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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, 23 Nov 2008 07:14:40 -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/Nov/23/t12274497251zwzgsah2oeqyrz.htm/, Retrieved Sun, 23 Nov 2008 14:15:25 +0000
 
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/Nov/23/t12274497251zwzgsah2oeqyrz.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},
}
 
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
 
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Original text written by user:
 
IsPrivate?
No (this computation is public)
 
User-defined keywords:
 
Dataseries X:
» Textbox « » Textfile « » CSV «
299.63 0 305.945 0 382.252 0 348.846 0 335.367 0 373.617 0 312.612 0 312.232 0 337.161 0 331.476 0 350.103 0 345.127 0 297.256 0 295.979 0 361.007 0 321.803 0 354.937 0 349.432 0 290.979 0 349.576 0 327.625 0 349.377 0 336.777 0 339.134 0 323.321 0 318.86 0 373.583 0 333.03 0 408.556 0 414.646 0 291.514 0 348.857 0 349.368 0 375.765 0 364.136 0 349.53 0 348.167 1 332.856 1 360.551 1 346.969 1 392.815 1 372.02 1 371.027 1 342.672 1 367.343 1 390.786 1 343.785 1 362.6 1 349.468 1 340.624 1 369.536 1 407.782 1 392.239 1 404.824 1 373.669 1 344.902 1 396.7 1 398.911 1 366.009 1 392.484 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 time7 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24


Multiple Linear Regression - Estimated Regression Equation
x[t] = + 324.873316666667 + 2.36008333333332y[t] -24.4417625M1[t] -30.045075M2[t] + 19.6002125M3[t] + 1.01269999999999M4[t] + 25.2217875M5[t] + 30.459075M6[t] -25.3762375M7[t] -14.5763500000000M8[t] + 0.527537500000004M9[t] + 13.263425M10[t] -4.72528749999999M11[t] + 0.8877125t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)324.87331666666710.9960129.544700
y2.360083333333329.8747080.2390.8121650.406083
M1-24.441762512.257506-1.9940.0520970.026048
M2-30.04507512.1877-2.46520.0174860.008743
M319.600212512.1241961.61660.1127990.056399
M41.0126999999999912.0670930.08390.9334820.466741
M525.221787512.0164832.09890.0413410.02067
M630.45907511.9724482.54410.0143790.00719
M7-25.376237511.93506-2.12620.0388850.019443
M8-14.576350000000011.904383-1.22450.2270160.113508
M90.52753750000000411.8804680.04440.9647750.482387
M1013.26342511.8633571.1180.2693650.134683
M11-4.7252874999999911.853078-0.39870.6919920.345996
t0.88771250.2850583.11410.0031710.001586


Multiple Linear Regression - Regression Statistics
Multiple R0.8433620513171
R-squared0.711259549601787
Adjusted R-squared0.629658987532727
F-TEST (value)8.71635600989898
F-TEST (DF numerator)13
F-TEST (DF denominator)46
p-value1.44897841503067e-08
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation18.7359418727401
Sum Squared Residuals16147.6338215


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
1299.63301.319266666667-1.68926666666680
2305.945296.6036666666679.34133333333333
3382.252347.13666666666735.1153333333333
4348.846329.43686666666719.4091333333333
5335.367354.533666666667-19.1666666666666
6373.617360.65866666666712.9583333333333
7312.612305.7110666666676.90093333333334
8312.232317.398666666667-5.16666666666666
9337.161333.3902666666673.77073333333334
10331.476347.013866666667-15.5378666666667
11350.103329.91286666666720.1901333333333
12345.127335.5258666666679.60113333333335
13297.256311.971816666667-14.7158166666667
14295.979307.256216666667-11.2772166666667
15361.007357.7892166666673.21778333333334
16321.803340.089416666667-18.2864166666667
17354.937365.186216666667-10.2492166666666
18349.432371.311216666667-21.8792166666667
19290.979316.363616666667-25.3846166666667
20349.576328.05121666666721.5247833333333
21327.625344.042816666667-16.4178166666667
22349.377357.666416666667-8.28941666666665
23336.777340.565416666667-3.78841666666669
24339.134346.178416666667-7.04441666666665
25323.321322.6243666666670.696633333333397
26318.86317.9087666666670.951233333333345
27373.583368.4417666666675.14123333333335
28333.03350.741966666667-17.7119666666667
29408.556375.83876666666732.7172333333333
30414.646381.96376666666732.6822333333333
31291.514327.016166666667-35.5021666666667
32348.857338.70376666666710.1532333333333
33349.368354.695366666667-5.32736666666667
34375.765368.3189666666677.44603333333333
35364.136351.21796666666712.9180333333333
36349.53356.830966666667-7.30096666666669
37348.167335.63712.5300000000000
38332.856330.92141.9346
39360.551381.4544-20.9034
40346.969363.7546-16.7856
41392.815388.85143.96360000000000
42372.02394.9764-22.9564000000000
43371.027340.028830.9982
44342.672351.7164-9.04439999999999
45367.343367.708-0.364999999999983
46390.786381.33169.4544
47343.785364.2306-20.4456
48362.6369.8436-7.24359999999997
49349.468346.289553.17845000000006
50340.624341.57395-0.94994999999998
51369.536392.10695-22.57095
52407.782374.4071533.37485
53392.239399.50395-7.26495000000003
54404.824405.62895-0.804949999999996
55373.669350.6813522.98765
56344.902362.36895-17.4669500000000
57396.7378.3605518.3394500000000
58398.911391.984156.92684999999999
59366.009374.88315-8.87415
60392.484380.4961511.9878500000000


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.3926905682687030.7853811365374050.607309431731297
180.2879721949146960.5759443898293910.712027805085304
190.1993615441264770.3987230882529540.800638455873523
200.5132627420424540.9734745159150910.486737257957546
210.3954027641737190.7908055283474380.604597235826281
220.3624547992140170.7249095984280340.637545200785983
230.267632097035040.535264194070080.73236790296496
240.1807439690768350.3614879381536690.819256030923165
250.2138694023830290.4277388047660570.786130597616971
260.1727584404897340.3455168809794670.827241559510266
270.1288802785649700.2577605571299400.87111972143503
280.1049414947615360.2098829895230720.895058505238464
290.3962384774496080.7924769548992150.603761522550393
300.6391090947947060.7217818104105870.360890905205294
310.9232513199112140.1534973601775720.076748680088786
320.9132851338257280.1734297323485440.086714866174272
330.8939286708740630.2121426582518730.106071329125937
340.8633679336829140.2732641326341730.136632066317086
350.8869229040219020.2261541919561970.113077095978098
360.8238085571038050.3523828857923900.176191442896195
370.7768391615889020.4463216768221960.223160838411098
380.7046776574040580.5906446851918840.295322342595942
390.6854873028917290.6290253942165420.314512697108271
400.89672143176020.2065571364795990.103278568239800
410.8786166240761280.2427667518477450.121383375923872
420.8543441881815620.2913116236368760.145655811818438
430.8410847291665250.3178305416669510.158915270833476


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:
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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t12274497251zwzgsah2oeqyrz/68ruh1227449669.ps (open in new window)


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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t12274497251zwzgsah2oeqyrz/8jo8y1227449669.ps (open in new window)


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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t12274497251zwzgsah2oeqyrz/9o3ta1227449669.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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