b-r0245787

*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: Tue, 21 Dec 2010 11:38:58 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/21/t1292931463mqjj5xwmk1ld3pn.htm/, Retrieved Tue, 21 Dec 2010 12:37:43 +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/2010/Dec/21/t1292931463mqjj5xwmk1ld3pn.htm/}, year = {2010}, } @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 = {2010}, 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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0.86 2.0 0.88 2.3 0.93 2.8 0.98 2.4 0.97 2.3 1.03 2.7 1.06 2.7 1.06 2.9 1.08 3.0 1.09 2.2 1.04 2.3 1.00 2.8 1.01 2.8 1.02 2.8 1.04 2.2 1.06 2.6 1.06 2.8 1.06 2.5 1.06 2.4 1.06 2.3 1.02 1.9 0.98 1.7 0.99 2.0 0.99 2.1 0.94 1.7 0.96 1.8 0.98 1.8 1.01 1.8 1.01 1.3 1.02 1.3 1.04 1.3 1.03 1.2 1.05 1.4 1.08 2.2 1.17 2.9 1.11 3.1 1.11 3.5 1.11 3.6 1.11 4.4 1.21 4.1 1.31 5.1 1.37 5.8 1.37 5.9 1.26 5.4 1.23 5.5 1.17 4.8 1.06 3.2 0.95 2.7 0.92 2.1 0.92 1.9 0.90 0.6 0.93 0.7 0.93 -0.2 0.97 -1.0 0.96 -1.7 0.99 -0.7 0.98 -1.0 0.96 -0.9 1.00 0.0 0.99 0.3 1.03 0.8

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation Dieselprijs[t] = + 0.932633739673073 + 0.0486637713013503Inflatie[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) 0.932633739673073 0.015581 59.858 0 0 Inflatie 0.0486637713013503 0.005667 8.5868 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.745317394384877 R-squared 0.555498018372663 Adjusted R-squared 0.547964086480674 F-TEST (value) 73.7328165872263 F-TEST (DF numerator) 1 F-TEST (DF denominator) 59 p-value 5.61151125566539e-12 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.0719999123506779 Sum Squared Residuals 0.305855255331813 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 0.86 1.02996128227577 -0.169961282275773 2 0.88 1.04456041366618 -0.164560413666178 3 0.93 1.06889229931685 -0.138892299316854 4 0.98 1.04942679079631 -0.0694267907963135 5 0.97 1.04456041366618 -0.0745604136661785 6 1.03 1.06402592218672 -0.0340259221867186 7 1.06 1.06402592218672 -0.00402592218671855 8 1.06 1.07375867644699 -0.0137586764469886 9 1.08 1.07862505357712 0.00137494642287640 10 1.09 1.03969403653604 0.0503059634639566 11 1.04 1.04456041366618 -0.00456041366617844 12 1 1.06889229931685 -0.0688922993168536 13 1.01 1.06889229931685 -0.0588922993168536 14 1.02 1.06889229931685 -0.0488922993168536 15 1.04 1.03969403653604 0.000305963463956566 16 1.06 1.05915954505658 0.000840454943416483 17 1.06 1.06889229931685 -0.00889229931685356 18 1.06 1.05429316792645 0.00570683207355152 19 1.06 1.04942679079631 0.0105732092036865 20 1.06 1.04456041366618 0.0154395863338216 21 1.02 1.02509490514564 -0.00509490514563836 22 0.98 1.01536215088537 -0.0353621508853683 23 0.99 1.02996128227577 -0.0399612822757734 24 0.99 1.03482765940591 -0.0448276594059084 25 0.94 1.01536215088537 -0.0753621508853684 26 0.96 1.02022852801550 -0.0602285280155034 27 0.98 1.02022852801550 -0.0402285280155034 28 1.01 1.02022852801550 -0.0102285280155034 29 1.01 0.995896642364828 0.0141033576351718 30 1.02 0.995896642364828 0.0241033576351718 31 1.04 0.995896642364828 0.0441033576351718 32 1.03 0.991030265234693 0.0389697347653068 33 1.05 1.00076301949496 0.0492369805050368 34 1.08 1.03969403653604 0.0403059634639566 35 1.17 1.07375867644699 0.0962413235530113 36 1.11 1.08349143070726 0.0265085692927414 37 1.11 1.10295693922780 0.00704306077220132 38 1.11 1.10782331635793 0.00217668364206628 39 1.11 1.14675433339901 -0.0367543333990140 40 1.21 1.13215520200861 0.077844797991391 41 1.31 1.18081897330996 0.129181026690041 42 1.37 1.21488361322090 0.155116386779096 43 1.37 1.21974999035104 0.150250009648961 44 1.26 1.19541810470036 0.0645818952996357 45 1.23 1.2002844818305 0.0297155181695007 46 1.17 1.16621984191955 0.00378015808044583 47 1.06 1.08835780783739 -0.0283578078373937 48 0.95 1.06402592218672 -0.114025922186719 49 0.92 1.03482765940591 -0.114827659405908 50 0.92 1.02509490514564 -0.105094905145638 51 0.9 0.961832002453883 -0.061832002453883 52 0.93 0.966698379584018 -0.036698379584018 53 0.93 0.922900985412803 0.00709901458719719 54 0.97 0.883969968371723 0.0860300316282773 55 0.96 0.849905328460777 0.110094671539223 56 0.99 0.898569099762128 0.0914309002378723 57 0.98 0.883969968371723 0.0960300316282773 58 0.96 0.888836345501858 0.0711636544981423 59 1 0.932633739673073 0.0673662603269271 60 0.99 0.947232871063478 0.042767128936522 61 1.03 0.971564756714153 0.0584352432858469 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.477746124739975 0.95549224947995 0.522253875260025 6 0.474017292176766 0.948034584353531 0.525982707823234 7 0.491040821096978 0.982081642193956 0.508959178903022 8 0.370363013049602 0.740726026099204 0.629636986950398 9 0.261767504112556 0.523535008225112 0.738232495887444 10 0.722107938221049 0.555784123557902 0.277892061778951 11 0.709504857182107 0.580990285635787 0.290495142817893 12 0.657952401687157 0.684095196625686 0.342047598312843 13 0.59202970306113 0.815940593877739 0.407970296938870 14 0.51743383102294 0.96513233795412 0.48256616897706 15 0.514994636416432 0.970010727167136 0.485005363583568 16 0.465820391847396 0.931640783694792 0.534179608152604 17 0.395280711680036 0.790561423360073 0.604719288319963 18 0.356565576734254 0.713131153468507 0.643434423265746 19 0.327164642002635 0.654329284005271 0.672835357997365 20 0.303324586917944 0.606649173835887 0.696675413082056 21 0.259128499400883 0.518256998801766 0.740871500599117 22 0.209311905891885 0.418623811783770 0.790688094108115 23 0.168238088052152 0.336476176104304 0.831761911947848 24 0.136250494150307 0.272500988300614 0.863749505849693 25 0.130637991404905 0.26127598280981 0.869362008595095 26 0.115647208993161 0.231294417986322 0.884352791006839 27 0.0950970283010272 0.190194056602054 0.904902971698973 28 0.0765199998926208 0.153039999785242 0.92348000010738 29 0.0658478530638383 0.131695706127677 0.934152146936162 30 0.0546125684746073 0.109225136949215 0.945387431525393 31 0.0481325944966161 0.0962651889932322 0.951867405503384 32 0.0371387035759472 0.0742774071518943 0.962861296424053 33 0.0302140020019767 0.0604280040039533 0.969785997998023 34 0.0263329805709205 0.0526659611418409 0.97366701942908 35 0.0578524063206091 0.115704812641218 0.94214759367939 36 0.0471650031141178 0.0943300062282356 0.952834996885882 37 0.0348594129577996 0.0697188259155992 0.9651405870422 38 0.0246780435249802 0.0493560870499604 0.97532195647502 39 0.0200535062448543 0.0401070124897085 0.979946493755146 40 0.0221783796352896 0.0443567592705792 0.97782162036471 41 0.0390342018360532 0.0780684036721064 0.960965798163947 42 0.0847145639015494 0.169429127803099 0.91528543609845 43 0.232374419818654 0.464748839637308 0.767625580181346 44 0.320761217522758 0.641522435045515 0.679238782477242 45 0.516333318336688 0.967333363326624 0.483666681663312 46 0.872236666495514 0.255526667008972 0.127763333504486 47 0.973916584394017 0.0521668312119668 0.0260834156059834 48 0.96606054399965 0.0678789120007005 0.0339394560003502 49 0.951177516835946 0.0976449663281076 0.0488224831640538 50 0.936346005775489 0.127307988449023 0.0636539942245114 51 0.973473592093525 0.0530528158129507 0.0265264079064753 52 0.99150086022197 0.0169982795560610 0.00849913977803051 53 0.999812824002673 0.000374351994654194 0.000187175997327097 54 0.999262697098218 0.00147460580356452 0.000737302901782262 55 0.997012603397599 0.00597479320480232 0.00298739660240116 56 0.989042593382306 0.0219148132353871 0.0109574066176936 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 3 0.0576923076923077 NOK 5% type I error level 8 0.153846153846154 NOK 10% type I error level 19 0.365384615384615 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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