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WS6Q2nothing

R Software Module: rwasp_multipleregression.wasp (opens new window with default values)
Title produced by software: Multiple Regression
Date of computation: Sat, 17 Nov 2007 05:05:55 -0700
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2007/Nov/17/t1195300915ntxs10jkvcs2q83.htm/, Retrieved Sat, 17 Nov 2007 13:01:56 +0100
 
User-defined keywords:
 
Dataseries X:
» Textbox « » Textfile « » CSV «
-183,9235445 0 -177,0726091 0 -228,6351091 0 -237,4476091 0 -127,7601091 0 -193,0101091 0 -220,6351091 0 -164,5101091 0 -268,3226091 0 -333,6976091 0 -34,26010911 0 -154,8851091 0 -97,74528053 0 101,1056549 0 2,543154874 0 -43,26934513 0 -163,5818451 0 -162,8318451 0 46,54315487 0 26,66815487 0 -107,1443451 0 42,48065487 0 76,91815487 0 196,2931549 0 201,4329835 0 12,28391886 0 -0,278581137 0 42,90891886 0 87,59641886 0 84,34641886 0 57,72141886 0 173,8464189 0 -185,9660811 0 47,65891886 0 89,09641886 0 -68,52858114 0 272,6112475 0 146,4621829 0 162,8996829 0 10,08718285 0 279,7746829 0 212,5246829 0 248,8996829 0 -41,97531715 0 -5,787817149 0 52,83718285 0 274,2746829 0 414,6496829 0 310,7895114 0 362,6404468 0 26,07794684 0 403,2654468 0 327,9529468 0 193,7029468 0 317,0779468 0 202,2029468 0 321,3904468 0 178,0154468 0 16,45294684 0 -68,17205316 0 -157,0322246 0 -76,18128917 0 -81,74378917 0 -134,5562892 0 77,13121083 0 199,8812108 0 105,2562108 0 198,3812108 0 262,5687108 0 196,1937108 0 11,63121083 0 -145,9937892 0 -166,8539606 0 -202,0030252 0 43,43447482 0 -113,3780252 0 -113,6905252 0 -155,9405252 0 -210,5655252 0 -124,4405252 0 -64,25302518 0 -298,6280252 0 -154,1905252 0 23,18447482 0 -249,6756966 0 118,1752388 0 -180,3872612 0 -79,19976119 0 -81,51226119 0 -246,7622612 0 -105,3872612 0 -319,2622612 0 -72,07476119 0 -90,44976119 0 -80,01226119 0 119,3627388 0 -53,49743261 0 -114,6464972 0 -155,2089972 0 -50,02149721 0 -196,3339972 0 -14,58399721 0 -82,20899721 0 17,91600279 0 -162,8964972 0 -132,2714972 0 -16,83399721 0 81,54100279 0 275,6808314 0 -32,46823322 0 17,96926678 0 27,15676678 0 -123,1557332 0 108,5942668 0 67,96926678 0 34,09426678 0 -13,71823322 0 -113,0932332 0 54,34426678 0 149,7192668 0 153,8590954 0 -28,28996923 0 238,1475308 0 50,33503077 0 8,022530771 0 -61,22746923 0 -140,8524692 0 -28,72746923 0 9,460030771 0 -121,9149692 0 41,52253077 0 115,8975308 0 27,03735936 0 -91,11170524 0 3,325794759 0 -29,48670524 0 -73,79920524 0 50,95079476 0 -86,67420524 0 -9,54920524 0 -66,36170524 0 73,26329476 0 -216,2992052 0 -128,9242052 0 -142,7843767 0 27,06655875 0 60,50405875 0 35,69155875 0 16,37905875 0 -64,87094125 0 115,5040587 0 -30,37094125 0 87,81655875 0 205,4415587 0 -64,12094125 0 -322,7459413 0 -139,6061127 0 35,24482274 0 -4,317677263 0 17,86982274 0 2,557322737 0 129,3073227 0 -16,31767726 0 164,8073227 0 21,99482274 0 138,6198227 0 87,05732274 0 51,43232274 0 -80,42784867 0 -105,1918797 1 5,245620328 1 68,43312033 1 -0,879379672 1 -105,1293797 1 -82,75437967 1 -132,6293797 1 102,5581203 1 23,18312033 1 -180,3793797 1 -267,0043797 1 30,13544892 1 23,98638432 1 90,42388432 1 31,61138432 1 81,29888432 1 25,04888432 1 -13,57611568 1 33,54888432 1 140,7363843 1 132,3613843 1 94,79888432 1 4,173884316 1
 
Text written by user:
 
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 compuational 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
y[t] = + 1.77500390610615e-11 -6.88731608018628e-09x[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)1.77500390610615e-1111.348159010.5
x-6.88731608018628e-0932.787788010.5


Multiple Linear Regression - Regression Statistics
Multiple R1.52391567063411e-11
R-squared2.32231897120422e-22
Adjusted R-squared-0.00526315789473686
F-TEST (value)4.41240604528802e-20
F-TEST (DF numerator)1
F-TEST (DF denominator)190
p-value0.999999999832619
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation147.526070314389
Sum Squared Residuals4135148.87025712


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
1-183.92354451.77635683940025e-11-183.923544500018
2-177.07260911.77351466845721e-11-177.072609100018
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5-127.76010911.77635683940025e-11-127.760109100018
6-193.01010911.77351466845721e-11-193.010109100018
7-220.63510911.77351466845721e-11-220.635109100018
8-164.51010911.77351466845721e-11-164.510109100018
9-268.32260911.77351466845721e-11-268.322609100018
10-333.69760911.77919901034329e-11-333.697609100018
11-34.260109111.77493575392873e-11-34.2601091100178
12-154.88510911.77351466845721e-11-154.885109100018
13-97.745280531.77635683940025e-11-97.7452805300178
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152.5431548741.77489134500775e-112.54315487398225
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18-162.83184511.77351466845721e-11-162.831845100018
1946.543154871.77493575392873e-1146.5431548699823
2026.668154871.77564629666449e-1126.6681548699822
21-107.14434511.77635683940025e-11-107.144345100018
2242.480654871.77493575392873e-1142.4806548699823
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24196.29315491.77351466845721e-11196.293154899982
25201.43298351.77351466845721e-11201.432983499982
2612.283918861.77475811824479e-1112.2839188599823
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36-68.528581141.77493575392873e-11-68.5285811400177
37272.61124751.77919901034329e-11272.611247499982
38146.46218291.77351466845721e-11146.462182899982
39162.89968291.77351466845721e-11162.899682899982
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48414.64968291.77919901034329e-11414.649682899982
49310.78951141.77919901034329e-11310.789511399982
50362.64044681.77919901034329e-11362.640446799982
5126.077946841.77564629666449e-1126.0779468399822
52403.26544681.77919901034329e-11403.265446799982
53327.95294681.77919901034329e-11327.952946799982
54193.70294681.77351466845721e-11193.702946799982
55317.07794681.77919901034329e-11317.077946799982
56202.20294681.77351466845721e-11202.202946799982
57321.39044681.77919901034329e-11321.390446799982
58178.01544681.77351466845721e-11178.015446799982
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68198.38121081.77351466845721e-11198.381210799982
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80-124.44052521.77635683940025e-11-124.440525200018
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106-132.27149721.77635683940025e-11-132.271497200018
107-16.833997211.77493575392873e-11-16.8339972100177
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109275.68083141.77919901034329e-11275.680831399982
110-32.468233221.77493575392873e-11-32.4682332200178
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11227.156766781.77564629666449e-1127.1567667799822
113-123.15573321.77635683940025e-11-123.155733200018
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11567.969266781.77635683940025e-1167.9692667799822
11634.094266781.77493575392873e-1134.0942667799822
117-13.718233221.77493575392873e-11-13.7182332200177
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141-66.361705241.77493575392873e-11-66.3617052400178
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152-30.370941251.77493575392873e-11-30.3709412500178
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154205.44155871.77351466845721e-11205.441558699982
155-64.120941251.77493575392873e-11-64.1209412500178
156-322.74594131.77919901034329e-11-322.745941300018
157-139.60611271.77635683940025e-11-139.606112700018
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163-16.317677261.77493575392873e-11-16.3176772600177
164164.80732271.77351466845721e-11164.807322699982
16521.994822741.77564629666449e-1121.9948227399822
166138.61982271.77351466845721e-11138.619822699982
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179-180.3793797-6.86955559103808e-09-180.379379693130
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1924.173884316-6.86956269646544e-094.17388432286956
 
Charts produced by software:
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Parameters:
par1 = 1 ; par2 = Do not include Seasonal 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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