verbetering evelyn ongena 2e stap

*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, 28 Nov 2008 02:04:44 -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/28/t12278631855sym0q4agowwv53.htm/, Retrieved Fri, 28 Nov 2008 09:06:31 +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/28/t12278631855sym0q4agowwv53.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 «

46 0 48 0 48 0 48 0 45 0 44 0 45 0 45 0 45 0 42 0 43 0 50 0 46 0 46 0 45 0 49 0 46 0 45 0 49 0 47 0 45 0 48 0 51 0 48 0 49 0 51 0 54 0 52 0 52 0 53 0 51 0 55 0 53 0 51 0 52 0 54 0 58 0 57 0 52 0 50 0 53 0 50 0 50 0 51 0 53 0 49 0 54 0 57 0 58 0 56 0 60 0 55 0 54 0 52 0 55 0 56 0 54 0 53 0 59 1 62 1 63 1 64 1 75 1 77 1 79 1 77 1 82 1 83 1 81 1 78 1 79 1 79 1 73 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 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 50.388090349076 + 23.8357289527721d[t] -1.05544147843942M1[t] -0.694045174537988M2[t] + 1.30595482546201M3[t] + 0.80595482546201M4[t] + 0.472621492128678M5[t] -0.860711841204655M6[t] + 0.972621492128678M7[t] + 1.80595482546201M8[t] + 0.805954825462011M9[t] -0.860711841204656M10[t] -2M11[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) 50.388090349076 2.323669 21.6847 0 0 d 23.8357289527721 1.62544 14.6642 0 0 M1 -1.05544147843942 3.080314 -0.3426 0.733066 0.366533 M2 -0.694045174537988 3.207046 -0.2164 0.8294 0.4147 M3 1.30595482546201 3.207046 0.4072 0.6853 0.34265 M4 0.80595482546201 3.207046 0.2513 0.802435 0.401218 M5 0.472621492128678 3.207046 0.1474 0.883334 0.441667 M6 -0.860711841204655 3.207046 -0.2684 0.789326 0.394663 M7 0.972621492128678 3.207046 0.3033 0.762728 0.381364 M8 1.80595482546201 3.207046 0.5631 0.575451 0.287725 M9 0.805954825462011 3.207046 0.2513 0.802435 0.401218 M10 -0.860711841204656 3.207046 -0.2684 0.789326 0.394663 M11 -2 3.195583 -0.6259 0.533778 0.266889 Multiple Linear Regression - Regression Statistics Multiple R 0.88606940697026 R-squared 0.785118993968628 Adjusted R-squared 0.742142792762354 F-TEST (value) 18.2686922513292 F-TEST (DF numerator) 12 F-TEST (DF denominator) 60 p-value 8.88178419700125e-16 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 5.53491293848385 Sum Squared Residuals 1838.11567419576 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 46 49.3326488706365 -3.3326488706365 2 48 49.694045174538 -1.69404517453799 3 48 51.694045174538 -3.69404517453799 4 48 51.194045174538 -3.19404517453799 5 45 50.8607118412047 -5.86071184120466 6 44 49.5273785078713 -5.52737850787132 7 45 51.3607118412047 -6.36071184120466 8 45 52.194045174538 -7.19404517453799 9 45 51.194045174538 -6.19404517453799 10 42 49.5273785078713 -7.52737850787132 11 43 48.388090349076 -5.38809034907598 12 50 50.388090349076 -0.388090349075976 13 46 49.3326488706366 -3.33264887063656 14 46 49.694045174538 -3.69404517453799 15 45 51.694045174538 -6.69404517453799 16 49 51.194045174538 -2.19404517453799 17 46 50.8607118412047 -4.86071184120466 18 45 49.5273785078713 -4.52737850787132 19 49 51.3607118412047 -2.36071184120466 20 47 52.194045174538 -5.19404517453799 21 45 51.194045174538 -6.19404517453799 22 48 49.5273785078713 -1.52737850787132 23 51 48.388090349076 2.61190965092402 24 48 50.388090349076 -2.38809034907598 25 49 49.3326488706366 -0.332648870636558 26 51 49.694045174538 1.30595482546201 27 54 51.694045174538 2.30595482546201 28 52 51.194045174538 0.805954825462011 29 52 50.8607118412047 1.13928815879535 30 53 49.5273785078713 3.47262149212868 31 51 51.3607118412047 -0.360711841204655 32 55 52.194045174538 2.80595482546201 33 53 51.194045174538 1.80595482546201 34 51 49.5273785078713 1.47262149212868 35 52 48.388090349076 3.61190965092402 36 54 50.388090349076 3.61190965092402 37 58 49.3326488706366 8.66735112936344 38 57 49.694045174538 7.30595482546201 39 52 51.694045174538 0.305954825462013 40 50 51.194045174538 -1.19404517453799 41 53 50.8607118412047 2.13928815879534 42 50 49.5273785078713 0.472621492128678 43 50 51.3607118412047 -1.36071184120465 44 51 52.194045174538 -1.19404517453799 45 53 51.194045174538 1.80595482546201 46 49 49.5273785078713 -0.527378507871322 47 54 48.388090349076 5.61190965092402 48 57 50.388090349076 6.61190965092402 49 58 49.3326488706366 8.66735112936344 50 56 49.694045174538 6.30595482546201 51 60 51.694045174538 8.30595482546201 52 55 51.194045174538 3.80595482546201 53 54 50.8607118412047 3.13928815879535 54 52 49.5273785078713 2.47262149212868 55 55 51.3607118412047 3.63928815879535 56 56 52.194045174538 3.80595482546201 57 54 51.194045174538 2.80595482546201 58 53 49.5273785078713 3.47262149212868 59 59 72.223819301848 -13.2238193018480 60 62 74.223819301848 -12.2238193018481 61 63 73.1683778234086 -10.1683778234086 62 64 73.52977412731 -9.52977412731006 63 75 75.52977412731 -0.529774127310059 64 77 75.02977412731 1.97022587268994 65 79 74.6964407939767 4.30355920602327 66 77 73.3631074606434 3.63689253935661 67 82 75.1964407939767 6.80355920602327 68 83 76.02977412731 6.97022587268994 69 81 75.02977412731 5.97022587268994 70 78 73.3631074606434 4.63689253935661 71 79 72.223819301848 6.77618069815195 72 79 74.223819301848 4.77618069815195 73 73 73.1683778234086 -0.16837782340863 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.0286930733283604 0.0573861466567209 0.97130692667164 17 0.00785363940602773 0.0157072788120555 0.992146360593972 18 0.00210552431310607 0.00421104862621215 0.997894475686894 19 0.00317283507923773 0.00634567015847546 0.996827164920762 20 0.00145665148589239 0.00291330297178477 0.998543348514108 21 0.000505521385613619 0.00101104277122724 0.999494478614386 22 0.00227702036137225 0.00455404072274451 0.997722979638628 23 0.0107016447754357 0.0214032895508713 0.989298355224564 24 0.00568818352656621 0.0113763670531324 0.994311816473434 25 0.00372746020226085 0.0074549204045217 0.99627253979774 26 0.00306623304474357 0.00613246608948714 0.996933766955256 27 0.008382985417657 0.016765970835314 0.991617014582343 28 0.00576990507963537 0.0115398101592707 0.994230094920365 29 0.00820582414815466 0.0164116482963093 0.991794175851845 30 0.0168842400932632 0.0337684801865264 0.983115759906737 31 0.0131190802438414 0.0262381604876827 0.986880919756159 32 0.0235756183759057 0.0471512367518115 0.976424381624094 33 0.0300840231781138 0.0601680463562276 0.969915976821886 34 0.0269014682666883 0.0538029365333766 0.973098531733312 35 0.0210512372046433 0.0421024744092866 0.978948762795357 36 0.0162400770654611 0.0324801541309221 0.983759922934539 37 0.0398343259048979 0.0796686518097958 0.960165674095102 38 0.0555764011561446 0.111152802312289 0.944423598843855 39 0.0416079525858933 0.0832159051717866 0.958392047414107 40 0.0294126337817505 0.0588252675635009 0.97058736621825 41 0.0233093801311147 0.0466187602622295 0.976690619868885 42 0.0158845968018713 0.0317691936037426 0.984115403198129 43 0.0132247581973103 0.0264495163946206 0.98677524180269 44 0.0114684009391387 0.0229368018782773 0.988531599060861 45 0.00923252003160703 0.0184650400632141 0.990767479968393 46 0.00690441375304256 0.0138088275060851 0.993095586246957 47 0.00541225362890558 0.0108245072578112 0.994587746371094 48 0.00539962654650192 0.0107992530930038 0.994600373453498 49 0.0122302328044197 0.0244604656088394 0.98776976719558 50 0.0293318478481545 0.0586636956963089 0.970668152151846 51 0.0496477976526965 0.099295595305393 0.950352202347304 52 0.0351958396876439 0.0703916793752878 0.964804160312356 53 0.0216573049693172 0.0433146099386345 0.978342695030683 54 0.0118873083113626 0.0237746166227251 0.988112691688637 55 0.00662341201875224 0.0132468240375045 0.993376587981248 56 0.00336204046827808 0.00672408093655616 0.996637959531722 57 0.00135368172226656 0.00270736344453311 0.998646318277733 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 9 0.214285714285714 NOK 5% type I error level 32 0.761904761904762 NOK 10% type I error level 41 0.976190476190476 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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