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Multiple Regression - ref.17

*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: Mon, 22 Dec 2008 13:26:15 -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/22/t1229977617ayru1wfyo62rrwe.htm/, Retrieved Mon, 22 Dec 2008 21:26:57 +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/22/t1229977617ayru1wfyo62rrwe.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 «
101.1 103 100.7 102.4 100 102 100 101.8 100.8 101.6 101.9 101.4 102.7 101.3 103.1 101.4 103.5 101.7 103.9 102.4 104.4 103.1 105.2 103.8 106 104.4 107 105 108.2 105.7 109 106.4 109.1 107.1 109.3 107.9 110.1 108.8 110.7 109.6 110.8 110.3 110.7 110.8 110.9 111.2 111.3 111.7 111.6 112.3 111.8 112.8 112.1 113.1 112.3 113.1 112.5 113.1 113 113.2 113.6 113.1 114.4 112.8 114.9 112.5 115.2 112.3 116 112.5 117 112.9 118 113.5 119.4 114.1 121.1 114.6 123.1 114.9 125 115.4 126.3 115.7 127.4 116.1 129 116.5 131 117.1 133.3 117.5 135.9 117.7 138.4 117.7 140.3 117.7 141.7 117.6 143.1 117.5 144.5 117.6 146 117.9 147.7 118.2 149 118.5 149.7 118.7 150.2 118.8 150.5 118.9 150.7 119 150.9 119
 
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 time7 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001


Multiple Linear Regression - Estimated Regression Equation
Transportmiddelen[t] = + 117.173226126416 -0.169843653424948Machines[t] + 0.48124109623738t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)117.1732261264163.15397937.150900
Machines-0.1698436534249480.03383-5.02055e-063e-06
t0.481241096237380.03161515.221700


Multiple Linear Regression - Regression Statistics
Multiple R0.978222902425696
R-squared0.956920046830152
Adjusted R-squared0.955408469525947
F-TEST (value)633.060607729429
F-TEST (DF numerator)2
F-TEST (DF denominator)57
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation1.25524473150455
Sum Squared Residuals89.8114421502864


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
1103100.4832738613912.51672613860898
2102.4101.0324524189981.36754758100176
3102101.6325840726330.367415927366912
4101.8102.113825168870-0.313825168870474
5101.6102.459191342368-0.859191342367898
6101.4102.753604419838-1.35360441983782
7101.3103.098970593335-1.79897059333525
8101.4103.512274228203-2.11227422820265
9101.7103.92557786307-2.22557786307005
10102.4104.338881497937-1.93888149793745
11103.1104.735200767462-1.63520076746236
12103.8105.080566940960-1.28056694095978
13104.4105.425933114457-1.02593311445720
14105105.737330557270-0.737330557269635
15105.7106.014759269397-0.314759269397075
16106.4106.3601254428940.0398745571055057
17107.1106.8243821737890.275617826210609
18107.9107.2716545393420.62834546065823
19108.8107.6170207128391.1829792871608
20109.6107.9963556170221.60364438297839
21110.3108.4606123479161.83938765208350
22110.8108.9588378094961.84116219050363
23111.2109.4061101750491.79388982495124
24111.7109.8194138099161.88058619008384
25112.3110.2497018101262.05029818987394
26112.8110.6969741756782.10302582432155
27113.1111.1272621758881.97273782411165
28113.1111.5745345414411.52546545855926
29113.1112.0218069069931.07819309300687
30113.2112.4181261765180.781873823481975
31113.1112.7974610807000.302538919299554
32112.8113.142827254198-0.342827254197863
33112.5113.539146523723-1.03914652372277
34112.3113.969434523933-1.66943452393267
35112.5114.31480069743-1.81480069743008
36112.9114.626198140243-1.72619814024251
37113.5114.937595583055-1.43759558305495
38114.1115.181055564497-1.08105556449741
39114.6115.373562449912-0.773562449912378
40114.9115.515116239300-0.615116239299851
41115.4115.673654394030-0.273654394029829
42115.7115.934098740815-0.234098740814780
43116.1116.228511818285-0.128511818284725
44116.5116.4380030690420.0619969309578169
45117.1116.5795568584300.520443141570327
46117.5116.6701575517900.829842448210334
47117.7116.7098051491220.99019485087782
48117.7116.7664371117970.93356288820281
49117.7116.9249752665270.775024733472832
50117.6117.1684352479700.431564752030366
51117.5117.4118952294120.0881047705879203
52117.6117.655355210855-0.0553552108545378
53117.9117.8818308269540.0181691730455159
54118.2118.0743377123690.125662287630543
55118.5118.3347820591540.165217940845594
56118.7118.6971325979940.00286740200567820
57118.8119.093451867519-0.293451867519233
58118.9119.523739867729-0.623739867729118
59119119.971012233282-0.971012233281517
60119120.418284598834-1.41828459883390


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
60.000791955385131270.001583910770262540.999208044614869
75.92443941399478e-050.0001184887882798960.99994075560586
86.94457919729743e-050.0001388915839459490.999930554208027
90.0005001056603264440.001000211320652890.999499894339674
100.009102768959322910.01820553791864580.990897231040677
110.0544744189905430.1089488379810860.945525581009457
120.1424355564129930.2848711128259870.857564443587007
130.2359382219637610.4718764439275220.764061778036239
140.298726349103120.597452698206240.70127365089688
150.3307271297379730.6614542594759460.669272870262027
160.3863972362834330.7727944725668660.613602763716567
170.594846252380170.810307495239660.40515374761983
180.8732781756439740.2534436487120520.126721824356026
190.9665937385864460.06681252282710780.0334062614135539
200.9919353109694330.01612937806113450.00806468903056726
210.9988852972626530.002229405474694840.00111470273734742
220.9998746851178920.0002506297642153300.000125314882107665
230.9999689375105786.21249788447259e-053.10624894223629e-05
240.9999826398788723.47202422565387e-051.73601211282693e-05
250.9999819279258653.61441482704765e-051.80720741352383e-05
260.9999732103630925.35792738151183e-052.67896369075591e-05
270.9999538528079579.22943840860886e-054.61471920430443e-05
280.9999095100879330.0001809798241346649.0489912067332e-05
290.999826931473340.0003461370533207280.000173068526660364
300.9997070731659050.0005858536681891630.000292926834094582
310.9995258872137140.000948225572571530.000474112786285765
320.9994022452522930.001195509495414220.000597754747707111
330.9996024588148630.0007950823702750050.000397541185137502
340.9998965807504220.0002068384991550680.000103419249577534
350.9999855438683872.89122632261937e-051.44561316130968e-05
360.9999985627927832.87441443481162e-061.43720721740581e-06
370.99999972042575.59148599762233e-072.79574299881117e-07
380.999999880390732.39218541045211e-071.19609270522606e-07
390.9999999154689641.69062071741307e-078.45310358706535e-08
400.9999999629204727.41590551243254e-083.70795275621627e-08
410.9999999698830576.02338856723998e-083.01169428361999e-08
420.999999982688193.46236207927032e-081.73118103963516e-08
430.9999999892767162.14465687918093e-081.07232843959047e-08
440.9999999946531921.06936168358590e-085.34680841792949e-09
450.9999999798418974.0316205483992e-082.0158102741996e-08
460.9999998693657532.61268494857009e-071.30634247428504e-07
470.9999996452348967.09530208072773e-073.54765104036386e-07
480.9999995928087558.14382490773802e-074.07191245386901e-07
490.9999998982320142.03535972924929e-071.01767986462465e-07
500.999999997312915.37418169393732e-092.68709084696866e-09
510.9999999993667221.26655543400126e-096.33277717000632e-10
520.9999999768722824.62554367379826e-082.31277183689913e-08
530.9999997022393755.9552125005239e-072.97760625026195e-07
540.9999845921773643.08156452716056e-051.54078226358028e-05


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level380.775510204081633NOK
5% type I error level400.816326530612245NOK
10% type I error level410.836734693877551NOK
 
Charts produced by software:
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Parameters (Session):
par1 = 12 ;
 
Parameters (R input):
par1 = 2 ; 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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Software written by Ed van Stee & Patrick Wessa


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