*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: Thu, 19 Nov 2009 09:59:52 -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/19/t1258650105rug1ebobr6dn75p.htm/, Retrieved Thu, 19 Nov 2009 18:02:00 +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/19/t1258650105rug1ebobr6dn75p.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:

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54.8 0 56 56.6 52.7 0 54.8 56 50.9 0 52.7 54.8 50.6 0 50.9 52.7 52.1 0 50.6 50.9 53.3 0 52.1 50.6 53.9 0 53.3 52.1 54.3 0 53.9 53.3 54.2 0 54.3 53.9 54.2 0 54.2 54.3 53.5 0 54.2 54.2 51.4 0 53.5 54.2 50.5 0 51.4 53.5 50.3 0 50.5 51.4 49.8 0 50.3 50.5 50.7 0 49.8 50.3 52.8 0 50.7 49.8 55.3 0 52.8 50.7 57.3 0 55.3 52.8 57.5 0 57.3 55.3 56.8 0 57.5 57.3 56.4 0 56.8 57.5 56.3 0 56.4 56.8 56.4 0 56.3 56.4 57 0 56.4 56.3 57.9 0 57 56.4 58.9 0 57.9 57 58.8 0 58.9 57.9 56.5 1 58.8 58.9 51.9 1 56.5 58.8 47.4 1 51.9 56.5 44.9 1 47.4 51.9 43.9 1 44.9 47.4 43.4 1 43.9 44.9 42.9 1 43.4 43.9 42.6 1 42.9 43.4 42.2 1 42.6 42.9 41.2 1 42.2 42.6 40.2 1 41.2 42.2 39.3 1 40.2 41.2 38.5 1 39.3 40.2 38.3 1 38.5 39.3 37.9 1 38.3 38.5 37.6 1 37.9 38.3 37.3 1 37.6 37.9 36 1 37.3 37.6 34.5 1 36 37.3 33.5 1 34.5 36 32.9 1 33.5 34.5 32.9 1 32.9 33.5 32.8 1 32.9 32.9 31.9 1 32.8 32.9 30.5 1 31.9 32.8 29.2 1 30.5 31.9 28.7 1 29.2 30.5 28.4 1 28.7 29.2 28 1 28.4 28.7 27.4 1 28 28.4 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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 3.46094894308918 -1.35890812535706X[t] + 1.57594470852792Y1[t] -0.641364831745757Y2[t] + 0.301634497468656M1[t] + 0.112538207357399M2[t] + 0.0715051759643893M3[t] + 0.263299441206298M4[t] + 0.460167495643472M5[t] + 0.100278611311066M6[t] + 0.184482326076706M7[t] + 0.262352168000846M8[t] + 0.194356140873652M9[t] + 0.104842003651204M10[t] + 0.00988454894042862M11[t] -0.0031959243864679t + 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) 3.46094894308918 1.393426 2.4838 0.016975 0.008488 X -1.35890812535706 0.527899 -2.5742 0.013576 0.006788 Y1 1.57594470852792 0.106811 14.7545 0 0 Y2 -0.641364831745757 0.104974 -6.1098 0 0 M1 0.301634497468656 0.539082 0.5595 0.578701 0.28935 M2 0.112538207357399 0.538915 0.2088 0.835572 0.417786 M3 0.0715051759643893 0.538747 0.1327 0.89503 0.447515 M4 0.263299441206298 0.538875 0.4886 0.627601 0.3138 M5 0.460167495643472 0.546463 0.8421 0.404401 0.2022 M6 0.100278611311066 0.545736 0.1837 0.855074 0.427537 M7 0.184482326076706 0.540479 0.3413 0.734517 0.367258 M8 0.262352168000846 0.539049 0.4867 0.628947 0.314473 M9 0.194356140873652 0.538981 0.3606 0.720165 0.360082 M10 0.104842003651204 0.538855 0.1946 0.84665 0.423325 M11 0.00988454894042862 0.538931 0.0183 0.985452 0.492726 t -0.0031959243864679 0.016433 -0.1945 0.846713 0.423356 Multiple Linear Regression - Regression Statistics Multiple R 0.997691270248974 R-squared 0.995387870731012 Adjusted R-squared 0.993778988427876 F-TEST (value) 618.682838882126 F-TEST (DF numerator) 15 F-TEST (DF denominator) 43 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.801038532138557 Sum Squared Residuals 27.5914973887398 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 54.8 55.7110417169253 -0.911041716925267 2 52.7 54.0124347512415 -1.31243475124146 3 50.9 51.4283597056483 -0.528359705648272 4 50.6 50.1271237178195 0.472876282180463 5 52.1 51.0024691324542 1.09753086754576 6 53.3 53.195710836051 0.104289163949020 7 53.9 54.205805029045 -0.305805029045017 8 54.3 54.4564079736045 -0.156407973604542 9 54.2 54.6307750064546 -0.430775006454585 10 54.2 54.1239245412946 0.076075458705416 11 53.5 54.0899076453719 -0.589907645371917 12 51.4 52.9736658760755 -1.57366587607547 13 50.5 50.411575943471 0.0884240565289558 14 50.3 50.1477996379643 0.152200362035715 15 49.8 50.3656100890504 -0.565610089050398 16 50.7 49.894509041991 0.805490958008976 17 52.8 51.8272138255898 0.972786174410244 18 55.3 54.1963845562083 1.10361544379167 19 57.3 56.8703879712412 0.429612028758775 20 57.5 58.4935392264703 -0.99353922647035 21 56.8 57.4548065531708 -0.654806553170764 22 56.4 56.1306622292431 0.269337770756858 23 56.3 55.8510863489568 0.448913651043235 24 56.4 55.9369573374754 0.463042662524625 25 57 56.4571268645849 0.542873135415067 26 57.9 57.1462649920294 0.75373500797061 27 58.9 58.1355673748776 0.764432625122414 28 58.8 59.3228820756898 -0.522882075689771 29 56.5 57.3586867777849 -0.858686777784864 30 51.9 53.4350656226264 -1.53506562262635 31 47.4 47.7418668667923 -0.341866866792309 32 44.9 43.6750678219848 1.22493217801519 33 43.9 42.5501558420072 1.34984415799276 34 43.4 42.4849131512348 0.915086848765203 35 42.9 42.2401522496193 0.65984775038065 36 42.6 41.7597818379014 0.840218162098634 37 42.2 41.9061194142981 0.293880585701941 38 41.2 41.2758587659129 -0.0758587659128922 39 40.2 39.9122310343038 0.287768965696208 40 39.3 39.1662494983771 0.133750501622929 41 38.5 38.5829362224984 -0.0829362224983919 42 38.3 37.5363239955284 0.763676004471629 43 37.9 37.8152347095986 0.0847652904014438 44 37.6 37.3878037100742 0.212196289925788 45 37.3 37.1003742787005 0.199625721299517 46 36 36.7272902540569 -0.727290254056906 47 34.5 34.7728182033971 -0.272818203397096 48 33.5 33.2295949485478 0.270405051452204 49 32.9 32.9141360607207 -0.0141360607206959 50 32.9 32.4176418528520 0.482358147148027 51 32.8 32.7582317961200 0.0417682038800483 52 31.9 32.7892356661226 -0.889235666122597 53 30.5 31.6286940416727 -1.12869404167275 54 29.2 29.636514989586 -0.436514989585965 55 28.7 28.5667054233229 0.133294576677107 56 28.4 28.6871812678661 -0.287181267866087 57 28 28.4638883196669 -0.463888319666924 58 27.4 27.9332098241706 -0.533209824170572 59 26.9 27.1460355526549 -0.246035552654873 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 19 0.383797704894620 0.767595409789241 0.61620229510538 20 0.568013989745888 0.863972020508224 0.431986010254112 21 0.6815781411301 0.6368437177398 0.3184218588699 22 0.586269251241131 0.827461497517738 0.413730748758869 23 0.63852569768549 0.722948604629019 0.361474302314510 24 0.94794680983037 0.104106380339259 0.0520531901696295 25 0.92680831872781 0.14638336254438 0.07319168127219 26 0.911565973819178 0.176868052361644 0.0884340261808222 27 0.887915898499298 0.224168203001403 0.112084101500702 28 0.946247825801261 0.107504348397477 0.0537521741987387 29 0.996880616804502 0.00623876639099515 0.00311938319549758 30 0.996250261413407 0.00749947717318505 0.00374973858659253 31 0.992202923661093 0.0155941526778141 0.00779707633890706 32 0.996809611615654 0.00638077676869291 0.00319038838434646 33 0.995674568773917 0.00865086245216501 0.00432543122608251 34 0.99144085436057 0.0171182912788613 0.00855914563943065 35 0.986701273914209 0.0265974521715826 0.0132987260857913 36 0.97041615209434 0.0591676958113213 0.0295838479056607 37 0.94654085466774 0.106918290664519 0.0534591453322594 38 0.948693143622374 0.102613712755252 0.0513068563776259 39 0.8953786598597 0.209242680280600 0.104621340140300 40 0.798217131403275 0.403565737193449 0.201782868596725 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 4 0.181818181818182 NOK 5% type I error level 7 0.318181818181818 NOK 10% type I error level 8 0.363636363636364 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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