Verbetering evelyn ongena 1e 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 01:35:08 -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/t1227861562shaoc2xxidf3o99.htm/, Retrieved Fri, 28 Nov 2008 08:39:47 +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/t1227861562shaoc2xxidf3o99.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 5 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 50.4827586206896 + 23.583908045977d[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) 50.4827586206896 0.683784 73.8285 0 0 d 23.583908045977 1.508464 15.6344 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.880291613151604 R-squared 0.774913324185053 Adjusted R-squared 0.77174308931442 F-TEST (value) 244.434042210353 F-TEST (DF numerator) 1 F-TEST (DF denominator) 71 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 5.20754611178765 Sum Squared Residuals 1925.41609195402 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 46 50.4827586206897 -4.48275862068972 2 48 50.4827586206897 -2.48275862068966 3 48 50.4827586206897 -2.48275862068965 4 48 50.4827586206897 -2.48275862068965 5 45 50.4827586206897 -5.48275862068965 6 44 50.4827586206897 -6.48275862068965 7 45 50.4827586206897 -5.48275862068965 8 45 50.4827586206897 -5.48275862068965 9 45 50.4827586206897 -5.48275862068965 10 42 50.4827586206897 -8.48275862068965 11 43 50.4827586206897 -7.48275862068965 12 50 50.4827586206897 -0.482758620689654 13 46 50.4827586206897 -4.48275862068965 14 46 50.4827586206897 -4.48275862068965 15 45 50.4827586206897 -5.48275862068965 16 49 50.4827586206897 -1.48275862068965 17 46 50.4827586206897 -4.48275862068965 18 45 50.4827586206897 -5.48275862068965 19 49 50.4827586206897 -1.48275862068965 20 47 50.4827586206897 -3.48275862068965 21 45 50.4827586206897 -5.48275862068965 22 48 50.4827586206897 -2.48275862068965 23 51 50.4827586206897 0.517241379310346 24 48 50.4827586206897 -2.48275862068965 25 49 50.4827586206897 -1.48275862068965 26 51 50.4827586206897 0.517241379310346 27 54 50.4827586206897 3.51724137931035 28 52 50.4827586206897 1.51724137931035 29 52 50.4827586206897 1.51724137931035 30 53 50.4827586206897 2.51724137931035 31 51 50.4827586206897 0.517241379310346 32 55 50.4827586206897 4.51724137931035 33 53 50.4827586206897 2.51724137931035 34 51 50.4827586206897 0.517241379310346 35 52 50.4827586206897 1.51724137931035 36 54 50.4827586206897 3.51724137931035 37 58 50.4827586206897 7.51724137931035 38 57 50.4827586206897 6.51724137931035 39 52 50.4827586206897 1.51724137931035 40 50 50.4827586206897 -0.482758620689654 41 53 50.4827586206897 2.51724137931035 42 50 50.4827586206897 -0.482758620689654 43 50 50.4827586206897 -0.482758620689654 44 51 50.4827586206897 0.517241379310346 45 53 50.4827586206897 2.51724137931035 46 49 50.4827586206897 -1.48275862068965 47 54 50.4827586206897 3.51724137931035 48 57 50.4827586206897 6.51724137931035 49 58 50.4827586206897 7.51724137931035 50 56 50.4827586206897 5.51724137931035 51 60 50.4827586206897 9.51724137931035 52 55 50.4827586206897 4.51724137931035 53 54 50.4827586206897 3.51724137931035 54 52 50.4827586206897 1.51724137931035 55 55 50.4827586206897 4.51724137931035 56 56 50.4827586206897 5.51724137931035 57 54 50.4827586206897 3.51724137931035 58 53 50.4827586206897 2.51724137931035 59 59 74.0666666666667 -15.0666666666667 60 62 74.0666666666667 -12.0666666666667 61 63 74.0666666666667 -11.0666666666667 62 64 74.0666666666667 -10.0666666666667 63 75 74.0666666666667 0.933333333333333 64 77 74.0666666666667 2.93333333333333 65 79 74.0666666666667 4.93333333333333 66 77 74.0666666666667 2.93333333333333 67 82 74.0666666666667 7.93333333333333 68 83 74.0666666666667 8.93333333333333 69 81 74.0666666666667 6.93333333333333 70 78 74.0666666666667 3.93333333333333 71 79 74.0666666666667 4.93333333333333 72 79 74.0666666666667 4.93333333333333 73 73 74.0666666666667 -1.06666666666667 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.0375030876899058 0.0750061753798116 0.962496912310094 6 0.0330907931806386 0.0661815863612773 0.966909206819361 7 0.0140236457098927 0.0280472914197853 0.985976354290107 8 0.00561673807385996 0.0112334761477199 0.99438326192614 9 0.00214942646345278 0.00429885292690556 0.997850573536547 10 0.00517778436621533 0.0103555687324307 0.994822215633785 11 0.00422580152184518 0.00845160304369037 0.995774198478155 12 0.0082264054831971 0.0164528109663942 0.991773594516803 13 0.00396696623347524 0.00793393246695048 0.996033033766525 14 0.00187688238677571 0.00375376477355141 0.998123117613224 15 0.000964577088686928 0.00192915417737386 0.999035422911313 16 0.000946563437852798 0.00189312687570560 0.999053436562147 17 0.000464420549011615 0.00092884109802323 0.999535579450988 18 0.000264046748847605 0.000528093497695211 0.999735953251152 19 0.000254905735507767 0.000509811471015535 0.999745094264492 20 0.000134910783218938 0.000269821566437876 0.99986508921678 21 8.84451892327343e-05 0.000176890378465469 0.999911554810767 22 5.91632695876513e-05 0.000118326539175303 0.999940836730412 23 0.00016058911446856 0.00032117822893712 0.999839410885532 24 0.000103628119669374 0.000207256239338749 0.99989637188033 25 8.36874219121596e-05 0.000167374843824319 0.999916312578088 26 0.000143554599384681 0.000287109198769362 0.999856445400615 27 0.000973813119757342 0.00194762623951468 0.999026186880243 28 0.00137810628913748 0.00275621257827496 0.998621893710863 29 0.00170521340785633 0.00341042681571267 0.998294786592144 30 0.00254920798501165 0.00509841597002329 0.997450792014988 31 0.00214222768059222 0.00428445536118444 0.997857772319408 32 0.00491566612365644 0.00983133224731289 0.995084333876344 33 0.00522607595692614 0.0104521519138523 0.994773924043074 34 0.00397486127040893 0.00794972254081786 0.99602513872959 35 0.00331955562491549 0.00663911124983097 0.996680444375085 36 0.00384753570441777 0.00769507140883554 0.996152464295582 37 0.0123956102093044 0.0247912204186088 0.987604389790696 38 0.0212686937565284 0.0425373875130567 0.978731306243472 39 0.0159335317417667 0.0318670634835334 0.984066468258233 40 0.0114714174532729 0.0229428349065458 0.988528582546727 41 0.00895403814495855 0.0179080762899171 0.991045961855041 42 0.00638137419936534 0.0127627483987307 0.993618625800635 43 0.00457539340235958 0.00915078680471915 0.99542460659764 44 0.00320817137958689 0.00641634275917378 0.996791828620413 45 0.00238896065794844 0.00477792131589688 0.997611039342052 46 0.00195496779767944 0.00390993559535888 0.99804503220232 47 0.00157900358633406 0.00315800717266811 0.998420996413666 48 0.00204879049265999 0.00409758098531998 0.99795120950734 49 0.00304642308099835 0.0060928461619967 0.996953576919002 50 0.00277239435387854 0.00554478870775707 0.997227605646121 51 0.00590608745317306 0.0118121749063461 0.994093912546827 52 0.00438585355196655 0.0087717071039331 0.995614146448033 53 0.00289620855343551 0.00579241710687102 0.997103791446564 54 0.00175294937750792 0.00350589875501585 0.998247050622492 55 0.00118303838357845 0.00236607676715690 0.998816961616422 56 0.00088479406500188 0.00176958813000376 0.999115205934998 57 0.00051395204856656 0.00102790409713312 0.999486047951433 58 0.000268385839488712 0.000536771678977423 0.999731614160511 59 0.00257048097491195 0.00514096194982389 0.997429519025088 60 0.0168888151661020 0.0337776303322039 0.983111184833898 61 0.135252348937439 0.270504697874877 0.864747651062561 62 0.829112366622333 0.341775266755333 0.170887633377666 63 0.86865369442907 0.262692611141862 0.131346305570931 64 0.849719848523251 0.300560302953497 0.150280151476749 65 0.797755373103146 0.404489253793709 0.202244626896854 66 0.732142799733018 0.535714400533963 0.267857200266982 67 0.690570465137027 0.618859069725946 0.309429534862973 68 0.720516962198121 0.558966075603757 0.279483037801879 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 41 0.640625 NOK 5% type I error level 54 0.84375 NOK 10% type I error level 56 0.875 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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