*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, 10 Dec 2010 10:56:28 +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/10/t1291979518ncqvmyohxu9zau4.htm/, Retrieved Fri, 10 Dec 2010 12:12:08 +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/10/t1291979518ncqvmyohxu9zau4.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:

» Textbox « » Textfile « » CSV «

9700 0 9081 0 9084 0 9743 0 8587 0 9731 0 9563 0 9998 0 9437 0 10038 0 9918 0 9252 0 9737 0 9035 0 9133 0 9487 0 8700 0 9627 0 8947 0 9283 0 8829 0 9947 0 9628 0 9318 0 9605 0 8640 0 9214 0 9567 0 8547 0 9185 0 9470 0 9123 0 9278 0 10170 0 9434 0 9655 0 9429 0 8739 0 9552 0 9687 0 9019 1 9672 1 9206 1 9069 1 9788 1 10312 1 10105 1 9863 1 9656 1 9295 1 9946 1 9701 1 9049 1 10190 1 9706 1 9765 1 9893 1 9994 1 10433 1 10073 1 10112 1 9266 1 9820 1 10097 1 9115 1 10411 1 9678 1 10408 1 10153 1 10368 1 10581 1 10597 1 10680 1 9738 1 9556 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 11 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Geboortes[t] = + 9548.42203608247 + 489.155927835053X[t] + 87.5111377024945M1[t] -644.631719440353M2[t] -285.917433726068M3[t] + 2.19265463917518M4[t] -956.833333333334M5[t] + 9.66666666666654M6[t] -364.666666666667M7[t] -185.333333333334M8[t] -230.000000000000M9[t] + 345.166666666666M10[t] + 223.500000000000M11[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) 9548.42203608247 121.786909 78.4027 0 0 X 489.155927835053 66.745179 7.3287 0 0 M1 87.5111377024945 159.68598 0.548 0.585646 0.292823 M2 -644.631719440353 159.68598 -4.0369 0.000151 7.6e-05 M3 -285.917433726068 159.68598 -1.7905 0.078256 0.039128 M4 2.19265463917518 166.013225 0.0132 0.989504 0.494752 M5 -956.833333333334 165.640101 -5.7766 0 0 M6 9.66666666666654 165.640101 0.0584 0.95365 0.476825 M7 -364.666666666667 165.640101 -2.2016 0.031427 0.015713 M8 -185.333333333334 165.640101 -1.1189 0.267503 0.133751 M9 -230.000000000000 165.640101 -1.3886 0.169937 0.084969 M10 345.166666666666 165.640101 2.0838 0.041303 0.020652 M11 223.500000000000 165.640101 1.3493 0.182144 0.091072 Multiple Linear Regression - Regression Statistics Multiple R 0.852938681164412 R-squared 0.727504393826486 Adjusted R-squared 0.674763308760644 F-TEST (value) 13.7938837041042 F-TEST (DF numerator) 12 F-TEST (DF denominator) 62 p-value 2.55573340268711e-13 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 286.897071073320 Sum Squared Residuals 5103215.62220789 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 9700 9635.93317378503 64.0668262149703 2 9081 8903.79031664212 177.20968335788 3 9084 9262.5046023564 -178.504602356405 4 9743 9550.61469072165 192.38530927835 5 8587 8591.58870274914 -4.58870274914076 6 9731 9558.08870274914 172.91129725086 7 9563 9183.7553694158 379.244630584194 8 9998 9363.08870274914 634.91129725086 9 9437 9318.42203608247 118.577963917526 10 10038 9893.58870274914 144.411297250860 11 9918 9771.92203608247 146.077963917526 12 9252 9548.42203608247 -296.422036082474 13 9737 9635.93317378497 101.066826215031 14 9035 8903.79031664212 131.209683357880 15 9133 9262.5046023564 -129.504602356406 16 9487 9550.61469072165 -63.614690721649 17 8700 8591.58870274914 108.411297250860 18 9627 9558.08870274914 68.9112972508598 19 8947 9183.7553694158 -236.755369415807 20 9283 9363.08870274914 -80.08870274914 21 8829 9318.42203608247 -489.422036082473 22 9947 9893.58870274914 53.4112972508599 23 9628 9771.92203608247 -143.922036082474 24 9318 9548.42203608247 -230.422036082474 25 9605 9635.93317378497 -30.9331737849686 26 8640 8903.79031664212 -263.79031664212 27 9214 9262.5046023564 -48.5046023564059 28 9567 9550.61469072165 16.3853092783511 29 8547 8591.58870274914 -44.5887027491402 30 9185 9558.08870274914 -373.08870274914 31 9470 9183.7553694158 286.244630584193 32 9123 9363.08870274914 -240.08870274914 33 9278 9318.42203608247 -40.4220360824735 34 10170 9893.58870274914 276.41129725086 35 9434 9771.92203608247 -337.922036082474 36 9655 9548.42203608247 106.577963917526 37 9429 9635.93317378497 -206.933173784969 38 8739 8903.79031664212 -164.79031664212 39 9552 9262.5046023564 289.495397643594 40 9687 9550.61469072165 136.385309278351 41 9019 9080.7446305842 -61.744630584193 42 9672 10047.2446305842 -375.244630584193 43 9206 9672.91129725086 -466.91129725086 44 9069 9852.2446305842 -783.244630584193 45 9788 9807.57796391753 -19.5779639175265 46 10312 10382.7446305842 -70.7446305841933 47 10105 10261.0779639175 -156.077963917526 48 9863 10037.5779639175 -174.577963917527 49 9656 10125.0891016200 -469.089101620022 50 9295 9392.94624447717 -97.946244477173 51 9946 9751.66053019146 194.339469808541 52 9701 10039.7706185567 -338.770618556702 53 9049 9080.7446305842 -31.744630584193 54 10190 10047.2446305842 142.755369415807 55 9706 9672.91129725086 33.08870274914 56 9765 9852.2446305842 -87.2446305841929 57 9893 9807.57796391753 85.4220360824735 58 9994 10382.7446305842 -388.744630584193 59 10433 10261.0779639175 171.922036082473 60 10073 10037.5779639175 35.4220360824733 61 10112 10125.0891016200 -13.0891016200215 62 9266 9392.94624447717 -126.946244477173 63 9820 9751.66053019146 68.3394698085412 64 10097 10039.7706185567 57.2293814432981 65 9115 9080.7446305842 34.255369415807 66 10411 10047.2446305842 363.755369415807 67 9678 9672.91129725086 5.08870274914004 68 10408 9852.2446305842 555.755369415807 69 10153 9807.57796391753 345.422036082474 70 10368 10382.7446305842 -14.7446305841933 71 10581 10261.0779639175 319.922036082474 72 10597 10037.5779639175 559.422036082473 73 10680 10125.0891016200 554.910898379979 74 9738 9392.94624447717 345.053755522827 75 9556 9751.66053019146 -195.660530191459 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.0630388211182975 0.126077642236595 0.936961178881702 17 0.0253237597126573 0.0506475194253147 0.974676240287343 18 0.00973707430190853 0.0194741486038171 0.990262925698091 19 0.149017374937020 0.298034749874040 0.85098262506298 20 0.376322610958729 0.752645221917459 0.62367738904127 21 0.510518424652707 0.978963150694586 0.489481575347293 22 0.407513451231753 0.815026902463506 0.592486548768247 23 0.348488695967874 0.696977391935748 0.651511304032126 24 0.274190031051132 0.548380062102263 0.725809968948868 25 0.202970665839589 0.405941331679177 0.797029334160411 26 0.222576847717770 0.445153695435541 0.77742315228223 27 0.163762367280227 0.327524734560454 0.836237632719773 28 0.113492226028674 0.226984452057348 0.886507773971326 29 0.0770729718031561 0.154145943606312 0.922927028196844 30 0.113714303277493 0.227428606554985 0.886285696722507 31 0.102195838290823 0.204391676581647 0.897804161709177 32 0.128764138444980 0.257528276889959 0.87123586155502 33 0.095711507530766 0.191423015061532 0.904288492469234 34 0.086717737251797 0.173435474503594 0.913282262748203 35 0.0912570712313378 0.182514142462676 0.908742928768662 36 0.0827898217903253 0.165579643580651 0.917210178209675 37 0.0715029755211217 0.143005951042243 0.928497024478878 38 0.0621059092356678 0.124211818471336 0.937894090764332 39 0.0602771004790983 0.120554200958197 0.939722899520902 40 0.0400478875032021 0.0800957750064042 0.959952112496798 41 0.0253437719950878 0.0506875439901756 0.974656228004912 42 0.0300904208643591 0.0601808417287181 0.96990957913564 43 0.0351980890433704 0.0703961780867408 0.96480191095663 44 0.176960482957353 0.353920965914706 0.823039517042647 45 0.203300678468998 0.406601356937996 0.796699321531002 46 0.155090652972055 0.310181305944110 0.844909347027945 47 0.158106321827903 0.316212643655805 0.841893678172097 48 0.177541106156011 0.355082212312021 0.82245889384399 49 0.349503971848223 0.699007943696447 0.650496028151777 50 0.301108124559651 0.602216249119303 0.698891875440349 51 0.305339001260655 0.610678002521309 0.694660998739345 52 0.295185361245224 0.590370722490447 0.704814638754776 53 0.218853314793356 0.437706629586712 0.781146685206644 54 0.193341917338099 0.386683834676199 0.8066580826619 55 0.131213342801170 0.262426685602339 0.86878665719883 56 0.206155423921493 0.412310847842985 0.793844576078507 57 0.163711540232966 0.327423080465931 0.836288459767034 58 0.15032322418632 0.30064644837264 0.84967677581368 59 0.0949625925667216 0.189925185133443 0.905037407433278 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 1 0.0227272727272727 OK 10% type I error level 6 0.136363636363636 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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