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works paper V

R Software Module: rwasp_multipleregression.wasp (opens new window with default values)
Title produced by software: Multiple Regression
Date of computation: Fri, 30 Nov 2007 04:54:56 -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/30/t1196423054sg9e4be8kj5485u.htm/, Retrieved Fri, 30 Nov 2007 12:44:25 +0100
 
User-defined keywords:
 
Dataseries X:
» Textbox « » Textfile « » CSV «
106,7 0 110,2 0 125,9 0 100,1 0 106,4 0 114,8 0 81,3 0 87 0 104,2 0 108 0 105 0 94,5 0 92 0 95,9 0 108,8 0 103,4 0 102,1 0 110,1 0 83,2 0 82,7 0 106,8 0 113,7 0 102,5 0 96,6 0 92,1 0 95,6 0 102,3 0 98,6 0 98,2 0 104,5 0 84 0 73,8 0 103,9 0 106 0 97,2 0 102,6 0 89 0 93,8 0 116,7 1 106,8 1 98,5 1 118,7 1 90 1 91,9 1 113,3 1 113,1 1 104,1 1 108,7 1 96,7 1 101 1 116,9 1 105,8 1 99 1 129,4 1 83 1 88,9 1 115,9 1 104,2 1 113,4 1 112,2 1 100,8 1 107,3 1 126,6 1 102,9 1 117,9 1 128,8 1 87,5 1 93,8 1 122,7 1 126,2 1 124,6 1 116,7 1 115,2 1 111,1 1 129,9 1 113,3 1 118,5 1 133,5 1 102,1 1 102,4 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 time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
y[t] = + 97.545 + 5.53874999999998`x `[t] -5.30886408730163M1[t] -2.22558531746031M2[t] + 12.8950148809524M3[t] -0.964563492063498M4[t] + 0.304429563492081M5[t] + 14.3591369047619M6[t] -18.4290128968254M7[t] -17.2028769841270M8[t] + 6.26683035714287M9[t] + 6.88344246031746M10[t] + 2.70005456349207M11[t] + 0.116721230158731t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)97.5453.11727131.291800
`x `5.538749999999982.9694481.86520.0665930.033297
M1-5.308864087301633.660279-1.45040.1516830.075842
M2-2.225585317460313.658449-0.60830.5450490.272525
M312.89501488095243.6770183.50690.0008210.00041
M4-0.9645634920634983.671017-0.26280.7935610.39678
M50.3044295634920813.6661270.0830.9340720.467036
M614.35913690476193.6623513.92070.0002130.000106
M7-18.42901289682543.659693-5.03574e-062e-06
M8-17.20287698412703.658156-4.70261.4e-057e-06
M96.266830357142873.7990891.64960.1037850.051892
M106.883442460317463.7963861.81320.0743550.037177
M112.700054563492073.7947630.71150.4792690.239634
t0.1167212301587310.0640781.82150.0730570.036529


Multiple Linear Regression - Regression Statistics
Multiple R0.881461940737189
R-squared0.776975152968172
Adjusted R-squared0.733046016431599
F-TEST (value)17.6870117244694
F-TEST (DF numerator)13
F-TEST (DF denominator)66
p-value1.11022302462516e-16
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation6.57178533306778
Sum Squared Residuals2850.43192261904


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
1106.792.352857142857414.3471428571426
2110.295.552857142857114.6471428571429
3125.9110.79017857142915.1098214285714
4100.197.04732142857143.05267857142857
5106.498.43303571428577.9669642857143
6114.8112.6044642857142.19553571428574
781.379.93303571428571.36696428571428
88781.27589285714285.72410714285718
9104.2104.862321428571-0.662321428571399
10108105.5956547619052.40434523809523
11105101.5289880952383.47101190476192
1294.598.9456547619047-4.44565476190473
139293.7535119047619-1.75351190476185
1495.996.9535119047619-1.0535119047619
15108.8112.190833333333-3.39083333333333
16103.498.44797619047624.95202380952382
17102.199.83369047619052.26630952380952
18110.1114.005119047619-3.90511904761906
1983.281.33369047619051.86630952380953
2082.782.67654761904760.0234523809523808
21106.8106.2629761904760.537023809523803
22113.7106.9963095238106.70369047619048
23102.5102.929642857143-0.429642857142853
2496.6100.346309523810-3.74630952380952
2592.195.1541666666666-3.05416666666662
2695.698.3541666666667-2.75416666666667
27102.3113.591488095238-11.2914880952381
2898.699.848630952381-1.24863095238096
2998.2101.234345238095-3.03434523809524
30104.5115.405773809524-10.9057738095238
318482.73434523809521.26565476190476
3273.884.0772023809524-10.2772023809524
33103.9107.663630952381-3.76363095238096
34106108.396964285714-2.39696428571429
3597.2104.330297619048-7.13029761904762
36102.6101.7469642857140.85303571428571
378996.5548214285714-7.55482142857139
3893.899.7548214285714-5.95482142857143
39116.7120.530892857143-3.83089285714285
40106.8106.7880357142860.0119642857142910
4198.5108.17375-9.67375
42118.7122.345178571429-3.64517857142857
439089.673750.326250000000014
4491.991.01660714285710.883392857142863
45113.3114.603035714286-1.30303571428572
46113.1115.336369047619-2.23636904761905
47104.1111.269702380952-7.16970238095238
48108.7108.6863690476190.0136309523809659
4996.7103.494226190476-6.79422619047614
50101106.694226190476-5.69422619047618
51116.9121.931547619048-5.03154761904762
52105.8108.188690476190-2.38869047619048
5399109.574404761905-10.5744047619048
54129.4123.7458333333335.65416666666667
558391.0744047619048-8.07440476190475
5688.992.4172619047619-3.51726190476191
57115.9116.003690476190-0.103690476190482
58104.2116.737023809524-12.5370238095238
59113.4112.6703571428570.72964285714286
60112.2110.0870238095242.11297619047620
61100.8104.894880952381-4.09488095238091
62107.3108.094880952381-0.794880952380956
63126.6123.3322023809523.2677976190476
64102.9109.589345238095-6.68934523809524
65117.9110.9750595238106.92494047619047
66128.8125.1464880952383.6535119047619
6787.592.4750595238095-4.97505952380952
6893.893.8179166666667-0.0179166666666888
69122.7117.4043452380955.29565476190475
70126.2118.1376785714298.06232142857142
71124.6114.07101190476210.5289880952381
72116.7111.4876785714295.21232142857142
73115.2106.2955357142868.90446428571433
74111.1109.4955357142861.60446428571427
75129.9124.7328571428575.16714285714284
76113.3110.992.30999999999998
77118.5112.3757142857146.1242857142857
78133.5126.5471428571436.95285714285712
79102.193.87571428571438.2242857142857
80102.495.21857142857157.18142857142855
 
Charts produced by software:
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Parameters:
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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