*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 11:04:50 -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/t125865397704duzr8xnhai9rd.htm/, Retrieved Thu, 19 Nov 2009 19:06:29 +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/t125865397704duzr8xnhai9rd.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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29 27 24 26 28 29 26 25 26 21 19 26 23 19 21 22 19 23 21 20 22 16 16 21 19 22 16 16 21 19 25 25 16 27 29 25 23 28 27 22 25 23 23 26 22 20 24 23 24 28 20 23 28 24 20 28 23 21 28 20 22 32 21 17 31 22 21 22 17 19 29 21 23 31 19 22 29 23 15 32 22 23 32 15 21 31 23 18 29 21 18 28 18 18 28 18 18 29 18 10 22 18 13 26 10 10 24 13 9 27 10 9 27 9 6 23 9 11 21 6 9 19 11 10 17 9 9 19 10 16 21 9 10 13 16 7 8 10 7 5 7 14 10 7 11 6 14 10 6 11 6 8 10 8 11 6 13 12 8 12 13 13 15 19 12 16 19 15 16 18 16

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 s[t] = + 8.69448494597229 + 0.128118770999304consv[t] + 0.538300231532793`y(t-1)`[t] -0.344447299199426M1[t] -1.44883997873163M2[t] -3.2764835967175M3[t] -0.196764365358310M4[t] + 0.499140152070973M5[t] -1.07683655950044M6[t] -1.04275401159163M7[t] + 0.124585939396124M8[t] -0.656529404254919M9[t] -5.28497294610116M10[t] + 1.50084427465382M11[t] -0.100772349974912t + 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) 8.69448494597229 3.846623 2.2603 0.029048 0.014524 consv 0.128118770999304 0.070598 1.8148 0.076705 0.038353 `y(t-1)` 0.538300231532793 0.12977 4.1481 0.00016 8e-05 M1 -0.344447299199426 2.096805 -0.1643 0.870305 0.435152 M2 -1.44883997873163 2.101621 -0.6894 0.494368 0.247184 M3 -3.2764835967175 2.093383 -1.5652 0.125049 0.062525 M4 -0.196764365358310 2.105631 -0.0934 0.925993 0.462996 M5 0.499140152070973 2.092387 0.2386 0.812614 0.406307 M6 -1.07683655950044 2.106001 -0.5113 0.611806 0.305903 M7 -1.04275401159163 2.092644 -0.4983 0.620876 0.310438 M8 0.124585939396124 2.092669 0.0595 0.952809 0.476404 M9 -0.656529404254919 2.103696 -0.3121 0.756521 0.37826 M10 -5.28497294610116 2.214199 -2.3869 0.021573 0.010787 M11 1.50084427465382 2.270596 0.661 0.512228 0.256114 t -0.100772349974912 0.046164 -2.1829 0.034681 0.01734 Multiple Linear Regression - Regression Statistics Multiple R 0.89863671548725 R-squared 0.807547946421712 Adjusted R-squared 0.743397261895616 F-TEST (value) 12.5882981980217 F-TEST (DF numerator) 14 F-TEST (DF denominator) 42 p-value 8.20095102938012e-11 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.11547870816889 Sum Squared Residuals 407.660718404254 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 29 24.6276776705662 4.37232232943383 2 26 26.2421325697223 -0.242132569722334 3 26 22.3144595941652 3.68554040583475 4 21 24.5246938495537 -3.52469384955372 5 23 22.4283248593441 0.571675140655879 6 22 21.8281762608634 0.171823739136617 7 21 21.3513049982638 -0.351304998263802 8 16 21.3670972837466 -5.36709728374664 9 19 18.5624210584525 0.437578941547465 10 16 15.3199870902305 0.680012909769545 11 25 20.9026063504094 4.09739364959064 12 27 24.658166893573 2.34183310642702 13 23 25.1614289364649 -2.16142893646492 14 22 21.4187066678287 0.581293332171277 15 23 19.0801092393344 3.91989076066555 16 20 22.3411188102529 -2.34111881025292 17 24 21.8338253671061 2.16617463289388 18 23 22.3102772316910 0.689722768309033 19 20 21.7052871980921 -1.70528719809208 20 21 21.1569541045065 -0.156954104506540 21 22 21.3258417264106 0.674158273589407 22 17 17.0068072951229 -0.00680729512292821 23 21 19.8472820692453 1.15271793075470 24 19 21.2956977677429 -2.29569776774287 25 23 20.0301151975015 2.96988480249845 26 22 20.721913552127 1.27808644787300 27 15 18.6395536656313 -3.63955366563133 28 23 17.8503989262861 5.14960107371394 29 21 22.6238141750035 -1.62381417500347 30 18 19.6142271083929 -1.61422710839295 31 18 17.8045178407292 0.195482159270827 32 18 18.871085441742 -0.87108544174201 33 18 18.1173165191154 -0.117316519115359 34 10 12.4912692302991 -2.49126923029908 35 13 15.3823873328140 -2.38238733281402 36 10 15.1394338607851 -5.13943386078506 37 9 13.4636698300103 -4.46366983001026 38 9 11.7202045689703 -2.72020456897034 39 6 9.27931351701234 -3.27931351701234 40 11 10.3871221617996 0.61287783820036 41 9 13.4175179449194 -4.41751794491936 42 10 10.4079308783088 -0.407930878308846 43 9 11.1357788497742 -2.13577884977415 44 16 11.9202837612528 4.0797162387472 45 10 13.7815475203620 -3.78154752036197 46 7 5.18193638434754 1.81806361565246 47 7 9.86772424753132 -2.86772424753132 48 14 8.9067014778991 5.09329852210089 49 11 11.7171083654571 -0.7171083654571 50 10 8.8970426413516 1.10295735864839 51 6 6.68656398385663 -0.686563983856633 52 8 7.89666625210766 0.103333747892342 53 13 9.69651765362691 3.30348234637309 54 12 10.8393885207439 1.16061147925614 55 15 11.0031111131408 3.99688888685921 56 16 13.684579408752 2.31542059124799 57 16 13.2128731756595 2.78712682434046 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 18 0.00397625682874586 0.00795251365749173 0.996023743171254 19 0.00077298603271784 0.00154597206543568 0.999227013967282 20 0.00102233728037747 0.00204467456075494 0.998977662719623 21 0.00487394674012363 0.00974789348024726 0.995126053259876 22 0.00142037361172339 0.00284074722344677 0.998579626388277 23 0.00231155666673167 0.00462311333346334 0.997688443333268 24 0.00946155850416627 0.0189231170083325 0.990538441495834 25 0.0090344065646854 0.0180688131293708 0.990965593435315 26 0.00969868442173547 0.0193973688434709 0.990301315578265 27 0.119079009442639 0.238158018885278 0.880920990557361 28 0.187577116461207 0.375154232922414 0.812422883538793 29 0.139969507443143 0.279939014886286 0.860030492556857 30 0.105505787065326 0.211011574130652 0.894494212934674 31 0.114597541233191 0.229195082466381 0.88540245876681 32 0.0968714417301706 0.193742883460341 0.903128558269829 33 0.233473607358809 0.466947214717619 0.76652639264119 34 0.221135458938559 0.442270917877117 0.778864541061441 35 0.622980004149639 0.754039991700723 0.377019995850361 36 0.552071765322572 0.895856469354856 0.447928234677428 37 0.618165783893666 0.763668432212668 0.381834216106334 38 0.684790092921503 0.630419814156994 0.315209907078497 39 0.645862928243061 0.708274143513878 0.354137071756939 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 6 0.272727272727273 NOK 5% type I error level 9 0.409090909090909 NOK 10% type I error level 9 0.409090909090909 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

Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.

Privacy Policy

We may request personal information to be submitted to our servers in order to be able to:

• personalize online software applications according to your needs
• enforce strict security rules with respect to the data that you upload (e.g. statistical data)
• manage user sessions of online applications
• alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

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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