ws 7

*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 11:07:30 -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/19/t12586541506cjqdoxspnvq363.htm/, Retrieved Thu, 19 Nov 2009 19:09:22 +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/t12586541506cjqdoxspnvq363.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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8,3 98,6 8,2 8,7 8,5 96,5 8,3 8,2 8,6 95,9 8,5 8,3 8,5 103,7 8,6 8,5 8,2 103,1 8,5 8,6 8,1 103,7 8,2 8,5 7,9 112,1 8,1 8,2 8,6 86,9 7,9 8,1 8,7 95 8,6 7,9 8,7 111,8 8,7 8,6 8,5 108,8 8,7 8,7 8,4 109,3 8,5 8,7 8,5 101,4 8,4 8,5 8,7 100,5 8,5 8,4 8,7 100,7 8,7 8,5 8,6 113,5 8,7 8,7 8,5 106,1 8,6 8,7 8,3 111,6 8,5 8,6 8 114,9 8,3 8,5 8,2 88,6 8 8,3 8,1 99,5 8,2 8 8,1 115,1 8,1 8,2 8 118 8,1 8,1 7,9 111,4 8 8,1 7,9 107,3 7,9 8 8 105,3 7,9 7,9 8 105,3 8 7,9 7,9 117,9 8 8 8 110,2 7,9 8 7,7 112,4 8 7,9 7,2 117,5 7,7 8 7,5 93 7,2 7,7 7,3 103,5 7,5 7,2 7 116,3 7,3 7,5 7 120 7 7,3 7 114,3 7 7 7,2 104,7 7 7 7,3 109,8 7,2 7 7,1 112,6 7,3 7,2 6,8 114,4 7,1 7,3 6,4 115,7 6,8 7,1 6,1 114,7 6,4 6,8 6,5 118,4 6,1 6,4 7,7 94,9 6,5 6,1 7,9 103,8 7,7 6,5 7,5 115,1 7,9 7,7 6,9 113,7 7,5 7,9 6,6 104 6,9 7,5 6,9 94,3 6,6 6,9 7,7 92,5 6,9 6,6 8 93,2 7,7 6,9 8 104,7 8 7,7 7,7 94 8 8 7,3 98,1 7,7 8 7,4 102,7 7,3 7,7 8,1 82,4 7,4 7,3

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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 4.14999041251723 -0.0152438597880977X[t] + 1.34171092585125Y1[t] -0.632193949965465Y2[t] + 0.0835740790049867M1[t] + 0.0525149196902091M2[t] -0.176803720858912M3[t] -0.0232878832478820M4[t] -0.105116917657922M5[t] -0.129479933541223M6[t] + 0.0778523659487016M7[t] + 0.310812223645426M8[t] -0.447340912981457M9[t] -0.0193029508698561M10[t] + 0.00728265666300871M11[t] -0.00840207262544193t + 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) 4.14999041251723 0.990631 4.1892 0.00015 7.5e-05 X -0.0152438597880977 0.004999 -3.0491 0.004058 0.002029 Y1 1.34171092585125 0.116031 11.5634 0 0 Y2 -0.632193949965465 0.118245 -5.3465 4e-06 2e-06 M1 0.0835740790049867 0.126953 0.6583 0.514113 0.257056 M2 0.0525149196902091 0.13346 0.3935 0.696049 0.348025 M3 -0.176803720858912 0.134934 -1.3103 0.197569 0.098784 M4 -0.0232878832478820 0.123139 -0.1891 0.850957 0.425478 M5 -0.105116917657922 0.11934 -0.8808 0.38368 0.19184 M6 -0.129479933541223 0.117649 -1.1006 0.277666 0.138833 M7 0.0778523659487016 0.118305 0.6581 0.514266 0.257133 M8 0.310812223645426 0.161086 1.9295 0.060786 0.030393 M9 -0.447340912981457 0.161306 -2.7732 0.00839 0.004195 M10 -0.0193029508698561 0.13103 -0.1473 0.883622 0.441811 M11 0.00728265666300871 0.128388 0.0567 0.955048 0.477524 t -0.00840207262544193 0.002576 -3.2615 0.002269 0.001135 Multiple Linear Regression - Regression Statistics Multiple R 0.974568997085734 R-squared 0.949784730080693 Adjusted R-squared 0.930954003860953 F-TEST (value) 50.4380297922358 F-TEST (DF numerator) 15 F-TEST (DF denominator) 40 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.174779636784900 Sum Squared Residuals 1.22191685738646 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 8.3 8.22406007107107 0.0759399289289281 2 8.5 8.6668790122537 -0.166879012253704 3 8.6 8.6434274051257 -0.0434274051257002 4 8.5 8.67737136635616 -0.177371366356160 5 8.2 8.39889608761187 -0.198896087611866 6 8.1 8.01769080047143 0.0823091995285654 7 7.9 8.14405969752041 -0.244059697520411 8 8.6 8.54763995907805 0.0523600409219463 9 8.7 8.7232459236311 -0.0232459236311051 10 8.7 8.57842029628652 0.121579703713478 11 8.5 8.5791160155617 -0.0791160155616911 12 8.4 8.28746717120894 0.112532828791058 13 8.5 8.47533336732243 0.0246666326775733 14 8.7 8.64698209677317 0.0530179032268333 15 8.7 8.61133540181469 0.0886645981853136 16 8.6 8.43488897151953 0.165111028480468 17 8.5 8.32329133433085 0.176708665669152 18 8.3 8.13573331939899 0.164266680601011 19 8 8.07923601878905 -0.0792360187890467 20 8.2 8.42863282852502 -0.228632828525016 21 8.1 7.95391991774231 0.146080082257685 22 8.1 7.87514171195593 0.224858288044067 23 8 7.91233744847442 0.0876625515255819 24 7.9 7.86309110120229 0.0369088987977128 25 7.9 7.92981123512445 -0.0298112351244543 26 8 7.98405711775698 0.0159428822430233 27 8 7.88050749716754 0.119492502832462 28 7.9 7.77032923382655 0.129670766173451 29 8 7.6633047545743 0.336695245425706 30 7.7 7.7943936621134 -0.0943936621134074 31 7.2 7.44984753130667 -0.249847531306671 32 7.5 7.56668260325036 -0.0666826032503617 33 7.3 7.35867711896112 -0.0586771189611185 34 7 7.12519123299974 -0.125191232999737 35 7 6.81089799892892 0.189102001071084 36 7 7.07176145542226 -0.071761455422262 37 7.2 7.29327451576754 -0.0932745157675443 38 7.3 7.44441178407828 -0.144411784078277 39 7.1 7.17174056608907 -0.0717405660890719 40 6.8 6.95785380328929 -0.157853803289287 41 6.4 6.571731190767 -0.171731190766996 42 6.1 6.20718377669549 -0.107183776695492 43 6.5 6.20007602457482 0.299923975425178 44 7.7 7.50920706999654 0.190792930003459 45 7.9 7.96415703966546 -0.0641570396654613 46 7.5 7.72124675875781 -0.221246758757809 47 6.9 7.09764853703497 -0.197648537034974 48 6.6 6.67768027216651 -0.0776802721665084 49 6.9 6.8775208107145 0.0224791892854972 50 7.7 7.45766998913787 0.242330010862125 51 8 8.092989129803 -0.0929891298030035 52 8 7.95955662500847 0.0404433749915284 53 7.7 7.842776632716 -0.142776632715995 54 7.3 7.34499844132068 -0.0449984413206777 55 7.4 7.12678072780905 0.273219272190951 56 8.1 8.04783753915003 0.0521624608499723 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 19 0.0579517813761658 0.115903562752332 0.942048218623834 20 0.633095328491959 0.733809343016082 0.366904671508041 21 0.489142159225657 0.978284318451313 0.510857840774343 22 0.378595869534654 0.757191739069307 0.621404130465346 23 0.26144365379909 0.52288730759818 0.73855634620091 24 0.166170751466174 0.332341502932348 0.833829248533826 25 0.123668340175387 0.247336680350774 0.876331659824613 26 0.0702743195039103 0.140548639007821 0.92972568049609 27 0.04308655788192 0.08617311576384 0.95691344211808 28 0.0300358848603494 0.0600717697206987 0.96996411513965 29 0.370231502233012 0.740463004466024 0.629768497766988 30 0.407682545058558 0.815365090117116 0.592317454941442 31 0.532341696441734 0.935316607116532 0.467658303558266 32 0.443387063382272 0.886774126764544 0.556612936617728 33 0.361829756297596 0.723659512595192 0.638170243702404 34 0.283028299628391 0.566056599256783 0.716971700371609 35 0.579298503490978 0.841402993018044 0.420701496509022 36 0.451588126053134 0.903176252106268 0.548411873946866 37 0.362616537448729 0.725233074897457 0.637383462551271 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 0.105263157894737 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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