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R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Sat, 18 Dec 2010 12:00:02 +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/18/t1292673537o7ysf6dsbokdge4.htm/, Retrieved Sat, 18 Dec 2010 12:59:07 +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/18/t1292673537o7ysf6dsbokdge4.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:

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User-defined keywords:

Dataseries X:

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98,1 113 112,5 116,7 107,5 116,1 113,9 126,4 113 112,5 116,7 107,5 80,9 114,1 126,4 113 112,5 116,7 95,7 112,5 114,1 126,4 113 112,5 113,2 112,4 112,5 114,1 126,4 113 105,9 113,1 112,4 112,5 114,1 126,4 108,8 116,3 113,1 112,4 112,5 114,1 102,3 111,7 116,3 113,1 112,4 112,5 99 118,8 111,7 116,3 113,1 112,4 100,7 116,5 118,8 111,7 116,3 113,1 115,5 125,1 116,5 118,8 111,7 116,3 100,7 113,1 125,1 116,5 118,8 111,7 109,9 119,6 113,1 125,1 116,5 118,8 114,6 114,4 119,6 113,1 125,1 116,5 85,4 114 114,4 119,6 113,1 125,1 100,5 117,8 114 114,4 119,6 113,1 114,8 117 117,8 114 114,4 119,6 116,5 120,9 117 117,8 114 114,4 112,9 115 120,9 117 117,8 114 102 117,3 115 120,9 117 117,8 106 119,4 117,3 115 120,9 117 105,3 114,9 119,4 117,3 115 120,9 118,8 125,8 114,9 119,4 117,3 115 106,1 117,6 125,8 114,9 119,4 117,3 109,3 117,6 117,6 125,8 114,9 119,4 117,2 114,9 117,6 117,6 125,8 114,9 92,5 121,9 114,9 117,6 117,6 125,8 104,2 117 121,9 114,9 117,6 117,6 112,5 106,4 117 121,9 114,9 117,6 122,4 1 etc...

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 6 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y(t)[t] = + 20.0671702470839 + 0.688595272943731T.I.P.[t] + 0.278503576120453`Y(t-1)`[t] + 0.193058224490072`Y(t-2)`[t] -0.338193109465919`Y(t-3)`[t] + 0.070699095273498`Y(t-4)`[t] -1.27620287842946M1[t] + 1.02349878003249M2[t] + 12.4875141879310M3[t] + 5.84323690683027M4[t] -6.6780209838056M5[t] -3.98147706592191M6[t] -2.25560893189417M7[t] + 1.76076039900308M8[t] + 8.23238768247252M9[t] + 0.579379111442313M10[t] + 0.792972106293582M11[t] -0.0934952638383165t + 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) 20.0671702470839 12.063566 1.6635 0.104449 0.052225 T.I.P. 0.688595272943731 0.113198 6.0831 0 0 `Y(t-1)` 0.278503576120453 0.11864 2.3475 0.024212 0.012106 `Y(t-2)` 0.193058224490072 0.130147 1.4834 0.14622 0.07311 `Y(t-3)` -0.338193109465919 0.133198 -2.539 0.015332 0.007666 `Y(t-4)` 0.070699095273498 0.114835 0.6157 0.541791 0.270895 M1 -1.27620287842946 2.903066 -0.4396 0.662713 0.331357 M2 1.02349878003249 2.811965 0.364 0.71789 0.358945 M3 12.4875141879310 3.101382 4.0264 0.000261 0.000131 M4 5.84323690683027 2.680737 2.1797 0.035544 0.017772 M5 -6.6780209838056 2.684944 -2.4872 0.017381 0.008691 M6 -3.98147706592191 3.058419 -1.3018 0.200818 0.100409 M7 -2.25560893189417 2.598024 -0.8682 0.390734 0.195367 M8 1.76076039900308 2.766272 0.6365 0.52826 0.26413 M9 8.23238768247252 2.713911 3.0334 0.004344 0.002172 M10 0.579379111442313 2.706512 0.2141 0.831638 0.415819 M11 0.792972106293582 3.077052 0.2577 0.798025 0.399013 t -0.0934952638383165 0.035915 -2.6032 0.013099 0.00655 Multiple Linear Regression - Regression Statistics Multiple R 0.921362250010479 R-squared 0.848908395744372 Adjusted R-squared 0.781314783314223 F-TEST (value) 12.5590032138262 F-TEST (DF numerator) 17 F-TEST (DF denominator) 38 p-value 9.74198499648082e-11 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.59658263510853 Sum Squared Residuals 491.545452744239 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 113 111.962621185805 1.03737881419492 2 126.4 120.657651311703 5.74234868829665 3 114.1 115.203847217153 -1.10384721715255 4 112.5 117.352638178784 -4.85263817878449 5 112.4 109.471642298598 2.92835770140159 6 113.1 111.818345066454 1.28165493354592 7 116.3 115.294801012297 1.00519898770294 8 111.7 115.688858764459 -3.98885876445923 9 118.8 118.887491165437 -0.0874911654367105 10 116.5 112.368178268774 4.13182173122608 11 125.1 125.191566616575 -0.0915666165749797 12 113.1 113.338599129718 -0.238599129718491 13 119.6 117.902043043916 1.69795695608434 14 114.4 119.767153111741 -5.36715311174095 15 114 115.503680682146 -1.50368068214638 16 117.8 115.001748206051 2.79825179394927 17 117 115.433146042634 1.56685395736592 18 120.9 119.485267001214 1.41473299878611 19 115 118.257000802004 -3.25700080200372 20 117.3 114.323153419989 2.97684658001139 21 119.4 121.581668828844 -2.18166882884439 22 114.9 116.653105546511 -1.75310554651093 23 125.8 124.026426827266 1.77357317273388 24 117.6 116.014128849507 1.58587115049293 25 117.6 118.338877996084 -0.73887799608428 26 114.9 120.397458784236 -5.49745878423554 27 121.9 117.551519667162 4.34848033283803 28 117 119.718847061142 -2.71884706114193 29 106.4 113.719296116099 -7.31929611609895 30 110.5 116.683075441909 -6.18307544190925 31 113.6 113.296718714107 0.303281285892692 32 114.2 112.954596850896 1.24540314910410 33 125.4 125.330278773907 0.0697212260929037 34 124.6 121.506367650741 3.09363234925947 35 120.2 121.516380145983 -1.31638014598302 36 120.8 120.669171639553 0.130828360447137 37 111.4 114.033022571698 -2.63302257169836 38 124.1 119.851068546932 4.2489314530676 39 120.2 118.726798981052 1.47320101894758 40 125.5 119.192798663597 6.30720133640251 41 116 114.047683041306 1.95231695869420 42 117 116.487533148657 0.512466851343351 43 105.7 103.272103561592 2.42789643840797 44 102 104.316649295843 -2.31664929584264 45 106.4 104.200561231812 2.19943876818819 46 96.9 102.372348533975 -5.4723485339746 47 107.6 107.965626410176 -0.365626410175878 48 98.8 100.278100381222 -1.47810038122158 49 101.1 100.463435202497 0.636564797503383 50 105.7 104.826668245388 0.873331754612235 51 104.6 107.814153452487 -3.21415345248668 52 103.2 104.733967890425 -1.53396789042537 53 101.6 100.728232501363 0.871767498637248 54 106.7 103.725779341766 2.97422065823387 55 99.5 99.9793759099999 -0.479375909999884 56 101 98.9167416688136 2.08325833118638 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.767632385557414 0.464735228885171 0.232367614442586 22 0.639400373962384 0.721199252075233 0.360599626037616 23 0.543840950643266 0.912318098713468 0.456159049356734 24 0.443357912549657 0.886715825099314 0.556642087450343 25 0.31715734359401 0.63431468718802 0.68284265640599 26 0.339469209753477 0.678938419506953 0.660530790246523 27 0.480932667311437 0.961865334622875 0.519067332688563 28 0.368201468635594 0.736402937271189 0.631798531364406 29 0.379828861778287 0.759657723556574 0.620171138221713 30 0.673055854083896 0.653888291832207 0.326944145916103 31 0.543383170803837 0.913233658392326 0.456616829196163 32 0.41940663153474 0.83881326306948 0.58059336846526 33 0.515188212428611 0.969623575142778 0.484811787571389 34 0.370547429943248 0.741094859886496 0.629452570056752 35 0.312036852928394 0.624073705856788 0.687963147071606 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 0 0 OK 5% type I error level 0 0 OK 10% type I error level 0 0 OK

Charts produced by software:

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Parameters (Session):

par1 = 2 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 2 ; 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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