*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: Tue, 24 Nov 2009 05:16:30 -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/24/t1259065067wcul4jnvj5fzaei.htm/, Retrieved Tue, 24 Nov 2009 13:18:04 +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/24/t1259065067wcul4jnvj5fzaei.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:

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Dataseries X:

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105.4 119.5 109 116.7 102.7 115.1 119.5 109 98.1 107.1 115.1 119.5 104.5 109.7 107.1 115.1 87.4 110.4 109.7 107.1 89.9 105 110.4 109.7 109.8 115.8 105 110.4 111.7 116.4 115.8 105 98.6 111.1 116.4 115.8 96.9 119.5 111.1 116.4 95.1 110.9 119.5 111.1 97 115.1 110.9 119.5 112.7 125.2 115.1 110.9 102.9 116 125.2 115.1 97.4 112.9 116 125.2 111.4 121.7 112.9 116 87.4 123.2 121.7 112.9 96.8 116.6 123.2 121.7 114.1 136.2 116.6 123.2 110.3 120.9 136.2 116.6 103.9 119.6 120.9 136.2 101.6 125.9 119.6 120.9 94.6 116.1 125.9 119.6 95.9 107.5 116.1 125.9 104.7 116.7 107.5 116.1 102.8 112.5 116.7 107.5 98.1 113 112.5 116.7 113.9 126.4 113 112.5 80.9 114.1 126.4 113 95.7 112.5 114.1 126.4 113.2 112.4 112.5 114.1 105.9 113.1 112.4 112.5 108.8 116.3 113.1 112.4 102.3 111.7 116.3 113.1 99 118.8 111.7 116.3 100.7 116.5 118.8 111.7 115.5 125.1 116.5 118.8 100.7 113.1 125.1 116.5 109.9 119.6 113.1 125.1 114.6 114.4 119.6 113.1 85.4 114 114.4 119.6 100.5 117.8 114 114.4 114.8 117 117.8 114 etc...

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 5 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation ipchn[t] = -22.3389173229912 + 0.832240299372395Tip[t] + 0.254189299923941`y(t-1)`[t] + 0.234683807228363`y(t-2)`[t] -0.0702121144545338M1[t] -2.16350805662868M2[t] -2.81444431776765M3[t] -5.41334542375707M4[t] + 14.6770191833725M5[t] + 2.36848127661478M6[t] -5.65462648983423M7[t] -7.37323493898212M8[t] -4.1666523610624M9[t] + 4.95764267217371M10[t] + 3.66500467191191M11[t] -0.151732055011969t + 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) -22.3389173229912 26.834303 -0.8325 0.409849 0.204925 Tip 0.832240299372395 0.199177 4.1784 0.000145 7.3e-05 `y(t-1)` 0.254189299923941 0.127779 1.9893 0.053208 0.026604 `y(t-2)` 0.234683807228363 0.128752 1.8228 0.075464 0.037732 M1 -0.0702121144545338 3.98167 -0.0176 0.986014 0.493007 M2 -2.16350805662868 3.39199 -0.6378 0.527048 0.263524 M3 -2.81444431776765 3.206688 -0.8777 0.385111 0.192555 M4 -5.41334542375707 4.006826 -1.351 0.183919 0.09196 M5 14.6770191833725 4.079772 3.5975 0.00084 0.00042 M6 2.36848127661478 3.106035 0.7625 0.449998 0.224999 M7 -5.65462648983423 4.008324 -1.4107 0.165691 0.082846 M8 -7.37323493898212 4.059724 -1.8162 0.076483 0.038242 M9 -4.1666523610624 3.382125 -1.232 0.224816 0.112408 M10 4.95764267217371 3.082835 1.6081 0.115296 0.057648 M11 3.66500467191191 3.28568 1.1154 0.271 0.1355 t -0.151732055011969 0.053097 -2.8576 0.006613 0.003307 Multiple Linear Regression - Regression Statistics Multiple R 0.7068850117758 R-squared 0.499686419873272 Adjusted R-squared 0.32100299839944 F-TEST (value) 2.79649010384800 F-TEST (DF numerator) 15 F-TEST (DF denominator) 42 p-value 0.00440837369515834 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4.56808646868449 Sum Squared Residuals 876.431387385888 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 119.5 120.251500056653 -0.751500056652636 2 115.1 116.621345584704 -1.52134558470371 3 107.1 113.336118947672 -6.23611894767218 4 109.7 112.845700551458 -3.14570055145780 5 110.4 117.336445706283 -6.93644570628282 6 105 107.744886901685 -2.74488690168459 7 115.8 114.923285483205 0.876714516795172 8 116.4 116.112153427998 0.287846572002082 9 111.1 110.951754727148 0.148245272852022 10 119.5 117.303116191179 2.19688380882081 11 110.9 115.252079538086 -4.35207953808588 12 115.1 112.801915381342 2.29808461865809 13 125.2 124.695458229539 0.504541770461356 14 116 117.847459218094 -1.84745921809399 15 112.9 112.499234149101 0.400765850898923 16 121.7 118.452887323048 3.24711267695193 17 123.2 119.927098727151 3.27290127284901 18 116.6 117.736389032977 -1.13638903297727 19 136.2 122.633682722003 13.5663172779967 20 120.9 121.034026231030 -0.134026231030336 21 119.6 119.473245170794 0.126754829205624 22 125.9 122.610547119967 3.28945288003306 23 116.1 116.636798609210 -0.536798609210364 24 107.5 112.889427117755 -5.38942711775466 25 116.7 115.505268292581 1.19473170741862 26 112.5 111.999244543724 0.500755456275935 27 113 108.376542787343 4.62345721265675 28 126.4 117.916729016029 8.48327098397145 29 114.1 113.914910211452 0.185089788547831 30 112.5 113.790031308189 -1.29003130818944 31 112.4 116.886083016958 -4.48608301695821 32 113.1 108.539475305822 4.56052469417789 33 116.3 114.162286826134 2.13771317386629 34 111.7 118.702972283254 -7.00297228325375 35 118.8 114.093926643532 4.70607335646829 36 116.5 112.417196941750 4.08280305824957 37 125.1 125.594028844492 -0.494028844491673 38 113.1 112.678099639315 0.42190036068522 39 119.6 118.500051220466 1.09994877953351 40 114.4 118.496972229281 -4.09697222928062 41 114 114.337848427104 -0.337848427104201 42 117.8 113.122375468301 4.67762453169943 43 117 117.720617744684 -0.720617744684468 44 120.9 117.953532776986 2.94646722301371 45 115 118.815909446074 -3.81590944607412 46 117.3 118.132603139779 -0.832603139778518 47 119.4 119.217195209172 0.182804790827963 48 114.9 115.891460559153 -0.991460559152996 49 125.8 126.253744576736 -0.453744576735659 50 117.6 115.153851014163 2.44614898583654 51 117.6 117.488052895417 0.111947104582988 52 114.9 119.387710880185 -4.48771088018497 53 121.9 118.083696928010 3.81630307199018 54 117 116.506317288848 0.493682711151877 55 106.4 115.636331033149 -9.23633103314923 56 110.5 118.160812258163 -7.66081225816334 57 113.6 112.196803829850 1.40319617015018 58 114.2 111.850761265822 2.34923873417839 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 19 0.691086679733819 0.617826640532363 0.308913320266181 20 0.664736679999258 0.670526640001485 0.335263320000742 21 0.675288837996795 0.64942232400641 0.324711162003205 22 0.641897275547751 0.716205448904498 0.358102724452249 23 0.51609907315644 0.96780185368712 0.48390092684356 24 0.695828886027641 0.608342227944717 0.304171113972359 25 0.599940467140129 0.800119065719741 0.400059532859871 26 0.537315255538778 0.925369488922444 0.462684744461222 27 0.494781428862289 0.989562857724578 0.505218571137711 28 0.643927965987226 0.712144068025548 0.356072034012774 29 0.641905172318740 0.716189655362519 0.358094827681260 30 0.543873711613285 0.912252576773429 0.456126288386714 31 0.81621587276509 0.367568254469821 0.183784127234910 32 0.751589526125174 0.496820947749651 0.248410473874825 33 0.670331806649524 0.659336386700952 0.329668193350476 34 0.908353813768195 0.183292372463609 0.0916461862318046 35 0.89920171159073 0.201596576818539 0.100798288409269 36 0.830725089011113 0.338549821977775 0.169274910988887 37 0.749669861010074 0.500660277979851 0.250330138989926 38 0.622868709635998 0.754262580728004 0.377131290364002 39 0.447520000251892 0.895040000503784 0.552479999748108 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 0 0 OK 10% type I error level 0 0 OK

Charts produced by software:

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Parameters (Session):

par1 = 2 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 2 ; par2 = Include Monthly Dummies ; par3 = 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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