*Unverified author*

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

Title produced by software: Multiple Regression

Date of computation: Thu, 27 Nov 2008 15:40:18 -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/Nov/27/t12278256867ekxfk2387m4kuo.htm/, Retrieved Thu, 27 Nov 2008 22:41:35 +0000

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/Nov/27/t12278256867ekxfk2387m4kuo.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}, }

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

Feedback Forum:

2008-11-27 13:41:43 [a2386b643d711541400692649981f2dc]  [reply]  test Post a new message

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

2120.88 0 2174.56 0 2196.72 0 2350.44 0 2440.25 0 2408.64 0 2472.81 0 2407.6 0 2454.62 0 2448.05 0 2497.84 0 2645.64 0 2756.76 0 2849.27 0 2921.44 0 2981.85 0 3080.58 0 3106.22 0 3119.31 0 3061.26 0 3097.31 0 3161.69 0 3257.16 0 3277.01 0 3295.32 0 3363.99 0 3494.17 0 3667.03 0 3813.06 0 3917.96 0 3895.51 0 3801.06 0 3570.12 0 3701.61 0 3862.27 0 3970.1 0 4138.52 0 4199.75 0 4290.89 0 4443.91 0 4502.64 1 4356.98 1 4591.27 1 4696.96 1 4621.4 1 4562.84 1 4202.52 1 4296.49 1 4435.23 1 4105.18 1 4116.68 1 3844.49 1 3720.98 1 3674.4 1 3857.62 1 3801.06 1 3504.37 1 3032.6 1 3047.03 1 2962.34 1 2197.82 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 Bel20[t] = + 3167.8295 + 743.165738095238dummy[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) 3167.8295 104.133294 30.4209 0 0 dummy 743.165738095238 177.478143 4.1874 9.5e-05 4.8e-05 Multiple Linear Regression - Regression Statistics Multiple R 0.478645000748653 R-squared 0.229101036741678 Adjusted R-squared 0.216034952618655 F-TEST (value) 17.5340243170486 F-TEST (DF numerator) 1 F-TEST (DF denominator) 59 p-value 9.54339556555883e-05 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 658.596779322623 Sum Squared Residuals 25591233.3463138 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 2120.88 3167.82949999999 -1046.94949999999 2 2174.56 3167.8295 -993.269499999999 3 2196.72 3167.8295 -971.1095 4 2350.44 3167.8295 -817.3895 5 2440.25 3167.8295 -727.5795 6 2408.64 3167.8295 -759.1895 7 2472.81 3167.8295 -695.0195 8 2407.6 3167.8295 -760.2295 9 2454.62 3167.8295 -713.2095 10 2448.05 3167.8295 -719.7795 11 2497.84 3167.8295 -669.9895 12 2645.64 3167.8295 -522.1895 13 2756.76 3167.8295 -411.0695 14 2849.27 3167.8295 -318.5595 15 2921.44 3167.8295 -246.3895 16 2981.85 3167.8295 -185.979500000000 17 3080.58 3167.8295 -87.2495000000002 18 3106.22 3167.8295 -61.6095000000004 19 3119.31 3167.8295 -48.5195000000002 20 3061.26 3167.8295 -106.5695 21 3097.31 3167.8295 -70.5195000000002 22 3161.69 3167.8295 -6.1395000000001 23 3257.16 3167.8295 89.3304999999997 24 3277.01 3167.8295 109.1805 25 3295.32 3167.8295 127.4905 26 3363.99 3167.8295 196.160500000000 27 3494.17 3167.8295 326.3405 28 3667.03 3167.8295 499.2005 29 3813.06 3167.8295 645.2305 30 3917.96 3167.8295 750.1305 31 3895.51 3167.8295 727.6805 32 3801.06 3167.8295 633.2305 33 3570.12 3167.8295 402.2905 34 3701.61 3167.8295 533.7805 35 3862.27 3167.8295 694.4405 36 3970.1 3167.8295 802.2705 37 4138.52 3167.8295 970.6905 38 4199.75 3167.8295 1031.9205 39 4290.89 3167.8295 1123.0605 40 4443.91 3167.8295 1276.0805 41 4502.64 3910.99523809524 591.644761904762 42 4356.98 3910.99523809524 445.984761904761 43 4591.27 3910.99523809524 680.274761904762 44 4696.96 3910.99523809524 785.964761904762 45 4621.4 3910.99523809524 710.404761904761 46 4562.84 3910.99523809524 651.844761904762 47 4202.52 3910.99523809524 291.524761904762 48 4296.49 3910.99523809524 385.494761904762 49 4435.23 3910.99523809524 524.234761904761 50 4105.18 3910.99523809524 194.184761904762 51 4116.68 3910.99523809524 205.684761904762 52 3844.49 3910.99523809524 -66.5052380952383 53 3720.98 3910.99523809524 -190.015238095238 54 3674.4 3910.99523809524 -236.595238095238 55 3857.62 3910.99523809524 -53.3752380952382 56 3801.06 3910.99523809524 -109.935238095238 57 3504.37 3910.99523809524 -406.625238095238 58 3032.6 3910.99523809524 -878.395238095238 59 3047.03 3910.99523809524 -863.965238095238 60 2962.34 3910.99523809524 -948.655238095238 61 2197.82 3910.99523809524 -1713.17523809524 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.0202820401734225 0.0405640803468449 0.979717959826578 6 0.0068821190960028 0.0137642381920056 0.993117880903997 7 0.00313105999849223 0.00626211999698447 0.996868940001508 8 0.000960579186021053 0.00192115837204211 0.999039420813979 9 0.000356671051405787 0.000713342102811574 0.999643328948594 10 0.000127308221145192 0.000254616442290384 0.999872691778855 11 5.96713165636764e-05 0.000119342633127353 0.999940328683436 12 8.48464699580457e-05 0.000169692939916091 0.999915153530042 13 0.000206847411105738 0.000413694822211477 0.999793152588894 14 0.000555866476756624 0.00111173295351325 0.999444133523243 15 0.00133206646099600 0.00266413292199199 0.998667933539004 16 0.00277581115627553 0.00555162231255107 0.997224188843725 17 0.00607015304494153 0.0121403060898831 0.993929846955058 18 0.0103828065518594 0.0207656131037187 0.98961719344814 19 0.0149700487006891 0.0299400974013781 0.98502995129931 20 0.0172329404321067 0.0344658808642134 0.982767059567893 21 0.0201633187413655 0.0403266374827309 0.979836681258635 22 0.0248968459806482 0.0497936919612963 0.975103154019352 23 0.0333531253384105 0.066706250676821 0.96664687466159 24 0.0425009518089283 0.0850019036178565 0.957499048191072 25 0.052349977710571 0.104699955421142 0.947650022289429 26 0.0660012377098421 0.132002475419684 0.933998762290158 27 0.0890812492219279 0.178162498443856 0.910918750778072 28 0.130279838597752 0.260559677195504 0.869720161402248 29 0.190895929821679 0.381791859643359 0.80910407017832 30 0.262649597046458 0.525299194092915 0.737350402953542 31 0.312587302222563 0.625174604445127 0.687412697777437 32 0.331257181067604 0.662514362135208 0.668742818932396 33 0.325275738750669 0.650551477501339 0.674724261249331 34 0.326268331211377 0.652536662422755 0.673731668788623 35 0.336540621714159 0.673081243428318 0.663459378285841 36 0.351079444791613 0.702158889583226 0.648920555208387 37 0.37594178985137 0.75188357970274 0.62405821014863 38 0.395804068928364 0.791608137856729 0.604195931071636 39 0.414535884836298 0.829071769672597 0.585464115163702 40 0.439562398759731 0.879124797519462 0.560437601240269 41 0.401970282221898 0.803940564443796 0.598029717778102 42 0.351561237114994 0.703122474229988 0.648438762885006 43 0.340748617105303 0.681497234210606 0.659251382894697 44 0.365557459748193 0.731114919496386 0.634442540251807 45 0.392004114234944 0.784008228469889 0.607995885765056 46 0.427232981937761 0.854465963875523 0.572767018062239 47 0.397920565686945 0.79584113137389 0.602079434313055 48 0.397744065777513 0.795488131555025 0.602255934222487 49 0.469042300753793 0.938084601507587 0.530957699246207 50 0.467486690376657 0.934973380753314 0.532513309623343 51 0.494452448921199 0.988904897842398 0.505547551078801 52 0.462345456545101 0.924690913090203 0.537654543454899 53 0.409701148622091 0.819402297244182 0.590298851377909 54 0.353029138692385 0.70605827738477 0.646970861307615 55 0.378826194553106 0.757652389106213 0.621173805446894 56 0.467734198357009 0.935468396714018 0.532265801642991 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 10 0.192307692307692 NOK 5% type I error level 18 0.346153846153846 NOK 10% type I error level 20 0.384615384615385 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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