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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: Fri, 20 Nov 2009 06:03:57 -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/t1258722276c8orhknhvnd9ks6.htm/, Retrieved Fri, 20 Nov 2009 14:04:49 +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/t1258722276c8orhknhvnd9ks6.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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89.1 72.7 103.5 8.2 82.6 79.7 104.6 8.3 102.7 115.8 118.6 8.1 91.8 87.8 106.3 7.4 94.1 99.2 110.7 7.3 103.1 111.4 121.6 7.7 93.2 102.3 107 8 91 94.4 107.6 8 94.3 118.5 125.6 7.7 99.4 112.1 113.5 6.9 115.7 136.5 129.2 6.6 116.8 139.8 130.9 6.9 99.8 104.5 104.7 7.5 96 123.3 115.2 7.9 115.9 156.6 124.5 7.7 109.1 136.2 112.3 6.5 117.3 147.5 127.5 6.1 109.8 143.8 120.6 6.4 112.8 135.8 117.5 6.8 110.7 121.6 117.7 7.1 100 128 120.4 7.3 113.3 129.7 125 7.2 122.4 136.2 131.6 7 112.5 130.5 121.1 7 104.2 99.2 114.2 7 92.5 110.4 112.1 7.3 117.2 151.6 127 7.5 109.3 129.6 116.8 7.2 106.1 123.6 112 7.7 118.8 142.7 129.7 8 105.3 119 113.6 7.9 106 118.1 115.7 8 102 120 119.5 8 112.9 124.3 125.8 7.9 116.5 123.3 129.6 7.9 114.8 122.4 128 8 100.5 90.5 112.8 8.1 85.4 91 101.6 8.1 114.6 137 123.9 8.2 109.9 127.7 118.8 8 100.7 105.1 109.1 8.3 115.5 135.6 130.6 8.5 10 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 R Framework error message Warning: there are blank lines in the 'Data X' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values. Multiple Linear Regression - Estimated Regression Equation TotaleIndustrieleProductie[t] = + 9.66386270757074 + 0.297950401733887Investeringsgoederen[t] + 0.479360303731291Consumptiegoederen[t] + 0.57480776596739BrutoInflatie[t] + 3.14166191797486M1[t] -8.44973556391387M2[t] -2.96336432788968M3[t] -0.79174312654727M4[t] -1.03781182965360M5[t] -4.54220727709078M6[t] -1.99582303416013M7[t] -1.49535021102689M8[t] -9.69478239937884M9[t] -0.834699350408226M10[t] + 1.41278369982361M11[t] + 0.0554727893837077t + 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) 9.66386270757074 12.335208 0.7834 0.437567 0.218784 Investeringsgoederen 0.297950401733887 0.045435 6.5578 0 0 Consumptiegoederen 0.479360303731291 0.092236 5.1971 5e-06 3e-06 BrutoInflatie 0.57480776596739 0.99729 0.5764 0.567302 0.283651 M1 3.14166191797486 1.966625 1.5975 0.117314 0.058657 M2 -8.44973556391387 2.070683 -4.0807 0.000186 9.3e-05 M3 -2.96336432788968 1.902854 -1.5573 0.126558 0.063279 M4 -0.79174312654727 1.877271 -0.4218 0.675259 0.33763 M5 -1.03781182965360 1.815701 -0.5716 0.570518 0.285259 M6 -4.54220727709078 1.606294 -2.8278 0.00703 0.003515 M7 -1.99582303416013 1.957243 -1.0197 0.31344 0.15672 M8 -1.49535021102689 1.819997 -0.8216 0.415722 0.207861 M9 -9.69478239937884 1.545148 -6.2743 0 0 M10 -0.834699350408226 1.565288 -0.5333 0.59654 0.29827 M11 1.41278369982361 1.516176 0.9318 0.356521 0.178261 t 0.0554727893837077 0.027974 1.983 0.053628 0.026814 Multiple Linear Regression - Regression Statistics Multiple R 0.97719137439449 R-squared 0.954902982190994 Adjusted R-squared 0.939528998847014 F-TEST (value) 62.1116181035114 F-TEST (DF numerator) 15 F-TEST (DF denominator) 44 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.36700732314936 Sum Squared Residuals 246.519841385079 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 89.1 88.8492067381045 0.250793261895545 2 82.6 79.9837119684375 2.61628803156246 3 102.7 102.877648195483 -0.177648195483286 4 91.8 90.4636337655886 1.33636623441144 5 94.1 95.7213769914532 -1.62137699145319 6 103.1 101.362399651611 1.73760034838884 7 93.2 94.4266899234605 -1.22668992346050 8 91 92.9164435445185 -1.91644354451853 9 94.3 100.40913196471 -6.10913196470996 10 99.4 101.157699344045 -1.75769934404488 11 115.7 118.084159424758 -2.38415942475831 12 116.8 118.697439686174 -1.89743968617365 13 99.8 99.1625699141466 0.637430085853382 14 96 98.4913190698042 -2.49131906980418 15 115.9 118.298000744458 -2.39800074445802 16 109.1 107.908941515130 1.19105848486975 17 117.3 118.141538651329 -0.841538651329209 18 109.8 110.455055740905 -0.655055740904673 19 112.8 109.417215724168 3.38278427583211 20 110.7 106.010580022600 4.68941997739988 21 100 101.182737567997 -1.18273756799672 22 113.3 112.752385709866 0.547614290134157 23 122.4 120.040835612185 2.35916438781531 24 112.5 111.951924222683 0.548075777316919 25 104.2 102.515625260025 1.68437473997492 26 92.5 93.4825307588941 -0.982530758894103 27 117.2 118.557361414528 -1.35736141452783 28 109.3 109.167629139259 0.132370860740929 29 106.1 105.175805240207 0.92419475979337 30 118.8 116.074854961104 2.72514503889555 31 105.3 103.840105805655 1.45989419434482 32 106 105.192033471044 0.807966528955923 33 102 99.435748989549 2.56425101045088 34 112.9 112.594980692270 0.305019307730453 35 116.5 116.42155528433 0.0784447156698831 36 114.8 114.086593302956 0.713406697043607 37 100.5 100.550314354885 -0.0503143548850813 38 85.4 83.7945294614565 1.60547053854345 39 114.6 113.789307516428 0.810692483572234 40 109.9 110.685763668806 -0.785763668805665 41 100.7 99.284136059494 1.41586394050610 42 115.5 115.343908737740 0.156091262259794 43 100.7 102.366439698516 -1.66643969851565 44 99 99.35905268524 -0.359052685240045 45 102.3 96.7170659231868 5.58293407681323 46 108.8 106.707046578659 2.09295342134073 47 105.9 105.501351879146 0.398648120854041 48 113.2 113.27395651761 -0.0739565176100113 49 95.7 98.2222837328388 -2.52228373283876 50 80.9 81.6479087414076 -0.747908741407636 51 113.9 110.777682129103 3.12231787089691 52 98.1 99.9740319112165 -1.87403191121646 53 102.8 102.677143057517 0.122856942482923 54 104.7 108.663780908640 -3.96378090863950 55 95.9 97.8495488482008 -1.94954884820078 56 94.6 97.8218902765972 -3.22189027659723 57 101.6 102.455315554557 -0.855315554557427 58 103.9 105.087887675160 -1.18788767516046 59 110.3 110.752097799581 -0.452097799580933 60 114.1 113.390086270577 0.709913729423133 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 19 0.681391963538921 0.637216072922159 0.318608036461079 20 0.715493589703182 0.569012820593636 0.284506410296818 21 0.704911358682864 0.590177282634272 0.295088641317136 22 0.638104963872588 0.723790072254824 0.361895036127412 23 0.547012641980946 0.905974716038108 0.452987358019054 24 0.522504743653742 0.954990512692517 0.477495256346258 25 0.92466934021977 0.150661319560458 0.0753306597802289 26 0.944689691406915 0.110620617186169 0.0553103085930845 27 0.958345710292512 0.0833085794149764 0.0416542897074882 28 0.937574702956269 0.124850594087462 0.0624252970437309 29 0.917196623079453 0.165606753841093 0.0828033769205466 30 0.917631861765139 0.164736276469722 0.0823681382348612 31 0.916651711571624 0.166696576856753 0.0833482884283764 32 0.911073926801163 0.177852146397675 0.0889260731988373 33 0.910920421163925 0.178159157672149 0.0890795788360747 34 0.865088958563004 0.269822082873993 0.134911041436996 35 0.811514918510888 0.376970162978225 0.188485081489112 36 0.737389675304825 0.52522064939035 0.262610324695175 37 0.759230155682422 0.481539688635156 0.240769844317578 38 0.951872286252328 0.0962554274953438 0.0481277137476719 39 0.914326890367485 0.17134621926503 0.085673109632515 40 0.96766121071521 0.0646775785695804 0.0323387892847902 41 0.905732630027026 0.188534739945948 0.0942673699729742 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 3 0.130434782608696 NOK

Charts produced by software:

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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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