*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: Tue, 07 Dec 2010 12:28:40 +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/07/t1291724860xdy2wjji6qzjt6a.htm/, Retrieved Tue, 07 Dec 2010 13:27:40 +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/07/t1291724860xdy2wjji6qzjt6a.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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112.3 0 117.3 0 111.1 1 102.2 1 104.3 1 122.9 1 107.6 1 121.3 1 131.5 1 89 1 104.4 1 128.9 1 135.9 1 133.3 1 121.3 1 120.5 0 120.4 0 137.9 0 126.1 0 133.2 0 151.1 0 105 0 119 0 140.4 0 156.6 0 137.1 0 122.7 0 125.8 0 139.3 0 134.9 0 149.2 0 132.3 0 149 0 117.2 0 119.6 0 152 0 149.4 0 127.3 0 114.1 0 102.1 0 107.7 0 104.4 0 102.1 0 96 1 109.3 0 90 1 83.9 1 112 1 114.3 1 103.6 1 91.7 1 80.8 1 87.2 1 109.2 1 102.7 1 95.1 1 117.5 1 85.1 1 92.1 1 113.5 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 8 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation Promet[t] = + 140.995833333333 -19.3930555555555Dummy[t] + 0.461388888888867M1[t] -9.5186111111111M2[t] -17.18M3[t] -26.9586111111111M4[t] -21.4586111111111M5[t] -11.3786111111111M6[t] -15.6986111111111M7[t] -13.78M8[t] -1.55861111111111M9[t] -32.1M10[t] -25.56M11[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) 140.995833333333 6.407514 22.0048 0 0 Dummy -19.3930555555555 3.55973 -5.4479 2e-06 1e-06 M1 0.461388888888867 8.572965 0.0538 0.957307 0.478654 M2 -9.5186111111111 8.572965 -1.1103 0.272516 0.136258 M3 -17.18 8.543352 -2.0109 0.05009 0.025045 M4 -26.9586111111111 8.572965 -3.1446 0.002881 0.001441 M5 -21.4586111111111 8.572965 -2.5031 0.015846 0.007923 M6 -11.3786111111111 8.572965 -1.3273 0.190832 0.095416 M7 -15.6986111111111 8.572965 -1.8312 0.073417 0.036709 M8 -13.78 8.543352 -1.613 0.113451 0.056725 M9 -1.55861111111111 8.572965 -0.1818 0.856517 0.428259 M10 -32.1 8.543352 -3.7573 0.000474 0.000237 M11 -25.56 8.543352 -2.9918 0.004407 0.002204 Multiple Linear Regression - Regression Statistics Multiple R 0.772025713756316 R-squared 0.59602370270095 Adjusted R-squared 0.492880818284171 F-TEST (value) 5.77862162834755 F-TEST (DF numerator) 12 F-TEST (DF denominator) 47 p-value 5.27128218130724e-06 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 13.5082254732941 Sum Squared Residuals 8576.19130555557 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 112.3 141.457222222222 -29.1572222222224 2 117.3 131.477222222222 -14.1772222222222 3 111.1 104.422777777778 6.67722222222222 4 102.2 94.6441666666667 7.55583333333333 5 104.3 100.144166666667 4.15583333333331 6 122.9 110.224166666667 12.6758333333333 7 107.6 105.904166666667 1.69583333333333 8 121.3 107.822777777778 13.4772222222222 9 131.5 120.044166666667 11.4558333333333 10 89 89.5027777777778 -0.502777777777784 11 104.4 96.0427777777778 8.35722222222223 12 128.9 121.602777777778 7.29722222222223 13 135.9 122.064166666667 13.8358333333334 14 133.3 112.084166666667 21.2158333333333 15 121.3 104.422777777778 16.8772222222222 16 120.5 114.037222222222 6.46277777777778 17 120.4 119.537222222222 0.862777777777785 18 137.9 129.617222222222 8.28277777777778 19 126.1 125.297222222222 0.802777777777778 20 133.2 127.215833333333 5.98416666666666 21 151.1 139.437222222222 11.6627777777778 22 105 108.895833333333 -3.89583333333333 23 119 115.435833333333 3.56416666666667 24 140.4 140.995833333333 -0.595833333333324 25 156.6 141.457222222222 15.1427777777778 26 137.1 131.477222222222 5.62277777777778 27 122.7 123.815833333333 -1.11583333333333 28 125.8 114.037222222222 11.7627777777778 29 139.3 119.537222222222 19.7627777777778 30 134.9 129.617222222222 5.28277777777778 31 149.2 125.297222222222 23.9027777777778 32 132.3 127.215833333333 5.08416666666669 33 149 139.437222222222 9.56277777777779 34 117.2 108.895833333333 8.30416666666667 35 119.6 115.435833333333 4.16416666666666 36 152 140.995833333333 11.0041666666667 37 149.4 141.457222222222 7.94277777777782 38 127.3 131.477222222222 -4.17722222222222 39 114.1 123.815833333333 -9.71583333333333 40 102.1 114.037222222222 -11.9372222222222 41 107.7 119.537222222222 -11.8372222222222 42 104.4 129.617222222222 -25.2172222222222 43 102.1 125.297222222222 -23.1972222222222 44 96 107.822777777778 -11.8227777777778 45 109.3 139.437222222222 -30.1372222222222 46 90 89.5027777777778 0.497222222222222 47 83.9 96.0427777777778 -12.1427777777778 48 112 121.602777777778 -9.60277777777778 49 114.3 122.064166666667 -7.76416666666664 50 103.6 112.084166666667 -8.48416666666667 51 91.7 104.422777777778 -12.7227777777778 52 80.8 94.6441666666667 -13.8441666666667 53 87.2 100.144166666667 -12.9441666666667 54 109.2 110.224166666667 -1.02416666666667 55 102.7 105.904166666667 -3.20416666666666 56 95.1 107.822777777778 -12.7227777777778 57 117.5 120.044166666667 -2.54416666666667 58 85.1 89.5027777777778 -4.40277777777778 59 92.1 96.0427777777778 -3.94277777777779 60 113.5 121.602777777778 -8.10277777777778 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.701753311023599 0.596493377952803 0.298246688976401 17 0.696647832561954 0.606704334876093 0.303352167438046 18 0.642845370577563 0.714309258844875 0.357154629422437 19 0.583970542602611 0.832058914794777 0.416029457397389 20 0.473941417999722 0.947882835999445 0.526058582000278 21 0.435628121569585 0.87125624313917 0.564371878430415 22 0.356561194615606 0.713122389231211 0.643438805384394 23 0.2653313686351 0.5306627372702 0.7346686313649 24 0.185294611909995 0.370589223819989 0.814705388090005 25 0.322646631304417 0.645293262608835 0.677353368695583 26 0.250026996211291 0.500053992422582 0.749973003788709 27 0.182319621510035 0.364639243020071 0.817680378489965 28 0.170462968226818 0.340925936453637 0.829537031773182 29 0.28853740997838 0.57707481995676 0.71146259002162 30 0.24338551268679 0.48677102537358 0.75661448731321 31 0.554423181353809 0.891153637292382 0.445576818646191 32 0.511389357442927 0.977221285114146 0.488610642557073 33 0.608124335760759 0.783751328478483 0.391875664239241 34 0.579254838927339 0.841490322145322 0.420745161072661 35 0.543763008232741 0.912473983534518 0.456236991767259 36 0.700821830905684 0.598356338188633 0.299178169094317 37 0.80985981421043 0.380280371579139 0.190140185789569 38 0.80943607638322 0.381127847233561 0.190563923616781 39 0.843087427497762 0.313825145004476 0.156912572502238 40 0.916679644415352 0.166640711169296 0.0833203555846481 41 0.99735973663815 0.00528052672369979 0.00264026336184990 42 0.99389390847545 0.0122121830490987 0.00610609152454935 43 0.98962592246172 0.0207481550765607 0.0103740775382804 44 0.964140534640713 0.0717189307185746 0.0358594653592873 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 1 0.0344827586206897 NOK 5% type I error level 3 0.103448275862069 NOK 10% type I error level 4 0.137931034482759 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') }

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