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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: Sat, 29 Nov 2008 09:33:12 -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/29/t1227976467wzdwuex8znmtd6l.htm/, Retrieved Sat, 29 Nov 2008 16:34:27 +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/29/t1227976467wzdwuex8znmtd6l.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)
 
Feedback Forum:
2008-11-27 13:41:43 [a2386b643d711541400692649981f2dc] [reply
test

Post a new message
 
Original text written by user:
 
IsPrivate?
No (this computation is public)
 
User-defined keywords:
 
Dataseries X:
» Textbox « » Textfile « » CSV «
1.1608 0 1.1208 0 1.0883 0 1.0704 0 1.0628 0 1.0378 0 1.0353 0 1.0604 0 1.0501 0 1.0706 0 1.0338 0 1.011 0 1.0137 0 0.9834 0 0.9643 0 0.947 0 0.906 0 0.9492 0 0.9397 0 0.9041 0 0.8721 0 0.8552 0 0.8564 0 0.8973 0 0.9383 0 0.9217 0 0.9095 0 0.892 0 0.8742 0 0.8532 0 0.8607 0 0.9005 0 0.9111 0 0.9059 0 0.8883 0 0.8924 0 0.8833 0 0.87 0 0.8758 0 0.8858 0 0.917 0 0.9554 0 0.9922 0 0.9778 0 0.9808 0 0.9811 0 1.0014 0 1.0183 0 1.0622 0 1.0773 0 1.0807 0 1.0848 0 1.1582 0 1.1663 0 1.1372 0 1.1139 0 1.1222 0 1.1692 0 1.1702 0 1.2286 0 1.2613 0 1.2646 0 1.2262 0 1.1985 0 1.2007 0 1.2138 0 1.2266 0 1.2176 0 1.2218 0 1.249 0 1.2991 0 1.3408 0 1.3119 0 1.3014 0 1.3201 0 1.2938 0 1.2694 0 1.2165 0 1.2037 0 1.2292 0 1.2256 0 1.2015 0 1.1786 0 1.1856 0 1.2103 0 1.1938 0 1.202 0 1.2271 0 1.277 0 1.265 0 1.2684 0 1.2811 0 1.2727 0 1.2611 0 1.2881 0 1.3213 0 1.2999 0 1.3074 0 1.3242 0 1.3516 0 1.3511 0 1.3419 1 1.3716 1 1.3622 1 1.3896 1 1.4227 1 1.4684 1 1.457 1 1.4718 1 1.4748 1 1.5527 1 1.5751 1 1.5557 1 1.5553 1 1.577 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 time5 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001


Multiple Linear Regression - Estimated Regression Equation
y[t] = + 1.10883781640744 + 0.372759652333028x[t] + 0.0152362183592561M1[t] + 0.00540621835925587M2[t] + 0.00826621835925592M3[t] + 0.0064962183592559M4[t] + 0.0110962183592559M5[t] -0.0279497468740469M6[t] -0.0221497468740469M7[t] -0.0339444444444444M8[t] -0.0340333333333333M9[t] -0.0262222222222222M10[t] -0.0186666666666666M11[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)1.108837816407440.05206721.296400
x0.3727596523330280.0446198.354400
M10.01523621835925610.0714450.21330.8315510.415775
M20.005406218359255870.0714450.07570.939830.469915
M30.008266218359255920.0714450.11570.9081170.454059
M40.00649621835925590.0714450.09090.9277290.463865
M50.01109621835925590.0714450.15530.8768820.438441
M6-0.02794974687404690.071553-0.39060.6968960.348448
M7-0.02214974687404690.071553-0.30960.7575290.378765
M8-0.03394444444444440.073299-0.46310.6442820.322141
M9-0.03403333333333330.073299-0.46430.6434160.321708
M10-0.02622222222222220.073299-0.35770.7212750.360637
M11-0.01866666666666660.073299-0.25470.7994950.399747


Multiple Linear Regression - Regression Statistics
Multiple R0.640775064532684
R-squared0.410592683326865
Adjusted R-squared0.341250646071202
F-TEST (value)5.92126651562048
F-TEST (DF numerator)12
F-TEST (DF denominator)102
p-value1.00597258190227e-07
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.155490707653993
Sum Squared Residuals2.46609073700742


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
11.16081.124074034766700.0367259652333049
21.12081.114244034766700.00655596523330277
31.08831.11710403476670-0.0288040347666970
41.07041.11533403476670-0.044934034766697
51.06281.11993403476670-0.0571340347666971
61.03781.08088806953339-0.0430880695333942
71.03531.08668806953339-0.0513880695333941
81.06041.07489337196300-0.0144933719629967
91.05011.07480448307411-0.0247044830741079
101.07061.08261559418522-0.0120155941852191
111.03381.09017114974077-0.0563711497407745
121.0111.10883781640744-0.0978378164074413
131.01371.12407403476670-0.110374034766697
140.98341.11424403476670-0.130844034766697
150.96431.11710403476670-0.152804034766697
160.9471.11533403476670-0.168334034766697
170.9061.11993403476670-0.213934034766697
180.94921.08088806953339-0.131688069533394
190.93971.08668806953339-0.146988069533394
200.90411.07489337196300-0.170793371962997
210.87211.07480448307411-0.202704483074108
220.85521.08261559418522-0.227415594185219
230.85641.09017114974077-0.233771149740775
240.89731.10883781640744-0.211537816407441
250.93831.12407403476670-0.185774034766697
260.92171.11424403476670-0.192544034766697
270.90951.11710403476670-0.207604034766697
280.8921.11533403476670-0.223334034766697
290.87421.11993403476670-0.245734034766697
300.85321.08088806953339-0.227688069533394
310.86071.08668806953339-0.225988069533394
320.90051.07489337196300-0.174393371962997
330.91111.07480448307411-0.163704483074108
340.90591.08261559418522-0.176715594185219
350.88831.09017114974077-0.201871149740775
360.89241.10883781640744-0.216437816407441
370.88331.12407403476670-0.240774034766698
380.871.11424403476670-0.244244034766697
390.87581.11710403476670-0.241304034766697
400.88581.11533403476670-0.229534034766697
410.9171.11993403476670-0.202934034766697
420.95541.08088806953339-0.125488069533394
430.99221.08668806953339-0.0944880695333943
440.97781.07489337196300-0.0970933719629968
450.98081.07480448307411-0.094004483074108
460.98111.08261559418522-0.101515594185219
471.00141.09017114974077-0.0887711497407746
481.01831.10883781640744-0.0905378164074413
491.06221.12407403476670-0.0618740347666973
501.07731.11424403476670-0.0369440347666972
511.08071.11710403476670-0.0364040347666972
521.08481.11533403476670-0.0305340347666971
531.15821.119934034766700.0382659652333027
541.16631.080888069533390.0854119304666056
551.13721.086688069533390.0505119304666057
561.11391.074893371963000.0390066280370031
571.12221.074804483074110.0473955169258922
581.16921.082615594185220.086584405814781
591.17021.090171149740770.0800288502592253
601.22861.108837816407440.119762183592559
611.26131.124074034766700.137225965233303
621.26461.114244034766700.150355965233303
631.22621.117104034766700.109095965233303
641.19851.115334034766700.0831659652333027
651.20071.119934034766700.080765965233303
661.21381.080888069533390.132911930466606
671.22661.086688069533390.139911930466606
681.21761.074893371963000.142706628037003
691.22181.074804483074110.146995516925892
701.2491.082615594185220.166384405814781
711.29911.090171149740770.208928850259225
721.34081.108837816407440.231962183592559
731.31191.124074034766700.187825965233303
741.30141.114244034766700.187155965233303
751.32011.117104034766700.202995965233303
761.29381.115334034766700.178465965233303
771.26941.119934034766700.149465965233303
781.21651.080888069533390.135611930466606
791.20371.086688069533390.117011930466606
801.22921.074893371963000.154306628037003
811.22561.074804483074110.150795516925892
821.20151.082615594185220.118884405814781
831.17861.090171149740770.0884288502592255
841.18561.108837816407440.0767621835925588
851.21031.124074034766700.0862259652333026
861.19381.114244034766700.0795559652333028
871.2021.117104034766700.0848959652333028
881.22711.115334034766700.111765965233303
891.2771.119934034766700.157065965233303
901.2651.080888069533390.184111930466606
911.26841.086688069533390.181711930466606
921.28111.074893371963000.206206628037003
931.27271.074804483074110.197895516925892
941.26111.082615594185220.178484405814781
951.28811.090171149740770.197928850259225
961.32131.108837816407440.212462183592559
971.29991.124074034766700.175825965233303
981.30741.114244034766700.193155965233303
991.32421.117104034766700.207095965233303
1001.35161.115334034766700.236265965233303
1011.35111.119934034766700.231165965233303
1021.34191.45364772186642-0.111747721866423
1031.37161.45944772186642-0.0878477218664227
1041.36221.44765302429603-0.0854530242960251
1051.38961.44756413540714-0.0579641354071364
1061.42271.45537524651825-0.0326752465182474
1071.46841.462930802073800.00546919792619696
1081.4571.48159746874047-0.0245974687404695
1091.47181.49683368709973-0.0250336870997258
1101.47481.48700368709973-0.0122036870997254
1111.55271.489863687099730.0628363129002744
1121.57511.488093687099730.0870063129002745
1131.55571.492693687099730.0630063129002745
1141.55531.453647721866420.101652278133577
1151.5771.459447721866420.117552278133577
 
Charts produced by software:
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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/29/t1227976467wzdwuex8znmtd6l/2nigs1227976381.ps (open in new window)


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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/29/t1227976467wzdwuex8znmtd6l/6ypon1227976381.ps (open in new window)


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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/29/t1227976467wzdwuex8znmtd6l/733391227976381.ps (open in new window)


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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/29/t1227976467wzdwuex8znmtd6l/806wq1227976381.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/29/t1227976467wzdwuex8znmtd6l/92ta91227976381.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/29/t1227976467wzdwuex8znmtd6l/92ta91227976381.ps (open in new window)


 
Parameters (Session):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;
 
Parameters (R input):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;
 
R code (references can be found in the software module):
library(lattice)
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))
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$resid, main='Residual Normal Q-Q Plot')
grid()
dev.off()
(myerror <- as.ts(mysum$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()
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')
 





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