DSHW-WS7-MultipleRegressionND

*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: Fri, 20 Nov 2009 06:53:17 -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/20/t1258725267hvic6fee5y2h0ma.htm/, Retrieved Fri, 20 Nov 2009 14:54:39 +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/20/t1258725267hvic6fee5y2h0ma.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:

DSHW, SDHW

Dataseries X:

» Textbox « » Textfile « » CSV «

1.4 0.0 1.6 0.0 1.7 0.0 2.0 0.0 2.0 0.0 2.1 0.0 2.5 0.0 2.5 0.0 2.6 0.0 2.7 0.0 3.7 0.0 4.0 0.0 5.0 0.0 5.1 0.0 5.1 0.0 5.0 0.0 5.1 0.0 4.7 0.0 4.5 0.0 4.5 0.0 4.6 0.0 4.6 0.0 4.6 0.0 4.6 0.0 5.3 0.0 5.4 0.0 5.3 0.0 5.2 0.0 5.0 0.0 4.2 0.0 4.3 0.0 4.3 0.0 4.3 0.0 4.0 0.0 4.0 0.0 4.1 0.0 4.4 0.0 3.6 0.0 3.7 0.0 3.8 0.0 3.3 0.0 3.3 0.0 3.3 0.0 3.5 0.0 3.3 1.0 3.3 1.0 3.4 1.0 3.4 1.0 5.2 1.0 5.3 1.0 4.8 1.0 5.0 1.0 4.6 1.0 4.6 1.0 3.5 1.0 3.5 1.0

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 IndGez[t] = + 3.875 + 0.283333333333334InvlCrisis[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) 3.875 0.162436 23.8556 0 0 InvlCrisis 0.283333333333334 0.350901 0.8074 0.422953 0.211477 Multiple Linear Regression - Regression Statistics Multiple R 0.109221891825004 R-squared 0.0119294216538329 Adjusted R-squared -0.0063681816488741 F-TEST (value) 0.651966350809897 F-TEST (DF numerator) 1 F-TEST (DF denominator) 54 p-value 0.422953016391424 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.07747704853675 Sum Squared Residuals 62.6916666666667 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 1.4 3.87500000000001 -2.47500000000001 2 1.6 3.875 -2.275 3 1.7 3.875 -2.175 4 2 3.875 -1.875 5 2 3.875 -1.875 6 2.1 3.875 -1.775 7 2.5 3.875 -1.375 8 2.5 3.875 -1.375 9 2.6 3.875 -1.275 10 2.7 3.875 -1.175 11 3.7 3.875 -0.175000000000000 12 4 3.875 0.125000000000000 13 5 3.875 1.125 14 5.1 3.875 1.225 15 5.1 3.875 1.225 16 5 3.875 1.125 17 5.1 3.875 1.225 18 4.7 3.875 0.825 19 4.5 3.875 0.625 20 4.5 3.875 0.625 21 4.6 3.875 0.725 22 4.6 3.875 0.725 23 4.6 3.875 0.725 24 4.6 3.875 0.725 25 5.3 3.875 1.425 26 5.4 3.875 1.525 27 5.3 3.875 1.425 28 5.2 3.875 1.325 29 5 3.875 1.125 30 4.2 3.875 0.325000000000001 31 4.3 3.875 0.425 32 4.3 3.875 0.425 33 4.3 3.875 0.425 34 4 3.875 0.125000000000000 35 4 3.875 0.125000000000000 36 4.1 3.875 0.225 37 4.4 3.875 0.525000000000001 38 3.6 3.875 -0.275000000000000 39 3.7 3.875 -0.175000000000000 40 3.8 3.875 -0.075 41 3.3 3.875 -0.575 42 3.3 3.875 -0.575 43 3.3 3.875 -0.575 44 3.5 3.875 -0.375 45 3.3 4.15833333333333 -0.858333333333334 46 3.3 4.15833333333333 -0.858333333333334 47 3.4 4.15833333333333 -0.758333333333334 48 3.4 4.15833333333333 -0.758333333333334 49 5.2 4.15833333333333 1.04166666666667 50 5.3 4.15833333333333 1.14166666666667 51 4.8 4.15833333333333 0.641666666666666 52 5 4.15833333333333 0.841666666666667 53 4.6 4.15833333333333 0.441666666666666 54 4.6 4.15833333333333 0.441666666666666 55 3.5 4.15833333333333 -0.658333333333333 56 3.5 4.15833333333333 -0.658333333333333 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.0527094398563502 0.105418879712700 0.94729056014365 6 0.0337942673593572 0.0675885347187145 0.966205732640643 7 0.0651274295345408 0.130254859069082 0.934872570465459 8 0.079672604658547 0.159345209317094 0.920327395341453 9 0.104658246361076 0.209316492722153 0.895341753638924 10 0.147142636146951 0.294285272293902 0.85285736385305 11 0.537105652558234 0.925788694883531 0.462894347441766 12 0.814505527755719 0.370988944488562 0.185494472244281 13 0.984093402201489 0.0318131955970227 0.0159065977985114 14 0.997927546090891 0.00414490781821724 0.00207245390910862 15 0.999518990634363 0.000962018731273072 0.000481009365636536 16 0.999793172219192 0.000413655561617042 0.000206827780808521 17 0.999904937626932 0.000190124746135890 9.50623730679448e-05 18 0.999897062683922 0.000205874632155162 0.000102937316077581 19 0.99985030189858 0.000299396202839092 0.000149698101419546 20 0.999773976350987 0.000452047298025622 0.000226023649012811 21 0.999677606054362 0.00064478789127646 0.00032239394563823 22 0.999528455746485 0.000943088507030053 0.000471544253515027 23 0.99929952546569 0.00140094906862048 0.000700474534310241 24 0.998951243301706 0.00209751339658784 0.00104875669829392 25 0.999350073335156 0.00129985332968868 0.000649926664844341 26 0.999692470589756 0.000615058820488962 0.000307529410244481 27 0.999845106375087 0.000309787249826444 0.000154893624913222 28 0.999919598240511 0.000160803518977141 8.04017594885707e-05 29 0.999946197949832 0.000107604100335516 5.38020501677579e-05 30 0.99988804960212 0.000223900795759998 0.000111950397879999 31 0.999794128305176 0.00041174338964791 0.000205871694823955 32 0.999638802830798 0.000722394338404971 0.000361197169202485 33 0.999399036256876 0.00120192748624810 0.000600963743124051 34 0.998805590058363 0.00238881988327498 0.00119440994163749 35 0.997726043414507 0.00454791317098571 0.00227395658549285 36 0.996118034545108 0.00776393090978416 0.00388196545489208 37 0.995523032779726 0.00895393444054715 0.00447696722027357 38 0.99148247102881 0.0170350579423808 0.0085175289711904 39 0.984731123935926 0.0305377521281481 0.0152688760640740 40 0.975039507185397 0.0499209856292067 0.0249604928146034 41 0.957803852785228 0.084392294429545 0.0421961472147725 42 0.931238380912248 0.137523238175505 0.0687616190877525 43 0.892567873156454 0.214864253687092 0.107432126843546 44 0.835594126956946 0.328811746086107 0.164405873043054 45 0.814712316751411 0.370575366497179 0.185287683248589 46 0.805202202511108 0.389595594977785 0.194797797488893 47 0.798258124661317 0.403483750677367 0.201741875338684 48 0.820167897988967 0.359664204022065 0.179832102011033 49 0.785793418115662 0.428413163768677 0.214206581884338 50 0.780699374929222 0.438601250141556 0.219300625070778 51 0.670612407669893 0.658775184660214 0.329387592330107 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 24 0.51063829787234 NOK 5% type I error level 28 0.595744680851064 NOK 10% type I error level 30 0.638297872340426 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; 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') }

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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