paper_Multiple Regression_x1

*Unverified author*

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

Title produced by software: Multiple Regression

Date of computation: Sat, 20 Dec 2008 07:33:45 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/20/t12297852173ltxqmx0526xduh.htm/, Retrieved Sat, 20 Dec 2008 16:00:26 +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/2008/Dec/20/t12297852173ltxqmx0526xduh.htm/}, year = {2008}, } @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 = {2008}, 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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0,89 0 0,89 0 0,89 0 0,89 0 0,89 0 0,89 0 0,89 0 0,9 0 0,91 0 0,92 0 0,92 0 0,92 0 0,92 0 0,92 0 0,92 0 0,92 0 0,92 0 0,92 0 0,92 0 0,92 0 0,92 0 0,92 0 0,92 0 0,92 0 0,92 0 0,92 0 0,92 0 0,92 0 0,92 0 0,92 0 0,92 0 0,92 0 0,92 0 0,92 0 0,92 0 0,92 0 0,92 0 0,92 0 1,01 1 1,01 1 1,01 1 1,01 1 1,01 1 1,04 1 1,05 1 1,05 1 1,06 1 1,06 1 1,06 1 1,06 1 1,08 1 1,08 1 1,08 1 1,08 1 1,08 1 1,08 1 1,09 1 1,09 1 1,1 1 1,1 1 1,1 1

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 y[t] = + 0.913684210526315 + 0.14675057208238x[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) 0.913684210526315 0.003495 261.4558 0 0 x 0.14675057208238 0.005691 25.7858 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.958383012188892 R-squared 0.918497998052255 Adjusted R-squared 0.917116608188734 F-TEST (value) 664.90859843943 F-TEST (DF numerator) 1 F-TEST (DF denominator) 59 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.0215421788474474 Sum Squared Residuals 0.0273798627002292 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 0.89 0.913684210526322 -0.0236842105263218 2 0.89 0.913684210526316 -0.0236842105263156 3 0.89 0.913684210526316 -0.0236842105263157 4 0.89 0.913684210526316 -0.0236842105263157 5 0.89 0.913684210526316 -0.0236842105263157 6 0.89 0.913684210526316 -0.0236842105263157 7 0.89 0.913684210526316 -0.0236842105263157 8 0.9 0.913684210526316 -0.0136842105263156 9 0.91 0.913684210526316 -0.00368421052631563 10 0.92 0.913684210526316 0.00631578947368438 11 0.92 0.913684210526316 0.00631578947368438 12 0.92 0.913684210526316 0.00631578947368438 13 0.92 0.913684210526316 0.00631578947368438 14 0.92 0.913684210526316 0.00631578947368438 15 0.92 0.913684210526316 0.00631578947368438 16 0.92 0.913684210526316 0.00631578947368438 17 0.92 0.913684210526316 0.00631578947368438 18 0.92 0.913684210526316 0.00631578947368438 19 0.92 0.913684210526316 0.00631578947368438 20 0.92 0.913684210526316 0.00631578947368438 21 0.92 0.913684210526316 0.00631578947368438 22 0.92 0.913684210526316 0.00631578947368438 23 0.92 0.913684210526316 0.00631578947368438 24 0.92 0.913684210526316 0.00631578947368438 25 0.92 0.913684210526316 0.00631578947368438 26 0.92 0.913684210526316 0.00631578947368438 27 0.92 0.913684210526316 0.00631578947368438 28 0.92 0.913684210526316 0.00631578947368438 29 0.92 0.913684210526316 0.00631578947368438 30 0.92 0.913684210526316 0.00631578947368438 31 0.92 0.913684210526316 0.00631578947368438 32 0.92 0.913684210526316 0.00631578947368438 33 0.92 0.913684210526316 0.00631578947368438 34 0.92 0.913684210526316 0.00631578947368438 35 0.92 0.913684210526316 0.00631578947368438 36 0.92 0.913684210526316 0.00631578947368438 37 0.92 0.913684210526316 0.00631578947368438 38 0.92 0.913684210526316 0.00631578947368438 39 1.01 1.06043478260870 -0.0504347826086957 40 1.01 1.06043478260870 -0.0504347826086957 41 1.01 1.06043478260870 -0.0504347826086957 42 1.01 1.06043478260870 -0.0504347826086957 43 1.01 1.06043478260870 -0.0504347826086957 44 1.04 1.06043478260870 -0.0204347826086957 45 1.05 1.06043478260870 -0.0104347826086957 46 1.05 1.06043478260870 -0.0104347826086957 47 1.06 1.06043478260870 -0.000434782608695654 48 1.06 1.06043478260870 -0.000434782608695654 49 1.06 1.06043478260870 -0.000434782608695654 50 1.06 1.06043478260870 -0.000434782608695654 51 1.08 1.06043478260870 0.0195652173913044 52 1.08 1.06043478260870 0.0195652173913044 53 1.08 1.06043478260870 0.0195652173913044 54 1.08 1.06043478260870 0.0195652173913044 55 1.08 1.06043478260870 0.0195652173913044 56 1.08 1.06043478260870 0.0195652173913044 57 1.09 1.06043478260870 0.0295652173913044 58 1.09 1.06043478260870 0.0295652173913044 59 1.1 1.06043478260870 0.0395652173913044 60 1.1 1.06043478260870 0.0395652173913044 61 1.1 1.06043478260870 0.0395652173913044 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 3.12109876090732e-43 6.24219752181464e-43 1 6 2.05025748893310e-55 4.10051497786621e-55 1 7 6.92331633376045e-70 1.38466326675209e-69 1 8 0.000174559257899714 0.000349118515799429 0.9998254407421 9 0.00427794198061811 0.00855588396123621 0.995722058019382 10 0.0332914057915252 0.0665828115830504 0.966708594208475 11 0.0596892364119641 0.119378472823928 0.940310763588036 12 0.073030955571055 0.14606191114211 0.926969044428945 13 0.0752963729400936 0.150592745880187 0.924703627059906 14 0.0703136694272502 0.140627338854500 0.92968633057275 15 0.0613631210581403 0.122726242116281 0.93863687894186 16 0.050833731814473 0.101667463628946 0.949166268185527 17 0.0403150169344626 0.0806300338689252 0.959684983065537 18 0.0307607980664207 0.0615215961328415 0.96923920193358 19 0.0226490150383166 0.0452980300766332 0.977350984961683 20 0.0161228663910369 0.0322457327820737 0.983877133608963 21 0.0111097109399001 0.0222194218798002 0.9888902890601 22 0.00741602281103061 0.0148320456220612 0.99258397718897 23 0.0047980464152275 0.009596092830455 0.995201953584772 24 0.00300964631462626 0.00601929262925253 0.996990353685374 25 0.00183060824034011 0.00366121648068022 0.99816939175966 26 0.00107976448333356 0.00215952896666712 0.998920235516666 27 0.000617594817018899 0.00123518963403780 0.999382405182981 28 0.000342511122182856 0.000685022244365711 0.999657488877817 29 0.000184148831209654 0.000368297662419308 0.99981585116879 30 9.5959128681414e-05 0.000191918257362828 0.999904040871319 31 4.84506775764357e-05 9.69013551528715e-05 0.999951549322424 32 2.36949485686936e-05 4.73898971373871e-05 0.999976305051431 33 1.12194587744095e-05 2.24389175488189e-05 0.999988780541226 34 5.1408627644245e-06 1.0281725528849e-05 0.999994859137236 35 2.27825957576678e-06 4.55651915153356e-06 0.999997721740424 36 9.7587189845546e-07 1.95174379691092e-06 0.999999024128102 37 4.03723865347599e-07 8.07447730695198e-07 0.999999596276135 38 1.61180713140398e-07 3.22361426280796e-07 0.999999838819287 39 2.99560393662437e-07 5.99120787324874e-07 0.999999700439606 40 8.65694807990036e-07 1.73138961598007e-06 0.999999134305192 41 4.68665884150882e-06 9.37331768301763e-06 0.999995313341159 42 6.43696881182715e-05 0.000128739376236543 0.999935630311882 43 0.0036554014461175 0.007310802892235 0.996344598553883 44 0.0275578890468008 0.0551157780936015 0.9724421109532 45 0.0997371477815 0.199474295563 0.9002628522185 46 0.255106607314899 0.510213214629798 0.744893392685101 47 0.409367898507356 0.818735797014711 0.590632101492644 48 0.573947792220731 0.852104415558537 0.426052207779269 49 0.757820924104762 0.484358151790477 0.242179075895238 50 0.937310526839511 0.125378946320978 0.062689473160489 51 0.939729056720812 0.120541886558376 0.0602709432791881 52 0.934497354710252 0.131005290579497 0.0655026452897484 53 0.92485408443189 0.150291831136221 0.0751459155681106 54 0.914573990588823 0.170852018822354 0.0854260094111768 55 0.91331706397764 0.17336587204472 0.08668293602236 56 0.952354513163729 0.0952909736725417 0.0476454868362709 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 26 0.5 NOK 5% type I error level 30 0.576923076923077 NOK 10% type I error level 35 0.673076923076923 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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