*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, 21 Nov 2009 03:50:17 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Nov/21/t1258801064c1jr7xvn4560fbf.htm/, Retrieved Sat, 21 Nov 2009 11:57:56 +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/2009/Nov/21/t1258801064c1jr7xvn4560fbf.htm/}, year = {2009}, } @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 = {2009}, 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:

Dataseries X:

» Textbox « » Textfile « » CSV «

114 1 113.8 1 113.6 1 113.7 1 114.2 1 114.8 0 115.2 1 115.3 1 114.9 1 115.1 0 116 0 116 0 116 0 115.9 1 115.6 1 116.6 1 116.9 0 117.9 1 117.9 1 117.7 0 117.4 1 117.3 0 119 1 119.1 0 119 0 118.5 0 117 1 117.5 1 118.2 1 118.2 1 118.3 0 118.2 1 117.9 1 117.8 0 118.6 0 118.9 0 120.8 1 121.8 1 121.3 0 121.9 1 122 1 121.9 0 122 1 122.2 0 123 1 123.1 0 124.9 1 125.4 0 124.7 0 124.4 1 124 0 125 1 125.1 0 125.4 0 125.7 1 126.4 1 125.7 1 125.4 0 126.4 1 126.2 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 CPItot[t] = + 120.180769230769 -1.00429864253394CPIlandbouw[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) 120.180769230769 0.779113 154.2533 0 0 CPIlandbouw -1.00429864253394 1.034991 -0.9703 0.335904 0.167952 Multiple Linear Regression - Regression Statistics Multiple R 0.126390796284798 R-squared 0.0159746333855054 Adjusted R-squared -0.000991321211296192 F-TEST (value) 0.941569971460193 F-TEST (DF numerator) 1 F-TEST (DF denominator) 58 p-value 0.335903704370842 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.97271200924241 Sum Squared Residuals 915.381561085975 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 114 119.176470588235 -5.1764705882354 2 113.8 119.176470588235 -5.3764705882353 3 113.6 119.176470588235 -5.5764705882353 4 113.7 119.176470588235 -5.47647058823529 5 114.2 119.176470588235 -4.97647058823529 6 114.8 120.180769230769 -5.38076923076923 7 115.2 119.176470588235 -3.97647058823529 8 115.3 119.176470588235 -3.87647058823529 9 114.9 119.176470588235 -4.27647058823529 10 115.1 120.180769230769 -5.08076923076924 11 116 120.180769230769 -4.18076923076923 12 116 120.180769230769 -4.18076923076923 13 116 120.180769230769 -4.18076923076923 14 115.9 119.176470588235 -3.27647058823529 15 115.6 119.176470588235 -3.5764705882353 16 116.6 119.176470588235 -2.5764705882353 17 116.9 120.180769230769 -3.28076923076923 18 117.9 119.176470588235 -1.27647058823529 19 117.9 119.176470588235 -1.27647058823529 20 117.7 120.180769230769 -2.48076923076923 21 117.4 119.176470588235 -1.77647058823529 22 117.3 120.180769230769 -2.88076923076923 23 119 119.176470588235 -0.176470588235292 24 119.1 120.180769230769 -1.08076923076924 25 119 120.180769230769 -1.18076923076923 26 118.5 120.180769230769 -1.68076923076923 27 117 119.176470588235 -2.17647058823529 28 117.5 119.176470588235 -1.67647058823529 29 118.2 119.176470588235 -0.97647058823529 30 118.2 119.176470588235 -0.97647058823529 31 118.3 120.180769230769 -1.88076923076923 32 118.2 119.176470588235 -0.97647058823529 33 117.9 119.176470588235 -1.27647058823529 34 117.8 120.180769230769 -2.38076923076923 35 118.6 120.180769230769 -1.58076923076924 36 118.9 120.180769230769 -1.28076923076923 37 120.8 119.176470588235 1.62352941176471 38 121.8 119.176470588235 2.62352941176471 39 121.3 120.180769230769 1.11923076923077 40 121.9 119.176470588235 2.72352941176471 41 122 119.176470588235 2.82352941176471 42 121.9 120.180769230769 1.71923076923077 43 122 119.176470588235 2.82352941176471 44 122.2 120.180769230769 2.01923076923077 45 123 119.176470588235 3.82352941176471 46 123.1 120.180769230769 2.91923076923076 47 124.9 119.176470588235 5.72352941176471 48 125.4 120.180769230769 5.21923076923077 49 124.7 120.180769230769 4.51923076923077 50 124.4 119.176470588235 5.22352941176471 51 124 120.180769230769 3.81923076923077 52 125 119.176470588235 5.82352941176471 53 125.1 120.180769230769 4.91923076923076 54 125.4 120.180769230769 5.21923076923077 55 125.7 119.176470588235 6.52352941176471 56 126.4 119.176470588235 7.22352941176471 57 125.7 119.176470588235 6.52352941176471 58 125.4 120.180769230769 5.21923076923077 59 126.4 119.176470588235 7.22352941176471 60 126.2 120.180769230769 6.01923076923077 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.000563838874278702 0.00112767774855740 0.999436161125721 6 3.62903762636876e-05 7.25807525273753e-05 0.999963709623736 7 0.000312008010584382 0.000624016021168764 0.999687991989416 8 0.000239548546772747 0.000479097093545495 0.999760451453227 9 7.05731819191357e-05 0.000141146363838271 0.999929426818081 10 1.52420363534666e-05 3.04840727069332e-05 0.999984757963646 11 6.93421611405729e-06 1.38684322281146e-05 0.999993065783886 12 2.23635029216684e-06 4.47270058433369e-06 0.999997763649708 13 6.54587800517193e-07 1.30917560103439e-06 0.9999993454122 14 1.29756305011560e-06 2.59512610023120e-06 0.99999870243695 15 9.20567987729689e-07 1.84113597545938e-06 0.999999079432012 16 2.95605563438018e-06 5.91211126876036e-06 0.999997043944366 17 2.29781642879043e-06 4.59563285758086e-06 0.999997702183571 18 2.86686183108062e-05 5.73372366216124e-05 0.99997133138169 19 9.53882787803567e-05 0.000190776557560713 0.99990461172122 20 9.66546031441612e-05 0.000193309206288322 0.999903345396856 21 0.000131168862631615 0.00026233772526323 0.999868831137368 22 0.000105655508890632 0.000211311017781263 0.99989434449111 23 0.00042815392461487 0.00085630784922974 0.999571846075385 24 0.000667419771631853 0.00133483954326371 0.999332580228368 25 0.000797102845602684 0.00159420569120537 0.999202897154397 26 0.000768756856477058 0.00153751371295412 0.999231243143523 27 0.000892693625645242 0.00178538725129048 0.999107306374355 28 0.00120896226750475 0.00241792453500949 0.998791037732495 29 0.00197249793657804 0.00394499587315607 0.998027502063422 30 0.00339517681088687 0.00679035362177374 0.996604823189113 31 0.00425579906523941 0.00851159813047882 0.99574420093476 32 0.00885148395244072 0.0177029679048814 0.99114851604756 33 0.0239133455780247 0.0478266911560495 0.976086654421975 34 0.0512615302554676 0.102523060510935 0.948738469744532 35 0.111928159045906 0.223856318091812 0.888071840954094 36 0.272604120537736 0.545208241075471 0.727395879462264 37 0.519943662385076 0.960112675229847 0.480056337614924 38 0.729670019858861 0.540659960282277 0.270329980141139 39 0.843604931775572 0.312790136448855 0.156395068224427 40 0.92697471800978 0.146050563980441 0.0730252819902203 41 0.970589357179966 0.0588212856400677 0.0294106428200338 42 0.986774886753186 0.0264502264936280 0.0132251132468140 43 0.997466016916066 0.00506796616786795 0.00253398308393397 44 0.999443968712336 0.00111206257532805 0.000556031287664027 45 0.999929769468135 0.000140461063729022 7.02305318645112e-05 46 0.999988459812316 2.30803753674626e-05 1.15401876837313e-05 47 0.999985650489902 2.86990201963247e-05 1.43495100981624e-05 48 0.999968393775403 6.32124491940206e-05 3.16062245970103e-05 49 0.999921481627302 0.000157036745395768 7.85183726978839e-05 50 0.999942800316687 0.000114399366626491 5.71996833132457e-05 51 0.999973879583906 5.22408321877292e-05 2.61204160938646e-05 52 0.99997591022454 4.81795509190751e-05 2.40897754595375e-05 53 0.999905379008783 0.000189241982433516 9.4620991216758e-05 54 0.999437007022377 0.00112598595524500 0.000562992977622502 55 0.99703245044034 0.00593509911931967 0.00296754955965984 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 40 0.784313725490196 NOK 5% type I error level 43 0.843137254901961 NOK 10% type I error level 44 0.862745098039216 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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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