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dummy4

*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, 07 Dec 2008 06:11:11 -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/Dec/07/t1228655533aecae6v6esrl4tm.htm/, Retrieved Sun, 07 Dec 2008 13:12:22 +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/Dec/07/t1228655533aecae6v6esrl4tm.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 «
3030,29 0 2803,47 0 2767,63 0 2882,6 0 2863,36 0 2897,06 0 3012,61 0 3142,95 0 3032,93 0 3045,78 0 3110,52 0 3013,24 0 2987,1 0 2995,55 0 2833,18 0 2848,96 0 2794,83 0 2845,26 0 2915,02 0 2892,63 0 2604,42 0 2641,65 0 2659,81 0 2638,53 0 2720,25 0 2745,88 0 2735,7 0 2811,7 0 2799,43 0 2555,28 0 2304,98 0 2214,95 0 2065,81 0 1940,49 0 2042 0 1995,37 0 1946,81 0 1765,9 0 1635,25 0 1833,42 0 1910,43 0 1959,67 0 1969,6 0 2061,41 0 2093,48 0 2120,88 0 2174,56 0 2196,72 0 2350,44 0 2440,25 0 2408,64 0 2472,81 0 2407,6 0 2454,62 0 2448,05 0 2497,84 0 2645,64 0 2756,76 0 2849,27 0 2921,44 0 2981,85 0 3080,58 0 3106,22 0 3119,31 0 3061,26 0 3097,31 0 3161,69 0 3257,16 0 3277,01 0 3295,32 0 3363,99 0 3494,17 0 3667,03 0 3813,06 0 3917,96 0 3895,51 0 3801,06 0 3570,12 0 3701,61 0 3862,27 0 3970,1 0 4138,52 0 4199,75 0 4290,89 0 4443,91 0 4502,64 0 4356,98 0 4591,27 0 4696,96 0 4621,4 0 4562,84 1 4202,52 1 4296,49 1 4435,23 1 4105,18 1 4116,68 1 3844,49 1 3720,98 1 3674,4 1 3857,62 1 3801,06 1 3504,37 1 3032,6 1 3047,03 1 2962,34 1 2197,82 1 2014,45 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'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
BEL20[t] = + 2279.77806283829 -106.14423714479`Wel(1)_geen(0)_financiële_crisis`[t] + 98.8007714104707M1[t] + 72.1335498029745M2[t] + 8.96743930658927M3[t] + 91.3113288102044M4[t] + 56.4941072027082M5[t] -28.7331144047884M6[t] -76.076531885086M7[t] -83.4526423814712M8[t] -124.195419544523M9[t] -181.074863374241M10[t] -202.082084981738M11[t] + 15.1272216074964t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0		2-tail p-value1-tail p-value
(Intercept)2279.77806283829267.2819388.529500
`Wel(1)_geen(0)_financiële_crisis`-106.14423714479228.219743-0.46510.6429490.321475
M198.8007714104707322.0298690.30680.7596770.379838
M272.1335498029745321.9458260.22410.8232060.411603
M38.96743930658927321.884150.02790.9778340.488917
M491.3113288102044321.8448530.28370.7772620.388631
M556.4941072027082321.8279430.17550.8610360.430518
M6-28.7331144047884321.833424-0.08930.9290520.464526
M7-76.076531885086322.476483-0.23590.8140190.407009
M8-83.4526423814712322.393489-0.25890.796320.39816
M9-124.195419544523322.332831-0.38530.7008940.350447
M10-181.074863374241322.294521-0.56180.5755830.287792
M11-202.082084981738322.278567-0.6270.5321680.266084
t15.12722160749642.6844295.635200


Multiple Linear Regression - Regression Statistics
Multiple R0.585745590243383
R-squared0.343097896489569
Adjusted R-squared0.251272871267680
F-TEST (value)3.73643127960486
F-TEST (DF numerator)13
F-TEST (DF denominator)93
p-value8.57632805393305e-05
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation662.295598720762
Sum Squared Residuals40793097.7878949


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast		Residuals
Prediction Error
13030.292393.70605585627636.583944143732
22803.472382.16605585626421.303944143737
32767.632334.12716696737433.502833032627
42882.62431.59827807848451.001721921516
52863.362411.90827807848451.451721921516
62897.062341.80827807848555.251721921515
73012.612309.59208220568703.017917794317
83142.952317.34319331679825.606806683206
93032.932291.72763776124741.202362238762
103045.782249.97541553902795.804584460984
113110.522244.09541553902866.424584460984
123013.242461.30472212825551.935277871749
132987.12575.23271514622411.867284853782
142995.552563.69271514622431.857284853782
152833.182515.65382625733317.52617374267
162848.962613.12493736844235.835062631559
172794.832593.43493736844201.395062631559
182845.262523.33493736844321.925062631559
192915.022491.11874149564423.90125850436
202892.632498.86985260675393.760147393249
212604.422473.25429705120131.165702948805
222641.652431.50207482897210.147925171027
232659.812425.62207482897234.187925171027
242638.532642.83138141821-4.30138141820711
252720.252756.75937443617-36.5093744361744
262745.882745.219374436170.660625563825185
272735.72697.1804855472938.5195144527138
282811.72794.651596658417.0484033416026
292799.432774.961596658424.4684033416025
302555.282704.8615966584-149.581596658397
312304.982672.64540078560-367.665400785596
322214.952680.39651189671-465.446511896707
332065.812654.78095634115-588.970956341152
341940.492613.02873411893-672.53873411893
3520422607.14873411893-565.148734118929
361995.372824.35804070816-828.988040708164
371946.812938.28603372613-991.476033726131
381765.92926.74603372613-1160.84603372613
391635.252878.70714483724-1243.45714483724
401833.422976.17825594835-1142.75825594835
411910.432956.48825594835-1046.05825594835
421959.672886.38825594835-926.718255948354
431969.62854.17206007555-884.572060075553
442061.412861.92317118666-800.513171186664
452093.482836.30761563111-742.827615631108
462120.882794.55539340889-673.675393408886
472174.562788.67539340889-614.115393408886
482196.723005.88469999812-809.16469999812
492350.443119.81269301609-769.372693016087
502440.253108.27269301609-668.022693016088
512408.643060.2338041272-651.593804127199
522472.813157.70491523831-684.89491523831
532407.63138.01491523831-730.41491523831
542454.623067.91491523831-613.29491523831
552448.053035.69871936551-587.648719365509
562497.843043.44983047662-545.60983047662
572645.643017.83427492106-372.194274921065
582756.762976.08205269884-219.322052698842
592849.272970.20205269884-120.932052698842
602921.443187.41135928808-265.971359288077
612981.853301.33935230604-319.489352306044
623080.583289.79935230604-209.219352306044
633106.223241.76046341716-135.540463417155
643119.313339.23157452827-219.921574528267
653061.263319.54157452827-258.281574528266
663097.313249.44157452827-152.131574528266
673161.693217.22537865547-55.5353786554654
683257.163224.9764897665832.1835102334236
693277.013199.3609342110277.6490657889794
703295.323157.6087119888137.711288011201
713363.993151.7287119888212.261288011201
723494.173368.93801857803125.231981421967
733667.033482.866011596184.163988404
743813.063471.326011596341.733988403999
753917.963423.28712270711494.672877292888
763895.513520.75823381822374.751766181777
773801.063501.06823381822299.991766181777
783570.123430.96823381822139.151766181777
793701.613398.75203794542302.857962054578
803862.273406.50314905653455.766850943467
813970.13380.88759350098589.212406499022
824138.523339.13537127876799.384628721245
834199.753333.25537127876866.494628721245
844290.893550.46467786799740.42532213201
854443.913664.39267088596779.517329114043
864502.643652.85267088596849.787329114044
874356.983604.81378199707752.166218002932
884591.273702.28489310818888.985106891821
894696.963682.594893108181014.36510689182
904621.43612.494893108181008.90510689182
914562.843474.134460090591088.70553990941
924202.523481.8855712017720.634428798302
934296.493456.27001564614840.219984353856
944435.233414.517793423921020.71220657608
954105.183408.63779342392696.542206576079
964116.683625.84710001316490.832899986845
973844.493739.77509303112104.714906968877
983720.983728.23509303112-7.25509303112316
993674.43680.19620414223-5.79620414223422
1003857.623777.6673152533579.9526847466544
1013801.063757.9773152533543.0826847466542
1023504.373687.87731525335-183.507315253346
1033032.63655.66111938054-623.061119380545
1043047.033663.41223049166-616.382230491655
1052962.343637.7966749361-675.4566749361
1062197.823596.04445271388-1398.22445271388
1072014.453590.16445271388-1575.71445271388
 
Charts produced by software:
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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/07/t1228655533aecae6v6esrl4tm/9azg01228655466.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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