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 06:37:34 -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/t1258724586iu4hpjost572j7u.htm/, Retrieved Fri, 20 Nov 2009 14:43:18 +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/t1258724586iu4hpjost572j7u.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:

Dataseries X:

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10284,5 1,038351422 1,4 12792 0,933031106 1,3 12823,61538 0,932783124 1,3 13845,66667 0,953755367 1,2 15335,63636 1,009865664 1,1 11188,5 0,979532493 1,4 13633,25 0,98651077 1,2 12298,46667 0,964661281 1,5 15353,63636 0,946761816 1,1 12696,15385 0,959068881 1,3 12213,93333 0,985710058 1,5 13683,72727 0,92582159 1,1 11214,14286 1,036865325 1,4 13950,23077 0,944443576 1,3 11179,13333 0,944901812 1,5 11801,875 0,989151445 1,6 11188,82353 1,054361624 1,7 16456,27273 1,033478919 1,1 11110,0625 1,001368875 1,6 16530,69231 1,019812646 1,3 10038,41176 0,993902155 1,7 11681,25 0,961444482 1,6 11148,88235 0,957449711 1,7 8631 0,93308639 1,9 9386,444444 1,045170549 1,8 9764,736842 0,953166261 1,9 12043,75 0,966782226 1,6 12948,06667 0,972992606 1,5 10987,125 1,013607482 1,6 11648,3125 0,984839518 1,6 10633,35294 0,973220775 1,7 10219,3 0,957284573 2 9037,6 0,972067159 2 10296,31579 0,986878944 1,9 11705,41176 0,954654488 1,7 10681,94444 0,978986976 1,8 9362,947368 1,003056035 1,9 113 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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Invoer/inflatie[t] = + 14821.9835564809 + 3533.54666618665`Uitvoer/inflatie`[t] -4143.3985152365Inflatie[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) 14821.9835564809 3900.87748 3.7997 0.000354 0.000177 `Uitvoer/inflatie` 3533.54666618665 4263.023216 0.8289 0.410628 0.205314 Inflatie -4143.3985152365 350.717647 -11.8141 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.882273496726411 R-squared 0.778406523025849 Adjusted R-squared 0.770631313307458 F-TEST (value) 100.113894186626 F-TEST (DF numerator) 2 F-TEST (DF denominator) 57 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1184.69780364966 Sum Squared Residuals 80000006.5004223 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 10284.5 12690.2888406881 -2405.78884068811 2 12792 12732.4744407282 59.5255592717623 3 12823.61538 12731.5981847589 92.0171952411318 4 13845.66667 13220.0444356176 625.622234382379 5 15335.63636 13832.6526400444 1502.98371995564 6 11188.5 12482.4494102115 -1293.94941021150 7 13633.25 13335.7871806879 297.462819312128 8 12298.46667 12015.5614371031 282.905232896909 9 15353.63636 13609.6722483204 1743.96411167959 10 12696.15385 12824.4801337744 -128.326283774408 11 12213.93333 12089.9382728987 123.995057101252 12 13683.72727 13535.6789825489 148.048287451079 13 11214.14286 12685.0376475881 -1470.89478758814 14 13950.23077 12772.8009360497 1177.42983395031 15 11179.13333 11945.7404312925 -766.607101292522 16 11801.875 11687.758722936 114.116277063995 17 11188.82353 11503.8420820192 -315.018552019241 18 16456.27273 13916.0911785274 2540.18155147257 19 11110.0625 11730.9295819819 -620.867081981874 20 16530.69231 13039.1210620818 3491.57124791821 21 10038.41176 11290.2057268949 -1251.79396689487 22 11681.25 11589.8548761972 91.3951238028015 23 11148.88235 11161.3993149243 -12.5169649243203 24 8631 10246.6306801802 -1615.63068018024 25 9386.444444 11057.0251380707 -1670.58069407067 26 9764.736842 10317.5838414097 -552.846999409744 27 12043.75 11608.7160437134 435.033956286644 28 12948.06667 12045.0005627818 903.066107218241 29 10987.125 11774.1752709455 -787.050270945493 30 11648.3125 11672.5223276603 -24.2098276603152 31 10633.35294 11217.1271055437 -583.774165543736 32 10219.3 9917.796237524 301.503762475989 33 9037.6 9970.03119500193 -932.431195001927 34 10296.31579 10436.7091800326 -140.393390032600 35 11705.41176 11151.5222640114 553.889495988579 36 10681.94444 10823.1623943402 -141.217954340199 37 9362.947368 10493.8716860042 -1130.92431800425 38 11306.35294 11206.0331152932 100.319824706810 39 10984.45 10038.2611366209 946.188863379075 40 10062.61905 9734.28344212218 328.335607877823 41 8118.583333 8729.04392818293 -610.460595182927 42 8867.48 8210.36675450854 657.113245491456 43 8346.72 7947.39688654352 399.32311345648 44 8529.307692 7715.24506509635 814.062626903653 45 10697.18182 9329.57643103423 1367.60538896577 46 8591.84 8019.56612139174 572.273878608257 47 8695.607143 6820.31098043501 1875.29616256499 48 8125.571429 6810.61639127131 1314.95503772869 49 7009.758621 6736.8821381928 272.876482807193 50 7883.466667 6059.26913086023 1824.19753613977 51 7527.645161 5671.54510476251 1856.10005623749 52 6763.758621 6690.74772535993 73.0108956400724 53 6682.333333 7528.49608864802 -846.162755648021 54 7855.681818 9524.76891636953 -1669.08709836953 55 6738.88 8083.21275970032 -1344.33275970032 56 7895.434783 8911.51609762512 -1016.08131462512 57 6361.884615 7561.01679545063 -1199.13218045063 58 6935.956522 8772.48147440752 -1836.52495240752 59 8344.454545 9260.5166607155 -916.062115715505 60 9107.944444 10711.648481313 -1603.704037313 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 6 0.0147578160240361 0.0295156320480721 0.985242183975964 7 0.00370492173994261 0.00740984347988523 0.996295078260057 8 0.292412323096834 0.584824646193667 0.707587676903166 9 0.202605022563928 0.405210045127856 0.797394977436072 10 0.124847972066184 0.249695944132368 0.875152027933816 11 0.180824310682644 0.361648621365287 0.819175689317356 12 0.198783931355004 0.397567862710008 0.801216068644996 13 0.152822719122403 0.305645438244805 0.847177280877597 14 0.141039507477884 0.282079014955768 0.858960492522116 15 0.0964588024576054 0.192917604915211 0.903541197542395 16 0.112541274675112 0.225082549350224 0.887458725324888 17 0.129860346320053 0.259720692640106 0.870139653679947 18 0.314499865084808 0.628999730169616 0.685500134915192 19 0.243879439217359 0.487758878434718 0.756120560782641 20 0.878638492991819 0.242723014016362 0.121361507008181 21 0.84019079681006 0.319618406379881 0.159809203189941 22 0.814619298673089 0.370761402653822 0.185380701326911 23 0.78754779768207 0.424904404635861 0.212452202317930 24 0.790810972338374 0.418378055323252 0.209189027661626 25 0.75688981502237 0.48622036995526 0.24311018497763 26 0.729357081832116 0.541285836335768 0.270642918167884 27 0.709291126925903 0.581417746148194 0.290708873074097 28 0.755699870566599 0.488600258866802 0.244300129433401 29 0.696184270452485 0.60763145909503 0.303815729547515 30 0.657190385967748 0.685619228064504 0.342809614032252 31 0.583830019958369 0.832339960083263 0.416169980041631 32 0.600714205989983 0.798571588020033 0.399285794010017 33 0.546339049095368 0.907321901809264 0.453660950904632 34 0.492029470858186 0.984058941716373 0.507970529141814 35 0.499203039530228 0.998406079060455 0.500796960469772 36 0.446462139258082 0.892924278516164 0.553537860741918 37 0.373297906236627 0.746595812473253 0.626702093763373 38 0.365924080203314 0.731848160406628 0.634075919796686 39 0.544969807410384 0.910060385179231 0.455030192589616 40 0.615019375719077 0.769961248561846 0.384980624280923 41 0.545005125034492 0.909989749931016 0.454994874965508 42 0.583909467703874 0.832181064592252 0.416090532296126 43 0.528750953603785 0.94249809279243 0.471249046396215 44 0.511259012864017 0.977481974271967 0.488740987135983 45 0.889169719051245 0.22166056189751 0.110830280948755 46 0.873572523313501 0.252854953372998 0.126427476686499 47 0.920640539372197 0.158718921255606 0.079359460627803 48 0.913861765893373 0.172276468213255 0.0861382341066273 49 0.857771146451746 0.284457707096508 0.142228853548254 50 0.885893588572809 0.228212822854383 0.114106411427191 51 0.984396681281442 0.031206637437117 0.0156033187185585 52 0.988536957529628 0.0229260849407439 0.0114630424703719 53 0.970733800396987 0.058532399206025 0.0292661996030125 54 0.964664183791546 0.0706716324169074 0.0353358162084537 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 1 0.0204081632653061 NOK 5% type I error level 4 0.0816326530612245 NOK 10% type I error level 6 0.122448979591837 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') }

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