*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: Thu, 19 Nov 2009 00:51:21 -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/19/t12586174536nua1u3nk1iug1w.htm/, Retrieved Thu, 19 Nov 2009 08:57:45 +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/19/t12586174536nua1u3nk1iug1w.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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2.085 0 2.053 0 2.077 0 2.058 0 2.057 0 2.076 0 2.07 0 2.062 0 2.073 0 2.061 0 2.094 0 2.067 0 2.086 0 2.276 0 2.326 0 2.349 0 2.52 0 2.628 0 2.577 0 2.698 0 2.814 0 2.968 0 3.041 0 3.278 0 3.328 0 3.5 0 3.563 0 3.569 0 3.69 0 3.819 0 3.79 0 3.956 0 4.063 0 4.047 0 4.029 0 3.941 0 4.022 0 3.879 0 4.022 0 4.028 0 4.091 0 3.987 0 4.01 0 4.007 0 4.191 0 4.299 0 4.273 0 3.82 0 3.15 1 2.486 1 1.812 1 1.257 1 1.062 1 0.842 1 0.782 1 0.698 1 0.358 1 0.347 1 0.363 1 0.359 1 0.355 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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation intb[t] = + 3.10688684210527 -2.06943421052632x[t] + 0.0872578947368416M1[t] + 0.145799999999998M2[t] + 0.0669999999999987M3[t] -0.0408000000000015M4[t] -0.00900000000000142M5[t] -0.0226000000000013M6[t] -0.0472000000000012M7[t] -0.00880000000000143M8[t] + 0.00679999999999856M9[t] + 0.0513999999999987M10[t] + 0.0669999999999985M11[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) 3.10688684210527 0.429751 7.2295 0 0 x -2.06943421052632 0.298938 -6.9226 0 0 M1 0.0872578947368416 0.577603 0.1511 0.880554 0.440277 M2 0.145799999999998 0.601849 0.2423 0.809616 0.404808 M3 0.0669999999999987 0.601849 0.1113 0.911824 0.455912 M4 -0.0408000000000015 0.601849 -0.0678 0.946234 0.473117 M5 -0.00900000000000142 0.601849 -0.015 0.988131 0.494065 M6 -0.0226000000000013 0.601849 -0.0376 0.970201 0.485101 M7 -0.0472000000000012 0.601849 -0.0784 0.937816 0.468908 M8 -0.00880000000000143 0.601849 -0.0146 0.988395 0.494197 M9 0.00679999999999856 0.601849 0.0113 0.991032 0.495516 M10 0.0513999999999987 0.601849 0.0854 0.932296 0.466148 M11 0.0669999999999985 0.601849 0.1113 0.911824 0.455912 Multiple Linear Regression - Regression Statistics Multiple R 0.708445806051584 R-squared 0.501895460112078 Adjusted R-squared 0.377369325140098 F-TEST (value) 4.03044276789775 F-TEST (DF numerator) 12 F-TEST (DF denominator) 48 p-value 0.000253603796910418 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.951606738730537 Sum Squared Residuals 43.4666584894737 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 2.085 3.1941447368421 -1.10914473684210 2 2.053 3.25268684210526 -1.19968684210526 3 2.077 3.17388684210526 -1.09688684210526 4 2.058 3.06608684210526 -1.00808684210526 5 2.057 3.09788684210526 -1.04088684210526 6 2.076 3.08428684210526 -1.00828684210526 7 2.07 3.05968684210526 -0.989686842105263 8 2.062 3.09808684210526 -1.03608684210526 9 2.073 3.11368684210526 -1.04068684210526 10 2.061 3.15828684210526 -1.09728684210526 11 2.094 3.17388684210526 -1.07988684210526 12 2.067 3.10688684210526 -1.03988684210526 13 2.086 3.19414473684211 -1.10814473684211 14 2.276 3.25268684210526 -0.976686842105263 15 2.326 3.17388684210526 -0.847886842105262 16 2.349 3.06608684210526 -0.717086842105262 17 2.52 3.09788684210526 -0.577886842105263 18 2.628 3.08428684210526 -0.456286842105263 19 2.577 3.05968684210526 -0.482686842105263 20 2.698 3.09808684210526 -0.400086842105263 21 2.814 3.11368684210526 -0.299686842105263 22 2.968 3.15828684210526 -0.190286842105263 23 3.041 3.17388684210526 -0.132886842105263 24 3.278 3.10688684210526 0.171113157894736 25 3.328 3.19414473684211 0.133855263157894 26 3.5 3.25268684210526 0.247313157894738 27 3.563 3.17388684210526 0.389113157894738 28 3.569 3.06608684210526 0.502913157894737 29 3.69 3.09788684210526 0.592113157894737 30 3.819 3.08428684210526 0.734713157894737 31 3.79 3.05968684210526 0.730313157894737 32 3.956 3.09808684210526 0.857913157894737 33 4.063 3.11368684210526 0.949313157894737 34 4.047 3.15828684210526 0.888713157894737 35 4.029 3.17388684210526 0.855113157894737 36 3.941 3.10688684210526 0.834113157894736 37 4.022 3.19414473684211 0.827855263157894 38 3.879 3.25268684210526 0.626313157894738 39 4.022 3.17388684210526 0.848113157894738 40 4.028 3.06608684210526 0.961913157894737 41 4.091 3.09788684210526 0.993113157894737 42 3.987 3.08428684210526 0.902713157894737 43 4.01 3.05968684210526 0.950313157894736 44 4.007 3.09808684210526 0.908913157894737 45 4.191 3.11368684210526 1.07731315789474 46 4.299 3.15828684210526 1.14071315789474 47 4.273 3.17388684210526 1.09911315789474 48 3.82 3.10688684210526 0.713113157894736 49 3.15 1.12471052631579 2.02528947368421 50 2.486 1.18325263157895 1.30274736842105 51 1.812 1.10445263157895 0.707547368421053 52 1.257 0.996652631578947 0.260347368421053 53 1.062 1.02845263157895 0.0335473684210529 54 0.842 1.01485263157895 -0.172852631578947 55 0.782 0.990252631578947 -0.208252631578947 56 0.698 1.02865263157895 -0.330652631578947 57 0.358 1.04425263157895 -0.686252631578947 58 0.347 1.08885263157895 -0.741852631578948 59 0.363 1.10445263157895 -0.741452631578947 60 0.359 1.03745263157895 -0.678452631578949 61 0.355 1.12471052631579 -0.76971052631579 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.0216246604239485 0.0432493208478969 0.978375339576051 17 0.0204558964025943 0.0409117928051886 0.979544103597406 18 0.0225333673170088 0.0450667346340176 0.977466632682991 19 0.0203023852170628 0.0406047704341255 0.979697614782937 20 0.0251711940639224 0.0503423881278448 0.974828805936078 21 0.0357932192849327 0.0715864385698654 0.964206780715067 22 0.0608797794589089 0.121759558917818 0.939120220541091 23 0.0904247910905676 0.180849582181135 0.909575208909432 24 0.150593451833661 0.301186903667322 0.849406548166339 25 0.304292715138604 0.608585430277209 0.695707284861396 26 0.493747269709108 0.987494539418215 0.506252730290892 27 0.624589176944905 0.75082164611019 0.375410823055095 28 0.697180008447469 0.605639983105062 0.302819991552531 29 0.740056657500884 0.519886684998231 0.259943342499116 30 0.764293789907335 0.471412420185329 0.235706210092665 31 0.774120282256894 0.451759435486212 0.225879717743106 32 0.78243509093728 0.435129818125439 0.217564909062719 33 0.786274324472811 0.427451351054378 0.213725675527189 34 0.771994135905233 0.456011728189534 0.228005864094767 35 0.744266057159594 0.511467885680812 0.255733942840406 36 0.700740146812486 0.598519706375028 0.299259853187514 37 0.703409564891975 0.593180870216049 0.296590435108025 38 0.798693402358552 0.402613195282896 0.201306597641448 39 0.807460321269844 0.385079357460312 0.192539678730156 40 0.770075683238004 0.459848633523992 0.229924316761996 41 0.706955068428422 0.586089863143155 0.293044931571577 42 0.617321112942484 0.765357774115033 0.382678887057516 43 0.511872251031645 0.976255497936709 0.488127748968355 44 0.3901846910459 0.7803693820918 0.6098153089541 45 0.257122849880929 0.514245699761859 0.74287715011907 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 4 0.133333333333333 NOK 10% type I error level 6 0.2 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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