ws 8 multiple regression

*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: Mon, 29 Nov 2010 19:00:08 +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/Nov/29/t1291057130bolx6ga7gwt0w0h.htm/, Retrieved Mon, 29 Nov 2010 19:59:00 +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/Nov/29/t1291057130bolx6ga7gwt0w0h.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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167,16 179,84 174,44 180,35 193,17 195,16 202,43 189,91 195,98 212,09 205,81 204,31 196,07 199,98 199,10 198,31 195,72 223,04 238,41 259,73 326,54 335,15 321,81 368,62 369,59 425,00 439,72 362,23 328,76 348,55 328,18 329,34 295,55 237,38 226,85 220,14 239,36 224,69 230,98 233,47 256,70 253,41 224,95 210,37 191,09 198,85 211,04 206,25 201,19 194,37 191,08 192,87 181,61 157,67 196,14 246,35 271,90

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 8 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Tarweprijs[t] = + 246.070714285714 -14.5294523809523M1[t] -4.55276190476188M2[t] -2.39007142857144M3[t] -16.1333809523809M4[t] -18.5126904761905M5[t] -14.264M6[t] -11.9333095238095M7[t] -2.94061904761904M8[t] + 6.00607142857145M9[t] -3.71188095238094M10[t] -8.32719047619046M11[t] + 0.125309523809523t + 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) 246.070714285714 41.948476 5.866 1e-06 0 M1 -14.5294523809523 50.67244 -0.2867 0.775663 0.387831 M2 -4.55276190476188 50.639039 -0.0899 0.92877 0.464385 M3 -2.39007142857144 50.613044 -0.0472 0.96255 0.481275 M4 -16.1333809523809 50.594468 -0.3189 0.751329 0.375665 M5 -18.5126904761905 50.58332 -0.366 0.716131 0.358065 M6 -14.264 50.579603 -0.282 0.779257 0.389629 M7 -11.9333095238095 50.58332 -0.2359 0.814594 0.407297 M8 -2.94061904761904 50.594468 -0.0581 0.953915 0.476958 M9 6.00607142857145 50.613044 0.1187 0.90608 0.45304 M10 -3.71188095238094 53.329686 -0.0696 0.944825 0.472413 M11 -8.32719047619046 53.319109 -0.1562 0.876608 0.438304 t 0.125309523809523 0.613187 0.2044 0.839016 0.419508 Multiple Linear Regression - Regression Statistics Multiple R 0.115070824238089 R-squared 0.0132412945908331 Adjusted R-squared -0.255874715975303 F-TEST (value) 0.0492029239099433 F-TEST (DF numerator) 12 F-TEST (DF denominator) 44 p-value 0.99999874385495 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 75.3996204688767 Sum Squared Residuals 250144.521741429 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 167.16 231.666571428571 -64.5065714285712 2 179.84 241.768571428571 -61.9285714285715 3 174.44 244.056571428571 -69.6165714285714 4 180.35 230.438571428571 -50.0885714285714 5 193.17 228.184571428571 -35.0145714285715 6 195.16 232.558571428571 -37.3985714285715 7 202.43 235.014571428571 -32.5845714285714 8 189.91 244.132571428571 -54.2225714285715 9 195.98 253.204571428571 -57.2245714285714 10 212.09 243.611928571429 -31.5219285714286 11 205.81 239.121928571429 -33.3119285714286 12 204.31 247.574428571429 -43.2644285714286 13 196.07 233.170285714286 -37.1002857142858 14 199.98 243.272285714286 -43.2922857142857 15 199.1 245.560285714286 -46.4602857142857 16 198.31 231.942285714286 -33.6322857142857 17 195.72 229.688285714286 -33.9682857142857 18 223.04 234.062285714286 -11.0222857142857 19 238.41 236.518285714286 1.89171428571427 20 259.73 245.636285714286 14.0937142857143 21 326.54 254.708285714286 71.8317142857143 22 335.15 245.115642857143 90.0343571428571 23 321.81 240.625642857143 81.1843571428572 24 368.62 249.078142857143 119.541857142857 25 369.59 234.674 134.916 26 425 244.776 180.224 27 439.72 247.064 192.656 28 362.23 233.446 128.784 29 328.76 231.192 97.568 30 348.55 235.566 112.984 31 328.18 238.022 90.158 32 329.34 247.14 82.2 33 295.55 256.212 39.338 34 237.38 246.619357142857 -9.23935714285715 35 226.85 242.129357142857 -15.2793571428571 36 220.14 250.581857142857 -30.4418571428571 37 239.36 236.177714285714 3.1822857142857 38 224.69 246.279714285714 -21.5897142857143 39 230.98 248.567714285714 -17.5877142857143 40 233.47 234.949714285714 -1.47971428571428 41 256.7 232.695714285714 24.0042857142857 42 253.41 237.069714285714 16.3402857142857 43 224.95 239.525714285714 -14.5757142857143 44 210.37 248.643714285714 -38.2737142857143 45 191.09 257.715714285714 -66.6257142857143 46 198.85 248.123071428571 -49.2730714285714 47 211.04 243.633071428571 -32.5930714285714 48 206.25 252.085571428571 -45.8355714285714 49 201.19 237.681428571429 -36.4914285714286 50 194.37 247.783428571429 -53.4134285714286 51 191.08 250.071428571429 -58.9914285714285 52 192.87 236.453428571429 -43.5834285714286 53 181.61 234.199428571429 -52.5894285714285 54 157.67 238.573428571429 -80.9034285714286 55 196.14 241.029428571429 -44.8894285714286 56 246.35 250.147428571429 -3.79742857142858 57 271.9 259.219428571429 12.6805714285714 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.00022876016240949 0.00045752032481898 0.99977123983759 17 0.00044313196577878 0.00088626393155756 0.999556868034221 18 9.80847139554618e-05 0.000196169427910924 0.999901915286045 19 5.23562646792467e-05 0.000104712529358493 0.99994764373532 20 0.00136974153351684 0.00273948306703369 0.998630258466483 21 0.0662554735314624 0.132510947062925 0.933744526468538 22 0.114132126736021 0.228264253472043 0.885867873263979 23 0.12002708677003 0.24005417354006 0.87997291322997 24 0.232016922365438 0.464033844730876 0.767983077634562 25 0.298802332372312 0.597604664744624 0.701197667627688 26 0.58334066997409 0.833318660051821 0.416659330025911 27 0.891038044764429 0.217923910471142 0.108961955235571 28 0.894935958232893 0.210128083534215 0.105064041767107 29 0.859554488099745 0.28089102380051 0.140445511900255 30 0.88686892939257 0.226262141214857 0.113131070607429 31 0.900146051367485 0.199707897265029 0.0998539486325146 32 0.904745939952958 0.190508120094083 0.0952540600470416 33 0.913390029726315 0.173219940547371 0.0866099702736853 34 0.945155638999747 0.109688722000506 0.054844361000253 35 0.947474606529203 0.105050786941593 0.0525253934707965 36 0.946588747709606 0.106822504580788 0.053411252290394 37 0.925089720960622 0.149820558078757 0.0749102790393784 38 0.896389487851172 0.207221024297656 0.103610512148828 39 0.842742311523967 0.314515376952065 0.157257688476033 40 0.745379320679044 0.509241358641912 0.254620679320956 41 0.663553631326233 0.672892737347534 0.336446368673767 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 5 0.192307692307692 NOK 5% type I error level 5 0.192307692307692 NOK 10% type I error level 5 0.192307692307692 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/29/t1291057130bolx6ga7gwt0w0h/10xav21291057199.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/29/t1291057130bolx6ga7gwt0w0h/10xav21291057199.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/29/t1291057130bolx6ga7gwt0w0h/1qqyr1291057199.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/29/t1291057130bolx6ga7gwt0w0h/1qqyr1291057199.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/29/t1291057130bolx6ga7gwt0w0h/21ifc1291057199.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/29/t1291057130bolx6ga7gwt0w0h/21ifc1291057199.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/29/t1291057130bolx6ga7gwt0w0h/31ifc1291057199.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/29/t1291057130bolx6ga7gwt0w0h/31ifc1291057199.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/29/t1291057130bolx6ga7gwt0w0h/41ifc1291057199.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/29/t1291057130bolx6ga7gwt0w0h/41ifc1291057199.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/29/t1291057130bolx6ga7gwt0w0h/51ifc1291057199.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/29/t1291057130bolx6ga7gwt0w0h/51ifc1291057199.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/29/t1291057130bolx6ga7gwt0w0h/6trxw1291057199.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/29/t1291057130bolx6ga7gwt0w0h/6trxw1291057199.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/29/t1291057130bolx6ga7gwt0w0h/7mieh1291057199.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/29/t1291057130bolx6ga7gwt0w0h/7mieh1291057199.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/29/t1291057130bolx6ga7gwt0w0h/8mieh1291057199.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/29/t1291057130bolx6ga7gwt0w0h/8mieh1291057199.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/29/t1291057130bolx6ga7gwt0w0h/9mieh1291057199.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/29/t1291057130bolx6ga7gwt0w0h/9mieh1291057199.ps (open in new window)

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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