SHW 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 05:32:24 -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/t12587204412k910azzdmc4dnx.htm/, Retrieved Fri, 20 Nov 2009 13:34:16 +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/t12587204412k910azzdmc4dnx.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:

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No (this computation is public)

User-defined keywords:

Dataseries X:

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7.8 0 7.8 8.3 8.5 8.6 8 0 7.8 7.8 8.3 8.5 8.6 0 8 7.8 7.8 8.3 8.9 0 8.6 8 7.8 7.8 8.9 0 8.9 8.6 8 7.8 8.6 0 8.9 8.9 8.6 8 8.3 0 8.6 8.9 8.9 8.6 8.3 0 8.3 8.6 8.9 8.9 8.3 0 8.3 8.3 8.6 8.9 8.4 0 8.3 8.3 8.3 8.6 8.5 0 8.4 8.3 8.3 8.3 8.4 0 8.5 8.4 8.3 8.3 8.6 0 8.4 8.5 8.4 8.3 8.5 0 8.6 8.4 8.5 8.4 8.5 0 8.5 8.6 8.4 8.5 8.5 0 8.5 8.5 8.6 8.4 8.5 0 8.5 8.5 8.5 8.6 8.5 0 8.5 8.5 8.5 8.5 8.5 0 8.5 8.5 8.5 8.5 8.5 0 8.5 8.5 8.5 8.5 8.5 0 8.5 8.5 8.5 8.5 8.5 0 8.5 8.5 8.5 8.5 8.5 0 8.5 8.5 8.5 8.5 8.5 0 8.5 8.5 8.5 8.5 8.6 0 8.5 8.5 8.5 8.5 8.4 0 8.6 8.5 8.5 8.5 8.1 0 8.4 8.6 8.5 8.5 8 0 8.1 8.4 8.6 8.5 8 0 8 8.1 8.4 8.6 8 0 8 8 8.1 8.4 8 0 8 8 8 8.1 7.9 0 8 8 8 8 7.8 0 7.9 8 8 8 7.8 0 7.8 7.9 8 8 7.9 0 7.8 7.8 7.9 8 8.1 0 7.9 7.8 7.8 7.9 8 0 8.1 7.9 7.8 7.8 7.6 0 8 8.1 7.9 7.8 7.3 0 7.6 8 8.1 7.9 7 0 7.3 7.6 8 8.1 6.8 0 7 7.3 7.6 8 7 0 6.8 7 7.3 7.6 7.1 0 7 6.8 7 7.3 7.2 0 7.1 7 6.8 7 7.1 1 7.2 7.1 7 6.8 6.9 1 7.1 7.2 7.1 7 6.7 1 6.9 7.1 7.2 7.1 6.7 1 6.7 6.9 7.1 7.2 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 5 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 0.828054484333973 + 0.118092413961489X[t] + 1.39245913482402Y1[t] -0.532231626987506Y2[t] -0.386918622865897Y3[t] + 0.441898655528487Y4[t] + 0.0116479357493733M1[t] -0.0903743560875964M2[t] + 0.0488973179489897M3[t] -0.0144921933048258M4[t] -0.0978713441555035M5[t] + 0.0190056749325876M6[t] -0.0414326074099239M7[t] + 0.0444449825289134M8[t] -0.0775862591018103M9[t] -0.0350555474036831M10[t] + 0.00144550210597445M11[t] -0.00620621971200828t + 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) 0.828054484333973 0.66162 1.2516 0.218382 0.109191 X 0.118092413961489 0.083523 1.4139 0.165536 0.082768 Y1 1.39245913482402 0.133981 10.393 0 0 Y2 -0.532231626987506 0.24471 -2.175 0.035925 0.017963 Y3 -0.386918622865897 0.249732 -1.5493 0.129591 0.064795 Y4 0.441898655528487 0.149301 2.9598 0.005278 0.002639 M1 0.0116479357493733 0.091388 0.1275 0.899252 0.449626 M2 -0.0903743560875964 0.091278 -0.9901 0.32839 0.164195 M3 0.0488973179489897 0.091626 0.5337 0.596682 0.298341 M4 -0.0144921933048258 0.092508 -0.1567 0.876344 0.438172 M5 -0.0978713441555035 0.091328 -1.0717 0.290636 0.145318 M6 0.0190056749325876 0.092397 0.2057 0.838127 0.419063 M7 -0.0414326074099239 0.091657 -0.452 0.65381 0.326905 M8 0.0444449825289134 0.090965 0.4886 0.627939 0.313969 M9 -0.0775862591018103 0.095506 -0.8124 0.421641 0.210821 M10 -0.0350555474036831 0.095754 -0.3661 0.716321 0.358161 M11 0.00144550210597445 0.095608 0.0151 0.988016 0.494008 t -0.00620621971200828 0.00226 -2.7463 0.009159 0.004579 Multiple Linear Regression - Regression Statistics Multiple R 0.985809336202448 R-squared 0.971820047343912 Adjusted R-squared 0.95921322641882 F-TEST (value) 77.0868447420907 F-TEST (DF numerator) 17 F-TEST (DF denominator) 38 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.134663370271501 Sum Squared Residuals 0.689100485129412 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 7.8 7.78867509118724 0.0113249088127546 2 8 7.97975625215236 0.0202437478476421 3 8.6 8.49639311376899 0.103606886231010 4 8.9 8.93487721053583 -0.0348772105358308 5 8.9 8.86630687965467 0.0336931203453313 6 8.6 8.67353674832066 -0.0735367483206594 7 8.3 8.33821811227626 -0.0382181122762552 8 8.3 8.29239082681068 0.00760917318932146 9 8.3 8.43989844042397 -0.139898440423967 10 8.4 8.4597289226113 -0.0597289226113085 11 8.5 8.49670006923281 0.00329993076718614 12 8.4 8.57507109819848 -0.175071098198482 13 8.6 8.3493518757681 0.250648124231894 14 8.5 8.57833635714894 -0.07833635714894 15 8.5 8.54859130043305 -0.0485913004330537 16 8.5 8.41064514203995 0.0893548579600474 17 8.5 8.44813136486955 0.0518686351304466 18 8.5 8.51461229869279 -0.0146122986927875 19 8.5 8.44796779663827 0.0520322033617322 20 8.5 8.5276391668651 -0.0276391668650969 21 8.5 8.39940170552237 0.100598294477635 22 8.5 8.43572619750848 0.0642738024915162 23 8.5 8.46602102730613 0.0339789726938670 24 8.5 8.45836930548815 0.0416306945118497 25 8.6 8.46381102152552 0.136188978474484 26 8.4 8.49482842345894 -0.0948284234589384 27 8.1 8.29617888811996 -0.196178888119964 28 8 7.87659987981784 0.123400120182156 29 8 7.92901167399504 0.0709883260049633 30 8 8.12060149182394 -0.120601491823942 31 8 7.96007925539747 0.0399207446025346 32 7.9 7.99556076007145 -0.0955607600714455 33 7.8 7.72807738524631 0.0719226147536874 34 7.8 7.67837912644878 0.121620873551221 35 7.9 7.80058898123177 0.0994110187682314 36 8.1 7.92668516962993 0.173314830370070 37 8 8.1132056843805 -0.113205684380498 38 7.6 7.72059307166503 -0.120593071665028 39 7.3 7.31670417573842 -0.0167041757384182 40 7 7.16933494851268 -0.169334948512678 41 6.8 6.93225890919255 -0.132258909192549 42 7 6.86342349434845 0.136576505651547 43 7.1 7.16522313485746 -0.065223134857462 44 7.2 7.22250822108382 -0.0225082210838241 45 7.1 7.13262246880736 -0.0326224688073557 46 6.9 7.02616575343143 -0.126165753431428 47 6.7 6.83668992222928 -0.136689922229285 48 6.7 6.73987442668344 -0.0398744266834375 49 6.6 6.88495632713863 -0.284956327138635 50 6.9 6.62648589557474 0.273514104425264 51 7.3 7.14213252193957 0.157867478060426 52 7.5 7.50854281909369 -0.0085428190936946 53 7.3 7.3242911722882 -0.0242911722881923 54 7.1 7.02782596681416 0.072174033185842 55 6.9 6.88851170083055 0.0114882991694502 56 7.1 6.96190102516896 0.138098974831045 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.278221590987648 0.556443181975296 0.721778409012352 22 0.17158855835535 0.3431771167107 0.82841144164465 23 0.0819441977041649 0.163888395408330 0.918055802295835 24 0.0533285166655058 0.106657033331012 0.946671483334494 25 0.0552321289528983 0.110464257905797 0.944767871047102 26 0.0346061898081901 0.0692123796163802 0.96539381019181 27 0.164656486418927 0.329312972837854 0.835343513581073 28 0.183594429788114 0.367188859576229 0.816405570211886 29 0.180048508947094 0.360097017894188 0.819951491052906 30 0.318247792912090 0.636495585824179 0.68175220708791 31 0.239547552620547 0.479095105241094 0.760452447379453 32 0.169925244044864 0.339850488089729 0.830074755955136 33 0.105051802789158 0.210103605578316 0.894948197210842 34 0.0826147801972288 0.165229560394458 0.917385219802771 35 0.0467209952560467 0.0934419905120934 0.953279004743953 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 2 0.133333333333333 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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