ws 8 auitoregressie

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R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Mon, 29 Nov 2010 18:31:52 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Nov/29/t1291055459824okt6ukprehys.htm/, Retrieved Mon, 29 Nov 2010 19:30:59 +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/2010/Nov/29/t1291055459824okt6ukprehys.htm/}, year = {2010}, } @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 = {2010}, 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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98,1 102,8 104,7 95,9 94,6 113,9 98,1 102,8 104,7 95,9 80,9 113,9 98,1 102,8 104,7 95,7 80,9 113,9 98,1 102,8 113,2 95,7 80,9 113,9 98,1 105,9 113,2 95,7 80,9 113,9 108,8 105,9 113,2 95,7 80,9 102,3 108,8 105,9 113,2 95,7 99 102,3 108,8 105,9 113,2 100,7 99 102,3 108,8 105,9 115,5 100,7 99 102,3 108,8 100,7 115,5 100,7 99 102,3 109,9 100,7 115,5 100,7 99 114,6 109,9 100,7 115,5 100,7 85,4 114,6 109,9 100,7 115,5 100,5 85,4 114,6 109,9 100,7 114,8 100,5 85,4 114,6 109,9 116,5 114,8 100,5 85,4 114,6 112,9 116,5 114,8 100,5 85,4 102 112,9 116,5 114,8 100,5 106 102 112,9 116,5 114,8 105,3 106 102 112,9 116,5 118,8 105,3 106 102 112,9 106,1 118,8 105,3 106 102 109,3 106,1 118,8 105,3 106 117,2 109,3 106,1 118,8 105,3 92,5 117,2 109,3 106,1 118,8 104,2 92,5 117,2 109,3 106,1 112,5 104,2 92,5 117,2 109,3 122,4 112,5 104,2 92,5 117,2 113,3 122,4 112,5 104,2 92,5 100 113,3 122,4 112,5 104,2 110,7 100 113,3 122,4 112,5 112,8 110,7 100 113,3 122,4 109,8 112,8 110,7 100 113,3 117,3 109, 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 6 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation y[t] = + 18.1864437368423 + 0.206751675048763y1[t] + 0.333777650199015y2[t] + 0.520824147742392y3[t] -0.220361994936251y4[t] -3.29045670333491M1[t] + 4.25600909331611M2[t] -16.8638473658139M3[t] -5.88390147598205M4[t] + 9.7805082769888M5[t] + 19.3620595783345M6[t] -3.81998157203203M7[t] -16.2516899915533M8[t] -8.12360050980905M9[t] + 0.579419546771023M10[t] + 13.5708797465492M11[t] -0.0338081356043498t + 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) 18.1864437368423 11.164053 1.629 0.109995 0.054997 y1 0.206751675048763 0.142445 1.4514 0.153298 0.076649 y2 0.333777650199015 0.122211 2.7312 0.008859 0.00443 y3 0.520824147742392 0.120729 4.314 8.2e-05 4.1e-05 y4 -0.220361994936251 0.140102 -1.5729 0.122458 0.061229 M1 -3.29045670333491 3.05909 -1.0756 0.287582 0.143791 M2 4.25600909331611 3.379807 1.2592 0.21416 0.10708 M3 -16.8638473658139 2.998161 -5.6247 1e-06 0 M4 -5.88390147598205 5.004684 -1.1757 0.245644 0.122822 M5 9.7805082769888 4.764616 2.0527 0.045689 0.022844 M6 19.3620595783345 3.800405 5.0947 6e-06 3e-06 M7 -3.81998157203203 3.504889 -1.0899 0.281313 0.140657 M8 -16.2516899915533 3.468919 -4.6849 2.4e-05 1.2e-05 M9 -8.12360050980905 4.788879 -1.6963 0.096435 0.048217 M10 0.579419546771023 4.623816 0.1253 0.900811 0.450406 M11 13.5708797465492 3.550863 3.8219 0.000388 0.000194 t -0.0338081356043498 0.031047 -1.0889 0.281733 0.140866 Multiple Linear Regression - Regression Statistics Multiple R 0.937289648886527 R-squared 0.878511885909829 Adjusted R-squared 0.837154230049345 F-TEST (value) 21.2418201087945 F-TEST (DF numerator) 16 F-TEST (DF denominator) 47 p-value 3.33066907387547e-16 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4.09930331129844 Sum Squared Residuals 789.80151898705 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 98.1 100.163562116279 -2.0635621162787 2 113.9 110.367091275934 3.53290872406601 3 80.9 87.9825967548852 -7.08259675488519 4 95.7 95.3504304016376 0.349569598362421 5 113.2 112.291017263688 0.908982736311528 6 105.9 109.727907570237 -3.82790757023684 7 108.8 105.824023154376 2.97597684562353 8 102.3 97.3745746708748 4.92542532912516 9 99 97.434574124871 1.56542587512897 10 100.7 106.370983383380 -5.67098338337979 11 115.5 114.554240303839 0.945759696160877 12 100.7 104.290532497281 -3.5905324972813 13 109.9 104.458847725017 5.44115227498254 14 114.6 116.267293568763 -1.66729356876312 15 85.4 88.186561316945 -2.78656131694498 16 100.5 102.717244799970 -2.21724479997049 17 114.8 112.144032465738 2.65596753426219 18 116.5 113.444600612403 3.05539938759667 19 112.9 109.65226445491 3.24773554509007 20 102 101.130183064126 0.869816935874058 21 106 103.503496135092 2.49650386490848 22 105.3 107.111956045829 -1.81195604582879 23 118.8 116.376312509643 2.42368749035701 24 106.1 109.814370221283 -3.71437022128312 25 109.3 107.124332503747 2.17566749625341 26 117.2 118.244998758399 -1.04499875839947 27 92.5 90.2034072692194 2.29659273078056 28 104.2 103.144856694781 1.05514330521926 29 112.5 116.359497333671 -3.85949733367101 30 122.4 116.923261700412 5.47673829958794 31 113.3 110.061192297587 3.23880770241283 32 100 100.763239321996 -0.763239321995807 33 110.7 106.397501277855 4.30249872214511 34 112.8 105.918629879881 6.88137012011918 35 109.8 117.960214307733 -8.1602143077326 36 117.3 112.939837379346 4.36016262065359 37 109.1 108.900734517117 0.199265482883037 38 115.9 115.196128186663 0.703871813336926 39 96 97.278665343505 -1.2786653435051 40 99.8 100.456659812106 -0.65665981210601 41 116.8 115.579315118823 1.22068488117705 42 115.7 118.047329725509 -2.34732972550937 43 99.4 106.642609111021 -7.24260911102061 44 94.3 98.4565197682442 -4.15651976824419 45 91 95.7367313969585 -4.73673139695853 46 93.2 93.7743613604872 -0.57436136048724 47 103.1 107.021098228086 -3.92109822808631 48 94.1 95.6026892459783 -1.50268924597832 49 91.8 95.5950657768933 -3.79506577689333 50 102.7 104.299558407327 -1.59955840732663 51 82.6 77.7627973956157 4.83720260438433 52 89.1 88.976765283151 0.123234716848961 53 104.5 105.426137818080 -0.926137818079758 54 105.1 107.456900391438 -2.3569003914384 55 95.1 97.3199109821058 -2.21991098210582 56 88.7 89.5754831747592 -0.875483174759216 57 86.3 89.927697065224 -3.62769706522403 58 91.8 90.6240693304234 1.17593066957665 59 111.5 102.788134650699 8.71186534930103 60 99.7 95.2525706561109 4.44742934388914 61 97.5 99.457457360947 -1.95745736094696 62 111.7 111.624929802914 0.0750701970862843 63 86.2 82.1859719198296 4.01402808017039 64 95.4 94.0540430083541 1.34595699164586 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 20 0.285184637111776 0.570369274223551 0.714815362888224 21 0.168978881867090 0.337957763734181 0.83102111813291 22 0.0914589573802515 0.182917914760503 0.908541042619749 23 0.0514654753606256 0.102930950721251 0.948534524639374 24 0.0303539570935869 0.0607079141871738 0.969646042906413 25 0.0207334386589061 0.0414668773178123 0.979266561341094 26 0.0359951900878849 0.0719903801757699 0.964004809912115 27 0.0175878388488975 0.035175677697795 0.982412161151103 28 0.00790409483565242 0.0158081896713048 0.992095905164348 29 0.0323164571157184 0.0646329142314367 0.967683542884282 30 0.036380123046927 0.072760246093854 0.963619876953073 31 0.0257828959466976 0.0515657918933952 0.974217104053302 32 0.0438392193691378 0.0876784387382757 0.956160780630862 33 0.0882841086440164 0.176568217288033 0.911715891355984 34 0.160033594215683 0.320067188431367 0.839966405784317 35 0.269534321020045 0.539068642040091 0.730465678979955 36 0.572302033380081 0.855395933239837 0.427697966619919 37 0.517358033644948 0.965283932710104 0.482641966355052 38 0.464070351146251 0.928140702292503 0.535929648853749 39 0.363251568012598 0.726503136025196 0.636748431987402 40 0.315468915218751 0.630937830437502 0.684531084781249 41 0.336845561348906 0.673691122697811 0.663154438651094 42 0.344900622286897 0.689801244573794 0.655099377713103 43 0.454425029763287 0.908850059526574 0.545574970236713 44 0.391720319338617 0.783440638677233 0.608279680661383 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 0.12 NOK 10% type I error level 9 0.36 NOK

Charts produced by software:

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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) 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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