W8 - geboortecijfers Belgie - laatste 6 maanden

*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: Sat, 27 Nov 2010 18:40:39 +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/Nov/27/t1290883227fmdkkzzrikd26kw.htm/, Retrieved Sat, 27 Nov 2010 19:40:37 +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/Nov/27/t1290883227fmdkkzzrikd26kw.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:

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9563 9731 8587 9743 9084 9081 9700 9998 9563 9731 8587 9743 9084 9081 9437 9998 9563 9731 8587 9743 9084 10038 9437 9998 9563 9731 8587 9743 9918 10038 9437 9998 9563 9731 8587 9252 9918 10038 9437 9998 9563 9731 9737 9252 9918 10038 9437 9998 9563 9035 9737 9252 9918 10038 9437 9998 9133 9035 9737 9252 9918 10038 9437 9487 9133 9035 9737 9252 9918 10038 8700 9487 9133 9035 9737 9252 9918 9627 8700 9487 9133 9035 9737 9252 8947 9627 8700 9487 9133 9035 9737 9283 8947 9627 8700 9487 9133 9035 8829 9283 8947 9627 8700 9487 9133 9947 8829 9283 8947 9627 8700 9487 9628 9947 8829 9283 8947 9627 8700 9318 9628 9947 8829 9283 8947 9627 9605 9318 9628 9947 8829 9283 8947 8640 9605 9318 9628 9947 8829 9283 9214 8640 9605 9318 9628 9947 8829 9567 9214 8640 9605 9318 9628 9947 8547 9567 9214 8640 9605 9318 9628 9185 8547 9567 9214 8640 9605 9318 9470 9185 8547 9567 9214 8640 9605 9123 9470 9185 8547 9567 9214 8640 9278 9123 9470 9185 8547 9567 9214 10170 9278 9123 9470 9185 8547 9567 9434 101 etc...

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 8 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Yt[t] = + 2260.17634798631 + 0.0339916897977088`Yt-1`[t] + 0.0350118995045014`Yt-2`[t] + 0.112475389948693`Yt-3`[t] -0.0118409575464825`Yt-4`[t] + 0.316083003027646`Yt-5`[t] + 0.280257052615371`Yt-6`[t] -179.026837499072M1[t] + 129.398081382821M2[t] -238.937569078418M3[t] + 585.739880957251M4[t] + 356.88103897405M5[t] -33.0550838310867M6[t] + 33.6060774247566M7[t] -732.859928093813M8[t] -442.640351857356M9[t] -299.092191974960M10[t] -930.99474257794M11[t] + 5.03344278382246t + 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) 2260.17634798631 1654.976206 1.3657 0.17815 0.089075 `Yt-1` 0.0339916897977088 0.142601 0.2384 0.812569 0.406285 `Yt-2` 0.0350118995045014 0.138265 0.2532 0.801134 0.400567 `Yt-3` 0.112475389948693 0.141274 0.7961 0.429709 0.214854 `Yt-4` -0.0118409575464825 0.141917 -0.0834 0.933838 0.466919 `Yt-5` 0.316083003027646 0.138898 2.2757 0.027186 0.013593 `Yt-6` 0.280257052615371 0.146375 1.9147 0.061267 0.030633 M1 -179.026837499072 259.767839 -0.6892 0.493896 0.246948 M2 129.398081382821 243.254589 0.5319 0.59712 0.29856 M3 -238.937569078418 204.957972 -1.1658 0.249231 0.124616 M4 585.739880957251 240.233465 2.4382 0.018356 0.009178 M5 356.88103897405 288.871255 1.2354 0.222443 0.111221 M6 -33.0550838310867 227.53212 -0.1453 0.885077 0.442538 M7 33.6060774247566 226.529303 0.1484 0.882662 0.441331 M8 -732.859928093813 247.114973 -2.9657 0.00462 0.00231 M9 -442.640351857356 212.508568 -2.0829 0.042392 0.021196 M10 -299.092191974960 234.463331 -1.2756 0.207976 0.103988 M11 -930.99474257794 233.06605 -3.9946 0.000213 0.000106 t 5.03344278382246 2.594575 1.94 0.058032 0.029016 Multiple Linear Regression - Regression Statistics Multiple R 0.89795489295522 R-squared 0.80632298978222 Adjusted R-squared 0.73659926610382 F-TEST (value) 11.5645428448625 F-TEST (DF numerator) 18 F-TEST (DF denominator) 50 p-value 4.02222699591448e-12 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 257.046161709543 Sum Squared Residuals 3303636.46248043 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 9563 9294.73089451871 268.269105481290 2 9998 9332.17665696794 665.82334303206 3 9437 9329.27829841387 107.721701586127 4 10038 9942.00555477032 95.9944452296773 5 9918 9807.5053636531 110.494636346909 6 9252 9638.82844584766 -386.82844584766 7 9737 9848.3365645619 -111.336564561896 8 9035 9004.04783721894 30.9521627810618 9 9133 9251.67344476305 -118.673444763051 10 9487 9571.94904968688 -84.9490496868766 11 8700 8631.70145172327 68.2985482767323 12 9627 9539.356389478 87.6436105220005 13 8947 9322.00920289051 -375.009202890513 14 9283 9386.3350988341 -103.335098834102 15 8829 9263.58810156527 -434.588101565267 16 9947 9852.6246058825 94.3753941175044 17 9628 9769.1967390546 -141.196739054611 18 9318 9402.41347057719 -84.413470577186 19 9605 9499.1542287652 105.845771234796 20 8640 8638.17043852962 1.82956147038294 21 9214 9105.72388212366 108.276117876338 22 9567 9488.47827232477 78.5217276752287 23 8547 8594.38022448059 -47.3802244805868 24 9185 9587.91962019485 -402.919620194849 25 9470 9208.22156527509 261.778434724912 26 9123 9345.78398261948 -222.783982619483 27 9278 9336.9469736957 -58.946973695704 28 10170 9960.80448101153 209.195518988473 29 9434 9646.12164258592 -212.121642585919 30 9655 9557.86184637367 97.1381536263316 31 9429 9679.98501318263 -250.985013182631 32 8739 8777.00760542215 -38.0076054221482 33 9552 9399.8515569829 152.148443017093 34 9687 9541.22610375494 145.773896245058 35 9019 8736.06373864074 282.936261359261 36 9672 9744.22688432985 -72.2268843298488 37 9206 9293.16422736113 -87.16422736113 38 9069 9600.51125735992 -531.51125735992 39 9788 9568.1130214737 219.886978526304 40 10312 10184.0128881123 127.987111887713 41 10105 10012.4719377343 92.5280622656803 42 9863 9757.08440576917 105.915594230830 43 9656 9689.825855604 -33.8258556040025 44 9295 9072.26552889588 222.734471104124 45 9946 9690.36443296323 255.635567036772 46 9701 9909.44394991723 -208.44394991723 47 9049 9124.38179049164 -75.381790491636 48 10190 9973.91415489793 216.085845102074 49 9706 9608.49341188038 97.5065881196241 50 9765 9979.61269234782 -214.612692347825 51 9893 9842.4319647709 50.568035229107 52 9994 10335.8617787948 -341.861778794762 53 10433 10310.2412430103 122.758756989679 54 10073 10124.2844736471 -51.2844736471035 55 10112 10091.9611487737 20.0388512262703 56 9266 9424.4245280866 -158.424528086600 57 9820 9714.39400691482 105.605993085182 58 10097 10027.9026243162 69.0973756838201 59 9115 9343.47279466377 -228.472794663771 60 10411 10239.5829510994 171.417048900625 61 9678 9843.38069807418 -165.380698074183 62 10408 10001.5803118707 406.419688129269 63 10153 10037.6416400806 115.358359919432 64 10368 10553.6906914286 -185.690691428606 65 10581 10553.4630739617 27.5369260382612 66 10597 10277.5273577852 319.472642214788 67 10680 10409.7371891125 270.262810887464 68 9738 9797.08406184682 -59.084061846821 69 9556 10058.9926762523 -502.992676252335 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 22 0.756857971051039 0.486284057897922 0.243142028948961 23 0.618942493574353 0.762115012851294 0.381057506425647 24 0.508026964785724 0.983946070428552 0.491973035214276 25 0.867705574184534 0.264588851630933 0.132294425815466 26 0.807016959499261 0.385966081001478 0.192983040500739 27 0.806941582230313 0.386116835539374 0.193058417769687 28 0.911055653506033 0.177888692987935 0.0889443464939675 29 0.89425453619561 0.211490927608782 0.105745463804391 30 0.888994745453795 0.222010509092409 0.111005254546205 31 0.831288966286403 0.337422067427193 0.168711033713597 32 0.817237631024834 0.365524737950332 0.182762368975166 33 0.781444975632371 0.437110048735258 0.218555024367629 34 0.785304710259178 0.429390579481644 0.214695289740822 35 0.732540612827975 0.534918774344049 0.267459387172025 36 0.64844062497472 0.703118750050559 0.351559375025280 37 0.558827483234755 0.88234503353049 0.441172516765245 38 0.79800451141597 0.403990977168060 0.201995488584030 39 0.834835101358848 0.330329797282304 0.165164898641152 40 0.809625956220405 0.380748087559189 0.190374043779595 41 0.727589447761097 0.544821104477806 0.272410552238903 42 0.66263860925443 0.674722781491139 0.337361390745569 43 0.543458829954104 0.913082340091792 0.456541170045896 44 0.479817645922724 0.959635291845449 0.520182354077276 45 0.698446612386114 0.603106775227771 0.301553387613886 46 0.564038921651274 0.871922156697453 0.435961078348726 47 0.702770487101843 0.594459025796314 0.297229512898157 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 0 0 OK 10% type I error level 0 0 OK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = 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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