Model 2

*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: Sun, 20 Dec 2009 03:35:52 -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/Dec/20/t12613054466scd1pc09dzy7s8.htm/, Retrieved Sun, 20 Dec 2009 11:37:38 +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/Dec/20/t12613054466scd1pc09dzy7s8.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:

» Textbox « » Textfile « » CSV «

100,0 100,0 95,3 100,6 90,7 114,2 88,4 91,5 86,0 94,7 86,0 110,6 95,3 71,3 95,3 104,1 88,4 112,3 86,0 110,2 81,4 112,9 83,7 95,1 95,3 103,1 88,4 101,9 86,0 100,4 83,7 106,9 76,7 100,7 79,1 114,3 86,0 73,3 86,0 105,9 79,1 113,9 76,7 112,1 69,8 117,5 69,8 97,5 76,7 112,3 69,8 106,9 67,4 120,9 65,1 92,7 58,1 110,9 60,5 116,5 65,1 77,1 62,8 113,1 55,8 115,9 51,2 123,5 48,8 123,6 48,8 101,5 53,5 121,0 48,8 112,2 46,5 126,0 44,2 101,8 39,5 117,9 41,9 122,2 48,8 82,7 46,5 120,5 41,9 120,3 39,5 134,2 37,2 128,2 37,2 100,5 41,9 126,0 39,5 122,9 39,5 106,1 34,9 130,4 34,9 121,3 34,9 126,1 41,9 88,7 41,9 118,7 39,5 129,3 39,5 136,2 41,9 123,0 46,5 103,5

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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Werkloosheid[t] = + 249.415186059235 -1.92948389941011Productie[t] + 41.0931629464141M1[t] + 29.0656105865259M2[t] + 35.6398262018006M3[t] + 15.7845988530270M4[t] + 20.1315073664078M5[t] + 38.6281450371932M6[t] -30.2991618876123M7[t] + 34.0745732684258M8[t] + 39.8599385969573M9[t] + 46.9544097040668M10[t] + 39.9495451253646M11[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) 249.415186059235 21.071473 11.8366 0 0 Productie -1.92948389941011 0.202925 -9.5084 0 0 M1 41.0931629464141 8.803387 4.6679 2.6e-05 1.3e-05 M2 29.0656105865259 8.616018 3.3734 0.001495 0.000747 M3 35.6398262018006 8.868238 4.0188 0.00021 0.000105 M4 15.7845988530270 8.469683 1.8637 0.068624 0.034312 M5 20.1315073664078 8.624979 2.3341 0.023917 0.011958 M6 38.6281450371932 9.192931 4.2019 0.000117 5.9e-05 M7 -30.2991618876123 9.42599 -3.2144 0.002364 0.001182 M8 34.0745732684258 8.802185 3.8711 0.000333 0.000167 M9 39.8599385969573 9.226055 4.3204 8e-05 4e-05 M10 46.9544097040668 9.677977 4.8517 1.4e-05 7e-06 M11 39.9495451253646 9.464826 4.2208 0.00011 5.5e-05 Multiple Linear Regression - Regression Statistics Multiple R 0.82371411150098 R-squared 0.678504937485848 Adjusted R-squared 0.596421091737554 F-TEST (value) 8.2659983983505 F-TEST (DF numerator) 12 F-TEST (DF denominator) 47 p-value 4.50185317912855e-08 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 13.2937513016362 Sum Squared Residuals 8306.01971247849 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 100 97.559959064638 2.44004093536208 2 95.3 84.3747163651038 10.9252836348962 3 90.7 64.7079509484011 25.9920490515989 4 88.4 88.652008116237 -0.252008116237041 5 86 86.8245681515056 -0.824568151505607 6 86 74.6424118216702 11.3575881783298 7 95.3 81.543822143682 13.7561778563180 8 95.3 82.6304853990685 12.6695146009315 9 88.4 72.5940827524371 15.8059172475629 10 86 83.7404700483078 2.25952995169217 11 81.4 71.5259989411983 9.8740010588017 12 83.7 65.9212672253337 17.7787327746663 13 95.3 91.5785589764669 3.7214410235331 14 88.4 81.8663872958708 6.5336127041292 15 86 91.3348287602606 -5.33482876026065 16 83.7 58.9379560653214 24.7620439346786 17 76.7 75.2476647550449 1.45233524495508 18 79.1 67.5033213938528 11.5966786061472 19 86 77.6848543448618 8.31514565513822 20 86 79.1574143801303 6.84258561986969 21 79.1 69.5069085133809 9.59309148661911 22 76.7 80.0744506394286 -3.37445063942863 23 69.8 62.6503730039118 7.14962699608822 24 69.8 61.2905058667494 8.50949413325055 25 76.7 73.8273071018939 2.87269289810612 26 69.8 72.2189677988202 -2.41896779882024 27 67.4 51.7804088223534 15.6195911776466 28 65.1 86.336627436945 -21.2366274369449 29 58.1 55.5669289810618 2.53307101893821 30 60.5 63.2584568151505 -2.75845681515055 31 65.1 70.3528155271034 -5.25281552710338 32 62.8 65.2651303043775 -2.46513030437754 33 55.8 65.6479407145607 -9.84794071456066 34 51.2 58.0783341861534 -6.87833418615335 35 48.8 50.8805212175101 -2.08052121751012 36 48.8 53.572570269109 -4.772570269109 37 53.5 57.0407971770259 -3.54079717702592 38 48.8 61.9927031319467 -13.1927031319467 39 46.5 41.9400409353618 4.55995906463816 40 44.2 68.7783239523129 -24.5783239523129 41 39.5 42.060541685191 -2.56054168519102 42 41.9 52.2603985885129 -10.3603985885129 43 48.8 59.5477056904067 -10.7477056904067 44 46.5 50.9869494487427 -4.48694944874272 45 41.9 57.1582115571562 -15.2582115571562 46 39.5 37.4328564624652 2.06714353753480 47 37.2 42.0048952802236 -4.80489528022362 48 37.2 55.5020541685191 -18.3020541685191 49 41.9 47.3933776799754 -5.49337767997538 50 39.5 41.3472254082585 -1.84722540825847 51 39.5 80.336770533623 -40.8367705336230 52 34.9 13.5950844291838 21.3049155708162 53 34.9 35.5002964271967 -0.600296427196659 54 34.9 44.7354113808135 -9.8354113808135 55 41.9 47.9708022939461 -6.07080229394606 56 41.9 54.4600204676809 -12.5600204676809 57 39.5 39.7928564624652 -0.292856462465183 58 39.5 33.573888663645 5.92611133635502 59 41.9 52.0382115571562 -10.1382115571562 60 46.5 49.7136024702888 -3.21360247028878 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.0584433403247081 0.116886680649416 0.941556659675292 17 0.0421979965735385 0.084395993147077 0.957802003426461 18 0.0255127887464208 0.0510255774928416 0.97448721125358 19 0.0235144621849613 0.0470289243699226 0.976485537815039 20 0.0225423710621117 0.0450847421242235 0.977457628937888 21 0.0255877984721921 0.0511755969443841 0.974412201527808 22 0.0216448225276121 0.0432896450552242 0.978355177472388 23 0.0265045083702326 0.0530090167404651 0.973495491629767 24 0.0515754294011004 0.103150858802201 0.9484245705989 25 0.108168886066352 0.216337772132704 0.891831113933648 26 0.231538677925017 0.463077355850034 0.768461322074983 27 0.424992547712422 0.849985095424845 0.575007452287578 28 0.750739776924384 0.498520446151233 0.249260223075616 29 0.792232375883454 0.415535248233092 0.207767624116546 30 0.904799737380532 0.190400525238936 0.0952002626194682 31 0.96273313279414 0.0745337344117202 0.0372668672058601 32 0.988224135490755 0.0235517290184899 0.0117758645092449 33 0.996232585941848 0.00753482811630418 0.00376741405815209 34 0.996044557931862 0.00791088413627593 0.00395544206813797 35 0.996487885101533 0.00702422979693382 0.00351211489846691 36 0.996540108862986 0.00691978227402782 0.00345989113701391 37 0.997000690087874 0.0059986198242519 0.00299930991212595 38 0.996669184282144 0.00666163143571117 0.00333081571785559 39 0.998561720454548 0.00287655909090423 0.00143827954545211 40 0.997217459818329 0.00556508036334284 0.00278254018167142 41 0.992065942734206 0.0158681145315875 0.00793405726579374 42 0.985165292624985 0.0296694147500301 0.0148347073750150 43 0.971314576684839 0.0573708466303228 0.0286854233151614 44 0.93246646893748 0.135067062125039 0.0675335310625194 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 8 0.275862068965517 NOK 5% type I error level 14 0.482758620689655 NOK 10% type I error level 20 0.689655172413793 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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