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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 09:38:14 -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/t1227976742qkps6jygvi277wi.htm/, Retrieved Sat, 29 Nov 2008 16:39:11 +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/t1227976742qkps6jygvi277wi.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 time3 seconds
R Server'George Udny Yule' @ 72.249.76.132


Multiple Linear Regression - Estimated Regression Equation
y[t] = + 0.883858800039933 + 0.130031266846361x[t] + 0.0335349727130548M1[t] + 0.0195058254301020M2[t] + 0.0181666781471496M3[t] + 0.0121975308641974M4[t] + 0.0125983835812451M5[t] -0.00637389038634339M6[t] -0.00477303766929572M7[t] -0.0171478553126354M8[t] -0.0214358914844766M9[t] -0.0178239276563178M10[t] -0.0144675193837145M11[t] + 0.00419914728295231t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)0.8838588000399330.03707423.840300
x0.1300312668463610.0338393.84260.0002130.000106
M10.03353497271305480.0446680.75080.4545440.227272
M20.01950582543010200.0446590.43680.6632060.331603
M30.01816667814714960.0446520.40690.6849760.342488
M40.01219753086419740.0446470.27320.7852580.392629
M50.01259838358124510.0446450.28220.7783750.389187
M6-0.006373890386343390.044745-0.14240.8870090.443504
M7-0.004773037669295720.044733-0.10670.9152390.45762
M8-0.01714785531263540.045823-0.37420.7090230.354512
M9-0.02143589148447660.045814-0.46790.6408730.320437
M10-0.01782392765631780.045808-0.38910.6980220.349011
M11-0.01446751938371450.045805-0.31590.7527660.376383
t0.004199147282952310.00033212.657700


Multiple Linear Regression - Regression Statistics
Multiple R0.87869455699998
R-squared0.77210412450139
Adjusted R-squared0.74277099201147
F-TEST (value)26.3219117414996
F-TEST (DF numerator)13
F-TEST (DF denominator)101
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.097163759502998
Sum Squared Residuals0.9535204122364


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
11.16080.9215929200359340.239207079964066
21.12080.911762920035940.209037079964061
31.08830.9146229200359390.173677079964061
41.07040.912852920035940.157547079964061
51.06280.9174529200359390.145347079964061
61.03780.9026797933513030.135120206648697
71.03530.9084797933513030.126820206648697
81.06040.9003041229909160.160095877009084
91.05010.9002152341020270.149884765897973
101.07060.9080263452131380.162573654786862
111.03380.9155819007686930.118218099231307
121.0110.934248567435360.0767514325646397
131.01370.9719826874313670.0417173125686328
140.98340.9621526874313670.0212473125686328
150.96430.965012687431367-0.000712687431366661
160.9470.963242687431367-0.0162426874313669
170.9060.967842687431367-0.0618426874313668
180.94920.95306956074673-0.00386956074673059
190.93970.95886956074673-0.0191695607467307
200.90410.950693890386343-0.0465938903863432
210.87210.950605001497454-0.0785050014974544
220.85520.958416112608566-0.103216112608566
230.85640.965971668164121-0.109571668164121
240.89730.984638334830788-0.087338334830788
250.93831.02237245482680-0.0840724548267951
260.92171.01254245482679-0.0908424548267944
270.90951.01540245482679-0.105902454826795
280.8921.01363245482679-0.121632454826795
290.87421.01823245482679-0.144032454826795
300.85321.00345932814216-0.150259328142158
310.86071.00925932814216-0.148559328142158
320.90051.00108365778177-0.100583657781771
330.91111.00099476889288-0.0898947688928821
340.90591.00880588000399-0.102905880003993
350.88831.01636143555955-0.128061435559549
360.89241.03502810222622-0.142628102226216
370.88331.07276222222222-0.189462222222223
380.871.06293222222222-0.192932222222222
390.87581.06579222222222-0.189992222222222
400.88581.06402222222222-0.178222222222222
410.9171.06862222222222-0.151622222222222
420.95541.05384909553759-0.098449095537586
430.99221.05964909553759-0.0674490955375861
440.97781.05147342517720-0.0736734251771987
450.98081.05138453628831-0.0705845362883099
460.98111.05919564739942-0.078095647399421
471.00141.06675120295498-0.0653512029549765
481.01831.08541786962164-0.0671178696216434
491.06221.12315198961765-0.0609519896176506
501.07731.11332198961765-0.03602198961765
511.08071.11618198961765-0.0354819896176499
521.08481.11441198961765-0.02961198961765
531.15821.119011989617650.0391880103823499
541.16631.104238862933010.062061137066986
551.13721.110038862933010.0271611370669861
561.11391.101863192572630.0120368074273734
571.12221.101774303683740.0204256963162624
581.16921.109585414794850.0596145852051513
591.17021.117140970350400.0530590296495956
601.22861.135807637017070.0927923629829288
611.26131.173541757013080.0877582429869218
621.26461.163711757013080.100888242986922
631.22621.166571757013080.0596282429869223
641.19851.164801757013080.0336982429869222
651.20071.169401757013080.0312982429869224
661.21381.154628630328440.0591713696715584
671.22661.160428630328440.0661713696715583
681.21761.152252959968050.0653470400319458
691.22181.152164071079170.0696359289208346
701.2491.159975182190280.0890248178097236
711.29911.167530737745830.131569262254168
721.34081.18619740441250.154602595587501
731.31191.223931524408510.087968475591494
741.30141.214101524408510.0872984755914945
751.32011.216961524408510.103138475591495
761.29381.215191524408510.0786084755914946
771.26941.219791524408510.0496084755914946
781.21651.205018397723870.0114816022761307
791.20371.21081839772387-0.00711839772386933
801.22921.202642727363480.0265572726365181
811.22561.202553838474590.0230461615254069
821.20151.21036494958570-0.00886494958570423
831.17861.21792050514126-0.0393205051412597
841.18561.23658717180793-0.0509871718079266
851.21031.27432129180393-0.0640212918039339
861.19381.26449129180393-0.0706912918039331
871.2021.26735129180393-0.0653512918039331
881.22711.26558129180393-0.0384812918039332
891.2771.270181291803930.00681870819606661
901.2651.255408165119300.00959183488070291
911.26841.261208165119300.00719183488070291
921.28111.253032494758910.0280675052410902
931.27271.252943605870020.0197563941299791
941.26111.260754716981130.000345283018868117
951.28811.268310272536690.0197897274633126
961.32131.286976939203350.0343230607966455
971.29991.32471105919936-0.0248110591993615
981.30741.31488105919936-0.00748105919936094
991.32421.317741059199360.00645894080063922
1001.35161.315971059199360.0356289408006389
1011.35111.320571059199360.0305289408006389
1021.34191.43582919936109-0.093929199361086
1031.37161.44162919936109-0.0700291993610862
1041.36221.4334535290007-0.0712535290006987
1051.38961.43336464011181-0.0437646401118099
1061.42271.44117575122292-0.0184757512229210
1071.46841.448731306778480.0196686932215233
1081.4571.46739797344514-0.0103979734451434
1091.47181.50513209344115-0.0333320934411506
1101.47481.49530209344115-0.0205020934411498
1111.55271.498162093441150.05453790655885
1121.57511.496392093441150.0787079065588499
1131.55571.500992093441150.0547079065588501
1141.55531.486218966756510.0690810332434861
1151.5771.492018966756510.084981033243486
 
Charts produced by software:
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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/29/t1227976742qkps6jygvi277wi/1vo0z1227976690.ps (open in new window)


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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/29/t1227976742qkps6jygvi277wi/2ek4q1227976690.ps (open in new window)


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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/29/t1227976742qkps6jygvi277wi/5puv41227976690.ps (open in new window)


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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/29/t1227976742qkps6jygvi277wi/6p7361227976690.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/29/t1227976742qkps6jygvi277wi/7y2ky1227976690.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/29/t1227976742qkps6jygvi277wi/7y2ky1227976690.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/29/t1227976742qkps6jygvi277wi/8b1px1227976690.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/29/t1227976742qkps6jygvi277wi/8b1px1227976690.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/29/t1227976742qkps6jygvi277wi/94gao1227976690.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/29/t1227976742qkps6jygvi277wi/94gao1227976690.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)
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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