multiple lineair regression

*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: Mon, 22 Dec 2008 09:12:14 -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/Dec/22/t1229962377wt8wih6tkevsfqd.htm/, Retrieved Mon, 22 Dec 2008 17:13:06 +0100

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/22/t1229962377wt8wih6tkevsfqd.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}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

multiple lineair regression

Dataseries X:

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147768 0 1 0 137507 0 2 0 136919 0 3 0 136151 0 4 0 133001 0 5 0 125554 0 6 0 119647 0 7 0 114158 0 8 0 116193 0 9 0 152803 0 10 0 161761 0 11 0 160942 0 12 0 149470 0 13 0 139208 0 14 0 134588 0 15 0 130322 0 16 0 126611 0 17 0 122401 0 18 0 117352 0 19 0 112135 0 20 0 112879 0 21 0 148729 0 22 0 157230 0 23 0 157221 0 24 0 146681 0 25 0 136524 0 26 0 132111 0 0 27 125326 1 0 28 122716 1 0 29 116615 1 0 30 113719 1 0 31 110737 1 0 32 112093 1 0 33 143565 1 0 34 149946 1 0 35 149147 1 0 36 134339 1 0 37 122683 1 0 38 115614 1 0 39 116566 1 0 40 111272 1 0 41 104609 1 0 42 101802 1 0 43 94542 1 0 44 93051 1 0 45 124129 1 0 46 130374 1 0 47 123946 1 0 48 114971 1 0 49 105531 1 0 50 104919 1 51 0 104782 0 52 0 101281 0 53 0 94545 0 54 0 93248 0 55 0 84031 0 56 0 87486 0 57 0 115867 0 58 0 120327 0 59 0 117008 0 60 0 108811 0 61 0

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 Input view raw input (R code) Raw Output view raw output of R engine Computing time 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation y[t] = + 167775.447764236 + 5022.89079155974d[t] -747.243478626984t1[t] -820.519600667931t2[t] -11561.5724413985M1[t] -20776.0138886371M2[t] -23811.5853469903M3[t] -25235.8314195469M4[t] -28112.4774921035M5[t] -33567.3235646602M6[t] -36381.9696372168M7[t] -41638.4157097735M8[t] -39642.0617823301M9[t] -6187.30785488673M10[t] + 1498.24607255662M11[t] + e[t] Multiple Linear Regression - Ordinary Least Squares Variable Parameter S.D. T-STAT H0: parameter = 0 2-tail p-value 1-tail p-value (Intercept) 167775.447764236 2663.435451 62.9921 0 0 d 5022.89079155974 3658.958405 1.3728 0.176481 0.088241 t1 -747.243478626984 41.205036 -18.1348 0 0 t2 -820.519600667931 98.59321 -8.3223 0 0 M1 -11561.5724413985 3103.75551 -3.725 0.000532 0.000266 M2 -20776.0138886371 3263.347959 -6.3665 0 0 M3 -23811.5853469903 3271.17637 -7.2792 0 0 M4 -25235.8314195469 3263.76329 -7.7321 0 0 M5 -28112.4774921035 3257.208326 -8.6309 0 0 M6 -33567.3235646602 3251.516668 -10.3236 0 0 M7 -36381.9696372168 3246.692857 -11.2059 0 0 M8 -41638.4157097735 3242.740765 -12.8405 0 0 M9 -39642.0617823301 3239.663582 -12.2365 0 0 M10 -6187.30785488673 3237.463804 -1.9112 0.062227 0.031113 M11 1498.24607255662 3236.143219 0.463 0.645567 0.322783 Multiple Linear Regression - Regression Statistics Multiple R 0.972137718251645 R-squared 0.945051743247514 Adjusted R-squared 0.928328360757627 F-TEST (value) 56.510801198203 F-TEST (DF numerator) 14 F-TEST (DF denominator) 46 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 5116.09550432729 Sum Squared Residuals 1204023927.63231 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 147768 155466.631844209 -7698.63184420943 2 137507 145504.946918344 -7997.94691834445 3 136919 141722.131981364 -4803.1319813643 4 136151 139550.642430181 -3399.64243018062 5 133001 135926.752878997 -2925.75287899699 6 125554 129724.663327813 -4170.6633278134 7 119647 126162.773776630 -6515.77377662973 8 114158 120159.084225446 -6001.08422544613 9 116193 121408.194674263 -5215.19467426251 10 152803 154115.705123079 -1312.70512307890 11 161761 161054.015571895 706.984428104676 12 160942 158808.526020712 2133.47397928836 13 149470 146499.710100686 2970.28989931386 14 139208 136538.025174821 2669.97482517942 15 134588 132755.210237840 1832.78976215959 16 130322 130583.720686657 -261.720686656799 17 126611 126959.831135473 -348.831135473184 18 122401 120757.741584290 1643.25841571045 19 117352 117195.852033106 156.147966894064 20 112135 111192.162481922 942.837518077686 21 112879 112441.272930739 437.727069261307 22 148729 145148.783379555 3580.21662044493 23 157230 152087.093828371 5142.90617162857 24 157221 149841.604277188 7379.39572281217 25 146681 137532.788357162 9148.21164283768 26 136524 127571.103431297 8952.89656870325 27 132111 121809.833199211 10301.1668007890 28 125326 124587.958317546 738.041682453795 29 122716 120890.792644322 1825.20735567836 30 116615 114615.426971097 1999.57302890294 31 113719 110980.261297872 2738.7387021275 32 110737 104903.295624648 5833.70437535206 33 112093 106079.129951423 6013.87004857664 34 143565 138713.364278199 4851.6357218012 35 149946 145578.398604974 4367.60139502579 36 149147 143259.632931750 5887.36706825033 37 134339 130877.540889683 3461.45911031679 38 122683 120842.579841777 1840.42015822331 39 115614 116986.488782756 -1372.48878275559 40 116566 114741.723109531 1824.27689046896 41 111272 111044.557436306 227.442563693529 42 104609 104769.191763082 -160.191763081896 43 101802 101134.026089857 667.973910142655 44 94542 95057.0604166328 -515.060416632764 45 93051 96232.8947434082 -3181.89474340820 46 124129 128867.129070184 -4738.12907018363 47 130374 135732.163396959 -5358.16339695905 48 123946 133413.397723734 -9467.3977237345 49 114971 121031.305681668 -6060.30568166804 50 105531 110996.344633762 -5465.34463376153 51 104919 110877.335798829 -5958.33579882866 52 104782 103682.955456085 1099.04454391466 53 101281 100059.065904902 1221.93409509828 54 94545 93856.9763537181 688.023646281907 55 93248 90295.0868025345 2952.91319746551 56 84031 84291.3972513509 -260.397251350859 57 87486 85540.5077001672 1945.49229983276 58 115867 118248.018148984 -2381.01814898361 59 120327 125186.3285978 -4859.32859779998 60 117008 122940.839046616 -5932.83904661637 61 108811 110632.023126591 -1821.02312659086 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 18 0.401156911828098 0.802313823656196 0.598843088171902 19 0.291488780777332 0.582977561554664 0.708511219222668 20 0.226666354640196 0.453332709280393 0.773333645359804 21 0.249067091797973 0.498134183595945 0.750932908202028 22 0.232634285118997 0.465268570237995 0.767365714881003 23 0.209303233103363 0.418606466206727 0.790696766896636 24 0.146590192450254 0.293180384900507 0.853409807549746 25 0.129678227465610 0.259356454931221 0.87032177253439 26 0.120649317680551 0.241298635361102 0.879350682319449 27 0.0743917446076275 0.148783489215255 0.925608255392372 28 0.0928214347215187 0.185642869443037 0.907178565278481 29 0.107511549281261 0.215023098562522 0.892488450718739 30 0.143155854926668 0.286311709853336 0.856844145073332 31 0.492653623735453 0.985307247470906 0.507346376264547 32 0.627680223454173 0.744639553091654 0.372319776545827 33 0.690595804786564 0.618808390426872 0.309404195213436 34 0.631022518076117 0.737954963847766 0.368977481923883 35 0.62365135531668 0.75269728936664 0.37634864468332 36 0.942780711974545 0.114438576050910 0.0572192880254552 37 0.950745882302426 0.0985082353951488 0.0492541176975744 38 0.984825143004253 0.0303497139914931 0.0151748569957465 39 0.989385541863732 0.0212289162725361 0.0106144581362681 40 0.980677056798192 0.0386458864036165 0.0193229432018082 41 0.961494867991021 0.0770102640179582 0.0385051320089791 42 0.921608691599626 0.156782616800749 0.0783913084003743 43 0.829100932748917 0.341798134502165 0.170899067251083 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 0 0 OK 5% type I error level 3 0.115384615384615 NOK 10% type I error level 5 0.192307692307692 NOK

Charts produced by software:

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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) library(lmtest) n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test 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)) if (n > n25) { kp3 <- k + 3 nmkm3 <- n - k - 3 gqarr <- array(NA, dim=c(nmkm3-kp3+1,3)) numgqtests <- 0 numsignificant1 <- 0 numsignificant5 <- 0 numsignificant10 <- 0 for (mypoint in kp3:nmkm3) { j <- 0 numgqtests <- numgqtests + 1 for (myalt in c('greater', 'two.sided', 'less')) { j <- j + 1 gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value } if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1 if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1 if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1 } gqarr } bitmap(file='test0.png') plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index') points(x[,1]-mysum$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') qqline(mysum$resid) grid() dev.off() (myerror <- as.ts(mysum$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() if (n > n25) { bitmap(file='test9.png') plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint') grid() 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') if (n > n25) { a<-table.start() a<-table.row.start(a) a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'p-values',header=TRUE) a<-table.element(a,'Alternative Hypothesis',3,header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'breakpoint index',header=TRUE) a<-table.element(a,'greater',header=TRUE) a<-table.element(a,'2-sided',header=TRUE) a<-table.element(a,'less',header=TRUE) a<-table.row.end(a) for (mypoint in kp3:nmkm3) { a<-table.row.start(a) a<-table.element(a,mypoint,header=TRUE) a<-table.element(a,gqarr[mypoint-kp3+1,1]) a<-table.element(a,gqarr[mypoint-kp3+1,2]) a<-table.element(a,gqarr[mypoint-kp3+1,3]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable5.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Description',header=TRUE) a<-table.element(a,'# significant tests',header=TRUE) a<-table.element(a,'% significant tests',header=TRUE) a<-table.element(a,'OK/NOK',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'1% type I error level',header=TRUE) a<-table.element(a,numsignificant1) a<-table.element(a,numsignificant1/numgqtests) if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'5% type I error level',header=TRUE) a<-table.element(a,numsignificant5) a<-table.element(a,numsignificant5/numgqtests) if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'10% type I error level',header=TRUE) a<-table.element(a,numsignificant10) a<-table.element(a,numsignificant10/numgqtests) if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable6.tab') }

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