WS7

*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 05:03:12 -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/t12587187121gsoyokw53eqvkd.htm/, Retrieved Fri, 20 Nov 2009 13:05:25 +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/t12587187121gsoyokw53eqvkd.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:

bhschhwsw7l2

Dataseries X:

» Textbox « » Textfile « » CSV «

126.51 0 131.02 0 136.51 0 138.04 0 132.92 0 129.61 0 122.96 0 124.04 0 121.29 0 124.56 0 118.53 0 113.14 0 114.15 0 122.17 0 129.23 0 131.19 0 129.12 0 128.28 0 126.83 0 138.13 0 140.52 0 146.83 0 135.14 0 131.84 0 125.7 0 128.98 0 133.25 0 136.76 0 133.24 0 128.54 0 121.08 0 120.23 0 119.08 0 125.75 0 126.89 0 126.6 0 121.89 0 123.44 0 126.46 0 129.49 0 127.78 0 125.29 0 119.02 0 119.96 0 122.86 0 131.89 0 132.73 0 135.01 0 136.71 1 142.73 1 144.43 1 144.93 1 138.75 1 130.22 1 122.19 1 128.4 1 140.43 1 153.5 1 149.33 1 142.97 1

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 Y[t] = + 127.5625 + 11.7475000000000X[t] -4.92000000000005M1[t] -0.244000000000000M2[t] + 4.06399999999999M3[t] + 6.16999999999999M4[t] + 2.44999999999999M5[t] -1.52399999999999M6[t] -7.496M7[t] -3.76M8[t] -1.07600000000000M9[t] + 6.594M10[t] + 2.61200000000000M11[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) 127.5625 2.981426 42.7857 0 0 X 11.7475000000000 2.12959 5.5163 1e-06 1e-06 M1 -4.92000000000005 4.173128 -1.179 0.244343 0.122172 M2 -0.244000000000000 4.173128 -0.0585 0.953623 0.476811 M3 4.06399999999999 4.173128 0.9738 0.335117 0.167558 M4 6.16999999999999 4.173128 1.4785 0.145943 0.072972 M5 2.44999999999999 4.173128 0.5871 0.559953 0.279977 M6 -1.52399999999999 4.173128 -0.3652 0.716605 0.358303 M7 -7.496 4.173128 -1.7963 0.078883 0.039442 M8 -3.76 4.173128 -0.901 0.372181 0.18609 M9 -1.07600000000000 4.173128 -0.2578 0.797656 0.398828 M10 6.594 4.173128 1.5801 0.120789 0.060394 M11 2.61200000000000 4.173128 0.6259 0.534402 0.267201 Multiple Linear Regression - Regression Statistics Multiple R 0.732295623763541 R-squared 0.536256880583233 Adjusted R-squared 0.41785438200874 F-TEST (value) 4.52910104972019 F-TEST (DF numerator) 12 F-TEST (DF denominator) 47 p-value 8.29031147738801e-05 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 6.59829394455289 Sum Squared Residuals 2046.2617 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 126.51 122.642500000000 3.86749999999979 2 131.02 127.3185 3.7015 3 136.51 131.6265 4.88349999999999 4 138.04 133.7325 4.30749999999998 5 132.92 130.0125 2.90750000000000 6 129.61 126.0385 3.57150000000002 7 122.96 120.0665 2.89350000000001 8 124.04 123.8025 0.237500000000006 9 121.29 126.4865 -5.1965 10 124.56 134.1565 -9.5965 11 118.53 130.1745 -11.6445 12 113.14 127.5625 -14.4225 13 114.15 122.6425 -8.49249999999994 14 122.17 127.3185 -5.14849999999999 15 129.23 131.6265 -2.39650000000000 16 131.19 133.7325 -2.5425 17 129.12 130.0125 -0.892499999999997 18 128.28 126.0385 2.2415 19 126.83 120.0665 6.7635 20 138.13 123.8025 14.3275 21 140.52 126.4865 14.0335 22 146.83 134.1565 12.6735000000000 23 135.14 130.1745 4.96549999999999 24 131.84 127.5625 4.2775 25 125.7 122.6425 3.05750000000005 26 128.98 127.3185 1.6615 27 133.25 131.6265 1.62350000000001 28 136.76 133.7325 3.02750000000000 29 133.24 130.0125 3.22750000000001 30 128.54 126.0385 2.50149999999999 31 121.08 120.0665 1.01350000000000 32 120.23 123.8025 -3.57250000000000 33 119.08 126.4865 -7.4065 34 125.75 134.1565 -8.4065 35 126.89 130.1745 -3.28449999999999 36 126.6 127.5625 -0.962500000000005 37 121.89 122.6425 -0.752499999999949 38 123.44 127.3185 -3.87849999999999 39 126.46 131.6265 -5.1665 40 129.49 133.7325 -4.24249999999999 41 127.78 130.0125 -2.2325 42 125.29 126.0385 -0.748499999999996 43 119.02 120.0665 -1.04650000000001 44 119.96 123.8025 -3.84250000000001 45 122.86 126.4865 -3.6265 46 131.89 134.1565 -2.26650000000001 47 132.73 130.1745 2.55549999999999 48 135.01 127.5625 7.4475 49 136.71 134.39 2.32000000000005 50 142.73 139.066 3.66399999999999 51 144.43 143.374 1.05600000000000 52 144.93 145.48 -0.549999999999997 53 138.75 141.76 -3.01000000000001 54 130.22 137.786 -7.56600000000001 55 122.19 131.814 -9.62400000000001 56 128.4 135.55 -7.15 57 140.43 138.234 2.19600000000000 58 153.5 145.904 7.596 59 149.33 141.922 7.40800000000001 60 142.97 139.31 3.65999999999999 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.73589639937194 0.528207201256119 0.264103600628059 17 0.603539824719157 0.792920350561685 0.396460175280843 18 0.458752981488703 0.917505962977406 0.541247018511297 19 0.375541227317468 0.751082454634936 0.624458772682532 20 0.682367960220411 0.635264079559179 0.317632039779589 21 0.94868332322866 0.102633353542679 0.0513166767713394 22 0.996559451538348 0.0068810969233039 0.00344054846165195 23 0.997629070347254 0.00474185930549153 0.00237092965274576 24 0.99838775514341 0.00322448971317968 0.00161224485658984 25 0.997019279825688 0.00596144034862386 0.00298072017431193 26 0.99413419584067 0.0117316083186604 0.00586580415933019 27 0.989852532112003 0.0202949357759933 0.0101474678879966 28 0.98554748860594 0.0289050227881215 0.0144525113940608 29 0.981090134390577 0.0378197312188465 0.0189098656094232 30 0.978179059425586 0.0436418811488287 0.0218209405744143 31 0.976358851621372 0.0472822967572561 0.0236411483786281 32 0.971231406979726 0.0575371860405482 0.0287685930202741 33 0.970107691548494 0.0597846169030112 0.0298923084515056 34 0.982164009575174 0.0356719808496525 0.0178359904248263 35 0.980878990040457 0.0382420199190857 0.0191210099595428 36 0.975431066859627 0.0491378662807456 0.0245689331403728 37 0.953904334884833 0.0921913302303335 0.0460956651151668 38 0.941453642718261 0.117092714563478 0.0585463572817389 39 0.923791785954189 0.152416428091622 0.0762082140458112 40 0.882686447296683 0.234627105406635 0.117313552703317 41 0.802323648473791 0.395352703052418 0.197676351526209 42 0.762456024258438 0.475087951483125 0.237543975741562 43 0.821297603078206 0.357404793843588 0.178702396921794 44 0.789858940659552 0.420282118680897 0.210141059340448 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 4 0.137931034482759 NOK 5% type I error level 13 0.448275862068966 NOK 10% type I error level 16 0.551724137931034 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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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