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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: Sun, 20 Dec 2009 10:02:26 -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/Dec/20/t126132861944yr56w7wi8ftve.htm/, Retrieved Sun, 20 Dec 2009 18:03:51 +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/Dec/20/t126132861944yr56w7wi8ftve.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 «
5560 611 3922 594 3759 595 4138 591 4634 589 3996 584 4308 573 4143 567 4429 569 5219 621 4929 629 5755 628 5592 612 4163 595 4962 597 5208 593 4755 590 4491 580 5732 574 5731 573 5040 573 6102 620 4904 626 5369 620 5578 588 4619 566 4731 557 5011 561 5299 549 4146 532 4625 526 4736 511 4219 499 5116 555 4205 565 4121 542 5103 527 4300 510 4578 514 3809 517 5526 508 4247 493 3830 490 4394 469 4826 478 4409 528 4569 534 4106 518 4794 506 3914 502 3793 516 4405 528 4022 533 4100 536 4788 537 3163 524 3585 536 3903 4178 3863 4187
 
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] = + 5545.45096713486 -0.178613936386478X[t] + 43.6242818380755M1[t] -931.523238964048M2[t] -737.34522798693M3[t] -574.60293979709M4[t] -229.603780800123M5[t] -869.626245910535M6[t] -397.169978062677M7[t] -609.621116620415M8[t] -610.078828430576M9[t] + 70.0960717549703M10[t] -371.561402011425M11[t] -12.7493375297899t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)5545.45096713486299.69681318.503500
X-0.1786139363864780.128893-1.38570.1723640.086182
M143.6242818380755346.624690.12590.9003840.450192
M2-931.523238964048363.852446-2.56020.0137360.006868
M3-737.34522798693363.376425-2.02910.0481280.024064
M4-574.60293979709362.949809-1.58310.1200950.060047
M5-229.603780800123362.564867-0.63330.5296230.264811
M6-869.626245910535362.233019-2.40070.0203730.010186
M7-397.169978062677361.961702-1.09730.2781130.139057
M8-609.621116620415361.752756-1.68520.0985820.049291
M9-610.078828430576361.587572-1.68720.0981870.049094
M1070.0960717549703373.5694040.18760.8519680.425984
M11-371.561402011425373.494856-0.99480.3249170.162458
t-12.74933752978994.337665-2.93920.0050880.002544


Multiple Linear Regression - Regression Statistics
Multiple R0.623840267592213
R-squared0.389176679469524
Adjusted R-squared0.220225548258967
F-TEST (value)2.30348667499899
F-TEST (DF numerator)13
F-TEST (DF denominator)47
p-value0.0186249399858107
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation571.339391925744
Sum Squared Residuals15342148.9360057


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
155605467.1927963110292.8072036889818
239224482.33237489767-560.332374897667
337594663.58243440861-904.582434408608
441384814.2898408142-676.289840814204
546345146.89689015415-512.896890154154
639964495.01815719588-499.018157195885
743084956.6898408142-648.689840814204
841434732.56104834499-589.561048344993
944294718.99677113227-289.996771132271
1052195377.13440909593-158.134409095932
1149294921.298686308657.701313691347
1257555280.28936472668474.710635273324
1355925314.02213201714277.977867982856
1441634329.1617106038-166.161710603801
1549624510.23315617836451.766843821644
1652084660.94056258395547.059437416048
1747554993.72622586029-238.726225860288
1844914342.74056258395148.259437416048
1957324803.51917652034928.480823479661
2057314578.497314369201152.50268563080
2150404565.29026502925474.709734970753
2261025224.32097267484877.679027325162
2349044768.84247776033135.157522239666
2453695128.72622586029240.273774139712
2555785165.31681613294412.683183867059
2646194181.34946440153437.65053559847
2747314364.38566327634366.614336723664
2850114513.66415819084497.33584180916
2952994848.05734689465450.942653105345
3041464198.32198117302-52.3219811730241
3146254659.10059510941-34.1005951094108
3247364436.57932806768299.420671932320
3342194425.51564596437-206.515645964367
3451165082.9388281824833.0611718175198
3542054626.74587752243-421.74587752243
3641214989.66606254095-868.666062540955
3751035023.2202158950479.7797841049627
3843004038.35979448169261.640205518306
3945784219.07401218348358.925987816524
4038094368.53112103437-559.531121034367
4155264702.38846792902823.611532070978
4242474052.29587433462194.704125665382
4338304512.53864646185-682.538646461845
4443944291.08906303843102.910936961568
4548264276.27448827100549.725511728995
4644094934.76935410744-525.769354107436
4745694479.2908591929389.7091408070676
4841064840.96074665675-734.960746656751
4947944873.97905820167-79.9790582016743
5039143886.7966556153127.2033443846928
5137934065.72473395322-272.724733953224
5244054213.57431737664191.425682623363
5340224544.93106916188-522.931069161881
5441003891.62342471252208.376575287479
5547884351.1517410942436.848258905798
5631634128.2732461797-965.273246179697
5735854112.92282960311-527.92282960311
5839034129.83643593931-226.836435939314
5938633673.82209921565189.177900784350
6055604671.35760021533888.64239978467
6139224705.26898144219-783.268981442186


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.003523933396206390.007047866792412790.996476066603794
180.2792011085258880.5584022170517750.720798891474112
190.329425242478940.658850484957880.67057475752106
200.2729344008689300.5458688017378590.72706559913107
210.2080339870627360.4160679741254720.791966012937264
220.1767427392488490.3534854784976980.823257260751151
230.1245015514209670.2490031028419340.875498448579033
240.07476545375457070.1495309075091410.92523454624543
250.1002636930785610.2005273861571220.899736306921439
260.1213446193197450.242689238639490.878655380680255
270.09431508693195660.1886301738639130.905684913068043
280.06462690686864420.1292538137372880.935373093131356
290.04960151877719720.09920303755439440.950398481222803
300.03037582449309270.06075164898618550.969624175506907
310.02031433506958380.04062867013916770.979685664930416
320.01360876446628090.02721752893256180.986391235533719
330.007165311175387350.01433062235077470.992834688824613
340.004202816292860020.008405632585720040.99579718370714
350.002660778960859970.005321557921719930.99733922103914
360.004967866639148130.009935733278296250.995032133360852
370.002395523730878410.004791047461756810.997604476269122
380.001608253144553890.003216506289107780.998391746855446
390.0009658850604870310.001931770120974060.999034114939513
400.002026596725657130.004053193451314260.997973403274343
410.006686390662150630.01337278132430130.99331360933785
420.003073491054991550.006146982109983090.996926508945008
430.01018516423498020.02037032846996040.98981483576502
440.008192304296000750.01638460859200150.991807695704


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level90.321428571428571NOK
5% type I error level150.535714285714286NOK
10% type I error level170.607142857142857NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Dec/20/t126132861944yr56w7wi8ftve/104oup1261328540.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/20/t126132861944yr56w7wi8ftve/104oup1261328540.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/20/t126132861944yr56w7wi8ftve/18xnm1261328540.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/20/t126132861944yr56w7wi8ftve/18xnm1261328540.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/20/t126132861944yr56w7wi8ftve/2cbtq1261328540.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/20/t126132861944yr56w7wi8ftve/2cbtq1261328540.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/20/t126132861944yr56w7wi8ftve/3xqvb1261328540.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/20/t126132861944yr56w7wi8ftve/3xqvb1261328540.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/20/t126132861944yr56w7wi8ftve/4fblf1261328540.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/20/t126132861944yr56w7wi8ftve/4fblf1261328540.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/20/t126132861944yr56w7wi8ftve/5lgw41261328540.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Dec/20/t126132861944yr56w7wi8ftve/6a3pb1261328540.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/20/t126132861944yr56w7wi8ftve/6a3pb1261328540.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/20/t126132861944yr56w7wi8ftve/7oisr1261328540.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/20/t126132861944yr56w7wi8ftve/7oisr1261328540.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/20/t126132861944yr56w7wi8ftve/85i3o1261328540.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/20/t126132861944yr56w7wi8ftve/85i3o1261328540.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/20/t126132861944yr56w7wi8ftve/9c65i1261328540.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/20/t126132861944yr56w7wi8ftve/9c65i1261328540.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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