116364380.714839044181781
240.5962868790607390.8074262418785230.403713120939262
250.7628765604026850.4742468791946310.237123439597315
260.7007652017073460.5984695965853070.299234798292653
270.6907703627272570.6184592745454860.309229637272743
280.6205512915075810.7588974169848370.379448708492419
290.657466436138810.6850671277223790.342533563861189
300.5695940054232970.8608119891534050.430405994576703
310.5052275388004120.9895449223991770.494772461199588
320.5965537156743670.8068925686512650.403446284325633
330.6812065375167120.6375869249665770.318793462483288
340.8194171369109290.3611657261781410.180582863089071
350.719778776644510.5604424467109810.280221223355491
360.6386671517318450.722665696536310.361332848268155
370.6945000987686530.6109998024626930.305499901231347
380.5785466661331620.8429066677336760.421453333866838
390.4033528343136030.8067056686272050.596647165686397


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:
http://www.freestatistics.org/blog/date/2009/Nov/19/t12586619214nij0dxde3padqy/10rjvy1258661756.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/19/t12586619214nij0dxde3padqy/269we1258661756.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/19/t12586619214nij0dxde3padqy/380yp1258661756.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/19/t12586619214nij0dxde3padqy/63c431258661756.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/19/t12586619214nij0dxde3padqy/7y9nr1258661756.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/19/t12586619214nij0dxde3padqy/8zmlu1258661756.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/19/t12586619214nij0dxde3padqy/9bto71258661756.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t12586619214nij0dxde3padqy/9bto71258661756.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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Software written by Ed van Stee & Patrick Wessa


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