*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 04:23:58 -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/t1259062262bswo7xvpuvgt8jr.htm/, Retrieved Tue, 24 Nov 2009 12:31:21 +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/t1259062262bswo7xvpuvgt8jr.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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97.4 116.7 97 109 105.4 119.5 102.7 115.1 98.1 107.1 104.5 109.7 87.4 110.4 89.9 105 109.8 115.8 111.7 116.4 98.6 111.1 96.9 119.5 95.1 110.9 97 115.1 112.7 125.2 102.9 116 97.4 112.9 111.4 121.7 87.4 123.2 96.8 116.6 114.1 136.2 110.3 120.9 103.9 119.6 101.6 125.9 94.6 116.1 95.9 107.5 104.7 116.7 102.8 112.5 98.1 113 113.9 126.4 80.9 114.1 95.7 112.5 113.2 112.4 105.9 113.1 108.8 116.3 102.3 111.7 99 118.8 100.7 116.5 115.5 125.1 100.7 113.1 109.9 119.6 114.6 114.4 85.4 114 100.5 117.8 114.8 117 116.5 120.9 112.9 115 102 117.3 106 119.4 105.3 114.9 118.8 125.8 106.1 117.6 109.3 117.6 117.2 114.9 92.5 121.9 104.2 117 112.5 106.4 122.4 110.5 113.3 113.6 100 114.2

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] = + 95.1964775705906 + 0.202879658540295Tip[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) 95.1964775705906 8.031714 11.8526 0 0 Tip 0.202879658540295 0.077112 2.631 0.010888 0.005444 Multiple Linear Regression - Regression Statistics Multiple R 0.326528131701518 R-squared 0.106620620792484 Adjusted R-squared 0.0912175280475269 F-TEST (value) 6.92202680058462 F-TEST (DF numerator) 1 F-TEST (DF denominator) 58 p-value 0.0108877211807719 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 5.27332636197745 Sum Squared Residuals 1612.86231335572 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 116.7 114.956956312416 1.74304368758425 2 109 114.875804448999 -5.87580444899926 3 119.5 116.579993580738 2.9200064192623 4 115.1 116.032218502679 -0.932218502678914 5 107.1 115.098972073394 -7.99897207339356 6 109.7 116.397401888051 -6.69740188805143 7 110.4 112.928159727012 -2.5281597270124 8 105 113.435358873363 -8.43535887336314 9 115.8 117.472664078315 -1.672664078315 10 116.4 117.858135429542 -1.45813542954155 11 111.1 115.200411902664 -4.10041190266371 12 119.5 114.855516483145 4.6444835168548 13 110.9 114.490333097773 -3.59033309777267 14 115.1 114.875804448999 0.224195551000763 15 125.2 118.061015088082 7.13898491191815 16 116 116.072794434387 -0.0727944343869676 17 112.9 114.956956312415 -2.05695631241534 18 121.7 117.797271531979 3.90272846802053 19 123.2 112.928159727012 10.2718402729876 20 116.6 114.835228517291 1.76477148270882 21 136.2 118.345046610038 17.8549533899617 22 120.9 117.574103907585 3.32589609241486 23 119.6 116.275674092927 3.32432590707273 24 125.9 115.809050878285 10.0909491217154 25 116.1 114.388893268503 1.71110673149747 26 107.5 114.652636824605 -7.15263682460491 27 116.7 116.437977819759 0.262022180240506 28 112.5 116.052506468533 -3.55250646853294 29 113 115.098972073394 -2.09897207339355 30 126.4 118.304470678330 8.0955293216698 31 114.1 111.609441946500 2.4905580534995 32 112.5 114.612060892897 -2.11206089289685 33 112.4 118.162454917352 -5.76245491735199 34 113.1 116.681433410008 -3.58143341000786 35 116.3 117.269784419775 -0.969784419774704 36 111.7 115.951066639263 -4.25106663926279 37 118.8 115.281563766080 3.51843623392018 38 116.5 115.626459185598 0.87354081440168 39 125.1 118.629078131995 6.47092186800532 40 113.1 115.626459185598 -2.52645918559833 41 119.6 117.492952044169 2.10704795583097 42 114.4 118.446486439308 -4.0464864393084 43 114 112.522400409932 1.47759959006818 44 117.8 115.585883253890 2.21411674610974 45 117 118.487062371016 -1.48706237101647 46 120.9 118.831957790535 2.06804220946504 47 115 118.10159101979 -3.10159101978991 48 117.3 115.890202741701 1.40979725829930 49 119.4 116.701721375862 2.69827862413813 50 114.9 116.559705614884 -1.65970561488367 51 125.8 119.298581005178 6.50141899482235 52 117.6 116.722009341716 0.877990658284088 53 117.6 117.371224249045 0.228775750955146 54 114.9 118.973973551513 -4.07397355151317 55 121.9 113.962845985568 7.9371540144321 56 117 116.336537990489 0.66346200951065 57 106.4 118.020439156374 -11.6204391563738 58 110.5 120.028947775923 -9.5289477759227 59 113.6 118.182742883206 -4.58274288320603 60 114.2 115.48444342462 -1.28444342462011 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.430981937929004 0.861963875858008 0.569018062070996 6 0.523475437600216 0.953049124799569 0.476524562399784 7 0.412588145259399 0.825176290518798 0.587411854740601 8 0.388609447866592 0.777218895733184 0.611390552133408 9 0.275625665629396 0.551251331258792 0.724374334370604 10 0.185163819157073 0.370327638314146 0.814836180842927 11 0.124394909359656 0.248789818719311 0.875605090640344 12 0.246334656863434 0.492669313726869 0.753665343136566 13 0.180832350365894 0.361664700731787 0.819167649634106 14 0.142212846361368 0.284425692722735 0.857787153638632 15 0.201318969158368 0.402637938316736 0.798681030841632 16 0.143779244790235 0.28755848958047 0.856220755209765 17 0.101366125208590 0.202732250417181 0.89863387479141 18 0.0772833153682086 0.154566630736417 0.922716684631791 19 0.417788988959023 0.835577977918045 0.582211011040977 20 0.354531192768073 0.709062385536146 0.645468807231927 21 0.916722976563763 0.166554046872474 0.083277023436237 22 0.892621299831472 0.214757400337056 0.107378700168528 23 0.864529413284814 0.270941173430372 0.135470586715186 24 0.944311625254616 0.111376749490768 0.0556883747453842 25 0.923378067086969 0.153243865826062 0.0766219329130312 26 0.94715258577094 0.105694828458119 0.0528474142290594 27 0.924219713201563 0.151560573596875 0.0757802867984373 28 0.913525886663696 0.172948226672608 0.0864741133363041 29 0.887666288528875 0.224667422942251 0.112333711471125 30 0.936027195267452 0.127945609465096 0.0639728047325481 31 0.932387194402056 0.135225611195888 0.0676128055979438 32 0.915126719445238 0.169746561109524 0.084873280554762 33 0.930505708106249 0.138988583787503 0.0694942918937514 34 0.91994634234361 0.160107315312779 0.0800536576563893 35 0.889376542525103 0.221246914949795 0.110623457474897 36 0.887506905589005 0.224986188821989 0.112493094410995 37 0.85760330595386 0.284793388092279 0.142396694046139 38 0.807090195988412 0.385819608023175 0.192909804011588 39 0.876664721976324 0.246670556047353 0.123335278023676 40 0.853317040083518 0.293365919832964 0.146682959916482 41 0.819302032673474 0.361395934653052 0.180697967326526 42 0.789099223491208 0.421801553017585 0.210900776508792 43 0.767522255526932 0.464955488946137 0.232477744473068 44 0.696075873656859 0.607848252686283 0.303924126343141 45 0.623399823863064 0.753200352273872 0.376600176136936 46 0.625167945573741 0.749664108852517 0.374832054426259 47 0.545547439974018 0.908905120051963 0.454452560025982 48 0.446967187611859 0.893934375223717 0.553032812388141 49 0.374800321442782 0.749600642885565 0.625199678557218 50 0.288683831212053 0.577367662424105 0.711316168787947 51 0.824441769251564 0.351116461496873 0.175558230748436 52 0.747734155159822 0.504531689680356 0.252265844840178 53 0.696066704403977 0.607866591192045 0.303933295596023 54 0.682818786167544 0.634362427664911 0.317181213832456 55 0.619467756586638 0.761064486826725 0.380532243413363 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 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 2 ; 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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