*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 13:05:09 -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/t125866122187ga0zsyst1232l.htm/, Retrieved Thu, 19 Nov 2009 21:07:12 +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/t125866122187ga0zsyst1232l.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 «

100.4 120.2 17 74 79.9 72.9 72.9 103 122.1 16 76 74 79.9 72.9 99 119.3 20 69.6 76 74 79.9 104.8 121.7 24 77.3 69.6 76 74 104.5 113.5 23 75.2 77.3 69.6 76 104.8 123.7 20 75.8 75.2 77.3 69.6 103.8 123.4 21 77.6 75.8 75.2 77.3 106.3 126.4 19 76.7 77.6 75.8 75.2 105.2 124.1 23 77 76.7 77.6 75.8 108.2 125.6 23 77.9 77 76.7 77.6 106.2 124.8 23 76.7 77.9 77 76.7 103.9 123 23 71.9 76.7 77.9 77 104.9 126.9 27 73.4 71.9 76.7 77.9 106.2 127.3 26 72.5 73.4 71.9 76.7 107.9 129 17 73.7 72.5 73.4 71.9 106.9 126.2 24 69.5 73.7 72.5 73.4 110.3 125.4 26 74.7 69.5 73.7 72.5 109.8 126.3 24 72.5 74.7 69.5 73.7 108.3 126.3 27 72.1 72.5 74.7 69.5 110.9 128.4 27 70.7 72.1 72.5 74.7 109.8 127.2 26 71.4 70.7 72.1 72.5 109.3 128.5 24 69.5 71.4 70.7 72.1 109 129 23 73.5 69.5 71.4 70.7 107.9 128.9 23 72.4 73.5 69.5 71.4 108.4 128.3 24 74.5 72.4 73.5 69.5 107.2 124.6 17 72.2 74.5 72.4 73.5 109.5 126.2 21 73 72.2 74.5 72.4 109.9 129.1 19 73.3 73 72.2 74.5 108 127.3 22 71.3 73.3 73 72.2 114.7 129.2 22 73.6 71.3 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 R Framework error message The field 'Names of X columns' contains a hard return which cannot be interpreted. Please, resubmit your request without hard returns in the 'Names of X columns'. Multiple Linear Regression - Estimated Regression Equation Y[t] = + 20.2513189201664 + 0.425341901487542totid[t] -0.0455449630743466ndzcg[t] + 0.0436802973309247indc[t] + 0.188344373020551y1[t] + 0.163567515100477y2[t] -0.130967620439291`y3 `[t] + 0.296514116202145M1[t] -0.835837579481557M2[t] -3.76745489042413M3[t] -2.08061356471506M4[t] -1.12030986429559M5[t] -1.97031879592753M6[t] -1.21767349589456M7[t] -1.11620771659602M8[t] + 1.25633708049614M9[t] + 0.269097496660407M10[t] -0.08551092511179M11[t] -0.166442807258652t + 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) 20.2513189201664 23.268082 0.8703 0.391022 0.195511 totid 0.425341901487542 0.244499 1.7396 0.092173 0.046086 ndzcg -0.0455449630743466 0.268582 -0.1696 0.866482 0.433241 indc 0.0436802973309247 0.104583 0.4177 0.67917 0.339585 y1 0.188344373020551 0.189551 0.9936 0.328348 0.164174 y2 0.163567515100477 0.16883 0.9688 0.340378 0.170189 `y3 ` -0.130967620439291 0.163436 -0.8013 0.429237 0.214619 M1 0.296514116202145 2.127164 0.1394 0.89007 0.445035 M2 -0.835837579481557 2.415932 -0.346 0.731781 0.36589 M3 -3.76745489042413 2.405121 -1.5664 0.127737 0.063868 M4 -2.08061356471506 2.526785 -0.8234 0.416765 0.208383 M5 -1.12030986429559 2.680751 -0.4179 0.67899 0.339495 M6 -1.97031879592753 2.718052 -0.7249 0.474129 0.237065 M7 -1.21767349589456 2.517465 -0.4837 0.632118 0.316059 M8 -1.11620771659602 2.409731 -0.4632 0.646558 0.323279 M9 1.25633708049614 2.385667 0.5266 0.602331 0.301165 M10 0.269097496660407 2.362987 0.1139 0.910091 0.455046 M11 -0.08551092511179 2.259958 -0.0378 0.970068 0.485034 t -0.166442807258652 0.077479 -2.1482 0.039892 0.019946 Multiple Linear Regression - Regression Statistics Multiple R 0.90975669067051 R-squared 0.827657236219756 Adjusted R-squared 0.72425157795161 F-TEST (value) 8.00398401868412 F-TEST (DF numerator) 18 F-TEST (DF denominator) 30 p-value 4.22611395878292e-07 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.10793514765004 Sum Squared Residuals 289.777826459955 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 74 75.7790253566907 -1.7790253566907 2 76 75.489644875326 0.510355124674 3 69.6 69.4873313009797 0.112668699020267 4 77.3 73.4345661294644 3.8654338705356 5 75.2 74.5720971867943 0.627902813205723 6 75.8 74.7897879567408 1.01021204325918 7 77.6 73.7690564989996 3.83094350100039 8 76.7 75.2556311242933 1.44436887570675 9 77 77.319662646084 -0.319662646083947 10 77.9 77.0472393463657 0.852760653634317 11 76.7 76.0483913334632 0.651608666536769 12 71.9 74.9530612412628 -3.05306124126283 13 73.4 74.287365418013 -0.887365418013026 14 72.5 73.1341707360195 -0.634170736019501 15 73.7 70.9931286521832 2.70687134781680 16 69.5 72.403824300446 -2.90382430044602 17 74.7 74.2907497336154 0.409250266384581 18 72.5 73.06852201431 -0.568522014310007 19 72.1 74.134010010568 -2.03401001056808 20 70.7 73.9630595953059 -3.26305959530586 21 71.4 75.6712787885589 -4.27127878855884 22 69.5 74.1135899882116 -4.61358998821163 23 73.5 73.3384810303127 0.161518969687286 24 72.4 73.1451494319208 -0.745149431920782 25 74.5 74.2548286956975 0.245171304302463 26 72.2 72.0001066280042 0.199893371995791 27 73 70.036546237876 2.96345376212398 28 73.3 71.0070787401068 2.29292125989316 29 71.3 71.6943946969648 -0.394394696964843 30 73.6 73.0088056803371 0.591194319662869 31 71.3 73.8152074810518 -2.51520748105184 32 71.2 70.6700354480265 0.529964551973485 33 81.4 75.1719542420652 6.22804575793478 34 76.1 74.8211134934189 1.27888650658112 35 71.1 74.1638782899017 -3.0638782899017 36 75.7 70.7356335169924 4.96436648300763 37 70 70.876052990832 -0.876052990831986 38 68.5 68.5760777606503 -0.0760777606502896 39 56.7 62.482993808961 -5.78299380896104 40 57.9 61.1545308299827 -3.25453082998274 41 58.8 59.4427583826255 -0.64275838262546 42 59.3 60.332884348612 -1.03288434861204 43 61.3 60.5817260093805 0.718273990619535 44 62.9 61.6112738323744 1.28872616762563 45 61.4 63.037104323292 -1.63710432329199 46 64.5 62.0180571720038 2.48194282799619 47 63.8 61.5492493463223 2.25075065367765 48 61.6 62.766155809824 -1.16615580982402 49 64.7 61.4027275387668 3.29727246123325 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 22 0.0716374951492726 0.143274990298545 0.928362504850727 23 0.0489277650497474 0.0978555300994948 0.951072234950253 24 0.0409123541930088 0.0818247083860176 0.959087645806991 25 0.276858783762207 0.553717567524414 0.723141216237793 26 0.41717679278587 0.83435358557174 0.58282320721413 27 0.306602647819216 0.613205295638432 0.693397352180784 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 2 0.333333333333333 NOK

Charts produced by software:

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Parameters (Session):

par1 = 4 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 4 ; 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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Software written by Ed van Stee & Patrick Wessa

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