*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: Sat, 18 Dec 2010 12:49:35 +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/Dec/18/t1292676454ko0jn6omkr9zwfo.htm/, Retrieved Sat, 18 Dec 2010 13:47:34 +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/Dec/18/t1292676454ko0jn6omkr9zwfo.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:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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104.31 103.88 103.88 103.86 103.89 103.98 103.98 104.29 104.29 104.24 103.98 103.54 103.44 103.32 103.3 103.26 103.14 103.11 102.91 103.23 103.23 103.14 102.91 102.42 102.1 102.07 102.06 101.98 101.83 101.75 101.56 101.66 101.65 101.61 101.52 101.31 101.19 101.11 101.1 101.07 100.98 100.93 100.92 101.02 101.01 100.97 100.89 100.62 100.53 100.48 100.48 100.47 100.52 100.49 100.47 100.44

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 kleding/schoeisel[t] = + 104.357875 -0.0560624999999774M1[t] -0.118550000000008M2[t] -0.0470375000000059M3[t] -0.0035250000000042M4[t] + 0.0199874999999958M5[t] + 0.0794999999999971M6[t] + 0.0750124999999974M7[t] + 0.314524999999997M8[t] + 0.333962500000001M9[t] + 0.358474999999994M10[t] + 0.272987499999995M11[t] -0.0795125000000003t + 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) 104.357875 0.13855 753.2161 0 0 M1 -0.0560624999999774 0.16658 -0.3365 0.738093 0.369047 M2 -0.118550000000008 0.166465 -0.7122 0.480211 0.240105 M3 -0.0470375000000059 0.166375 -0.2827 0.778748 0.389374 M4 -0.0035250000000042 0.166311 -0.0212 0.983188 0.491594 M5 0.0199874999999958 0.166272 0.1202 0.904877 0.452439 M6 0.0794999999999971 0.16626 0.4782 0.634953 0.317477 M7 0.0750124999999974 0.166272 0.4511 0.654154 0.327077 M8 0.314524999999997 0.166311 1.8912 0.065348 0.032674 M9 0.333962500000001 0.175363 1.9044 0.063561 0.03178 M10 0.358474999999994 0.175302 2.0449 0.047016 0.023508 M11 0.272987499999995 0.175265 1.5576 0.126666 0.063333 t -0.0795125000000003 0.002065 -38.4978 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.986049960445294 R-squared 0.972294524494166 Adjusted R-squared 0.964562763887886 F-TEST (value) 125.753314672535 F-TEST (DF numerator) 12 F-TEST (DF denominator) 43 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.247845260708803 Sum Squared Residuals 2.64137275000003 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 104.31 104.222300000000 0.0877000000001128 2 103.88 104.0803 -0.200300000000007 3 103.88 104.0723 -0.19230000000001 4 103.86 104.0363 -0.176300000000007 5 103.89 103.9803 -0.0903000000000056 6 103.98 103.9603 0.0196999999999969 7 103.98 103.8763 0.103699999999997 8 104.29 104.0363 0.253700000000000 9 104.29 103.976225 0.313774999999996 10 104.24 103.921225 0.318774999999992 11 103.98 103.756225 0.223775 12 103.54 103.403725 0.136274999999998 13 103.44 103.26815 0.171849999999969 14 103.32 103.12615 0.193849999999993 15 103.3 103.11815 0.181849999999995 16 103.26 103.08215 0.177850000000002 17 103.14 103.02615 0.113849999999997 18 103.11 103.00615 0.103849999999995 19 102.91 102.92215 -0.0121500000000073 20 103.23 103.08215 0.147850000000001 21 103.23 103.022075 0.207924999999997 22 103.14 102.967075 0.172925000000000 23 102.91 102.802075 0.107924999999996 24 102.42 102.449575 -0.0295750000000036 25 102.1 102.314 -0.214000000000034 26 102.07 102.172 -0.102000000000004 27 102.06 102.164 -0.103999999999997 28 101.98 102.128 -0.147999999999996 29 101.83 102.072 -0.242000000000002 30 101.75 102.052 -0.302000000000001 31 101.56 101.968 -0.407999999999998 32 101.66 102.128 -0.468000000000003 33 101.65 102.067925 -0.417924999999998 34 101.61 102.012925 -0.402924999999997 35 101.52 101.847925 -0.327925000000001 36 101.31 101.495425 -0.185424999999999 37 101.19 101.35985 -0.169850000000027 38 101.11 101.21785 -0.107849999999994 39 101.1 101.20985 -0.109850000000001 40 101.07 101.17385 -0.103850000000004 41 100.98 101.11785 -0.137849999999993 42 100.93 101.09785 -0.167849999999991 43 100.92 101.01385 -0.0938499999999962 44 101.02 101.17385 -0.153850000000001 45 101.01 101.113775 -0.103774999999995 46 100.97 101.058775 -0.088774999999995 47 100.89 100.893775 -0.00377499999999424 48 100.62 100.541275 0.0787250000000054 49 100.53 100.4057 0.124299999999980 50 100.48 100.2637 0.216300000000013 51 100.48 100.2557 0.224300000000012 52 100.47 100.2197 0.250300000000005 53 100.52 100.1637 0.356300000000003 54 100.49 100.1437 0.3463 55 100.47 100.0597 0.410300000000005 56 100.44 100.2197 0.220300000000004 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.0833942631665752 0.166788526333150 0.916605736833425 17 0.034775094735645 0.06955018947129 0.965224905264355 18 0.0276039668868906 0.0552079337737812 0.97239603311311 19 0.0630884924188008 0.126176984837602 0.9369115075812 20 0.0949486336142717 0.189897267228543 0.905051366385728 21 0.171652064259814 0.343304128519628 0.828347935740186 22 0.389423536251266 0.778847072502532 0.610576463748734 23 0.70164245782568 0.596715084348641 0.298357542174320 24 0.869114703340444 0.261770593319112 0.130885296659556 25 0.956022197939906 0.0879556041201878 0.0439778020600939 26 0.972703662134358 0.0545926757312844 0.0272963378656422 27 0.991410777207307 0.0171784455853860 0.00858922279269302 28 0.998596312159333 0.00280737568133428 0.00140368784066714 29 0.999400210295779 0.00119957940844249 0.000599789704221247 30 0.999796682979518 0.000406634040964429 0.000203317020482215 31 0.999729767633797 0.000540464732406409 0.000270232366203204 32 0.999814051014233 0.000371897971534784 0.000185948985767392 33 0.999780216036565 0.000439567926869993 0.000219783963434997 34 0.999618889785667 0.00076222042866534 0.00038111021433267 35 0.998997553779561 0.00200489244087735 0.00100244622043867 36 0.998455879536893 0.00308824092621459 0.00154412046310729 37 0.997367983720444 0.00526403255911142 0.00263201627955571 38 0.994931289554444 0.0101374208911128 0.00506871044555638 39 0.990931302763902 0.0181373944721956 0.00906869723609782 40 0.985140501402304 0.0297189971953915 0.0148594985976958 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 10 0.4 NOK 5% type I error level 14 0.56 NOK 10% type I error level 18 0.72 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') }

Copyright

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

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