Births met dummy variabele & trend & past4

*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, 26 Nov 2010 19:46:23 +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/26/t1290800735sqd82wvn3crcl6s.htm/, Retrieved Fri, 26 Nov 2010 20:45:45 +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/26/t1290800735sqd82wvn3crcl6s.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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8587 9743 9084 9081 9700 9731 8587 9743 9084 9081 9563 9731 8587 9743 9084 9998 9563 9731 8587 9743 9437 9998 9563 9731 8587 10038 9437 9998 9563 9731 9918 10038 9437 9998 9563 9252 9918 10038 9437 9998 9737 9252 9918 10038 9437 9035 9737 9252 9918 10038 9133 9035 9737 9252 9918 9487 9133 9035 9737 9252 8700 9487 9133 9035 9737 9627 8700 9487 9133 9035 8947 9627 8700 9487 9133 9283 8947 9627 8700 9487 8829 9283 8947 9627 8700 9947 8829 9283 8947 9627 9628 9947 8829 9283 8947 9318 9628 9947 8829 9283 9605 9318 9628 9947 8829 8640 9605 9318 9628 9947 9214 8640 9605 9318 9628 9567 9214 8640 9605 9318 8547 9567 9214 8640 9605 9185 8547 9567 9214 8640 9470 9185 8547 9567 9214 9123 9470 9185 8547 9567 9278 9123 9470 9185 8547 10170 9278 9123 9470 9185 9434 10170 9278 9123 9470 9655 9434 10170 9278 9123 9429 9655 9434 10170 9278 8739 9429 9655 9434 10170 9552 8739 9429 9655 9434 9687 9552 8739 9429 9655 9019 9687 9552 8739 9429 9672 9019 9687 9552 8739 9206 9672 9019 9687 9552 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 7 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation MontlyBirths[t] = + 3873.05299620334 + 0.124837319271829Y1[t] + 0.164886202883664Y2[t] + 0.243791599857208Y3[t] + 0.061698643855855Y4[t] -777.007128192618M1[t] + 184.930867387297M2[t] -260.922022455930M3[t] -1.62807770930776M4[t] -194.014625014349M5[t] + 383.21533040592M6[t] + 170.916446059259M7[t] -137.978095175717M8[t] -156.218164109860M9[t] -891.354225854479M10[t] -335.846833482281M11[t] + 5.57076871659979t + 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) 3873.05299620334 1593.649766 2.4303 0.018439 0.00922 Y1 0.124837319271829 0.143538 0.8697 0.388305 0.194152 Y2 0.164886202883664 0.136356 1.2092 0.231842 0.115921 Y3 0.243791599857208 0.136973 1.7798 0.080728 0.040364 Y4 0.061698643855855 0.145435 0.4242 0.673079 0.336539 M1 -777.007128192618 209.213307 -3.7139 0.000485 0.000242 M2 184.930867387297 235.63751 0.7848 0.435994 0.217997 M3 -260.922022455930 173.883914 -1.5006 0.139296 0.069648 M4 -1.62807770930776 239.647222 -0.0068 0.994605 0.497302 M5 -194.014625014349 219.030577 -0.8858 0.37966 0.18983 M6 383.21533040592 190.328241 2.0134 0.049063 0.024532 M7 170.916446059259 207.856546 0.8223 0.414533 0.207267 M8 -137.978095175717 234.700635 -0.5879 0.559057 0.279528 M9 -156.218164109860 214.477531 -0.7284 0.469536 0.234768 M10 -891.354225854479 190.692187 -4.6743 2e-05 1e-05 M11 -335.846833482281 219.28128 -1.5316 0.131464 0.065732 t 5.57076871659979 2.540908 2.1924 0.032678 0.016339 Multiple Linear Regression - Regression Statistics Multiple R 0.88379075383939 R-squared 0.781086096571998 Adjusted R-squared 0.716222717778516 F-TEST (value) 12.0420198747107 F-TEST (DF numerator) 16 F-TEST (DF denominator) 54 p-value 1.57818202950466e-12 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 271.206316240123 Sum Squared Residuals 3971854.76230103 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 8587 8628.08126909303 -41.0812690930296 2 9731 9522.47801426446 208.521985735539 3 9563 9195.24509608876 367.754903911242 4 9998 9386.6032728793 611.396727120699 5 9437 9433.96480402893 3.03519597107351 6 10038 10048.0835501038 -10.0835501037805 7 9918 9919.56547730846 -1.56547730845515 8 9252 9590.42965696794 -338.429656967944 9 9737 9586.73817008037 150.261829919629 10 9035 8815.73065875317 219.269341246828 11 9133 9199.37378734412 -66.3737873441204 12 9487 9514.42296153005 -27.4229615300546 13 8700 8662.1200001292 37.8799998708072 14 9627 9570.3306387788 56.6693612212096 15 8947 9208.35596439503 -261.355964395031 16 9283 9371.15814166392 -88.1581416639158 17 8829 9291.60306474299 -462.603064742991 18 9947 9764.54576505084 182.454234949163 19 9628 9662.48633598754 -34.4863359875382 20 9318 9413.73159144578 -95.7315914457795 21 9605 9554.31184786388 50.6881521361191 22 8640 8800.66970604934 -160.669706049338 23 9214 9193.34493092268 20.6550690773211 24 9567 9498.14557816456 68.8544218354422 25 8547 8647.87008977114 -100.870089771143 26 9185 9626.64680502546 -441.646805025463 27 9470 9219.30042297578 250.699577024220 28 9123 9398.05335929802 -275.053359298016 29 9278 9307.51802272002 -29.5180227200205 30 10170 9961.29735968273 208.702640317269 31 9434 9824.46992263858 -390.469922638577 32 9655 9592.72264466825 62.277355331751 33 9429 9713.3115435577 -284.311543557690 34 8739 8867.57744003605 -128.577440036045 35 9552 9313.7213106661 238.278689333894 36 9687 9601.39867216767 85.6013278323292 37 9019 8798.70773632487 220.292263675128 38 9672 9860.71531516047 -188.715315160469 39 9206 9474.8808434276 -268.880843427592 40 9069 9634.7185848091 -565.7185848091 41 9788 9471.94434354768 316.055656452324 42 10312 10048.5960193503 263.403980649657 43 10105 9963.6848216748 141.315178325191 44 9863 9887.75354046728 -24.7535404672839 45 9656 9982.85028824658 -326.850288246577 46 9295 9169.40643724147 125.593562758532 47 9946 9579.51769563261 366.48230436739 48 9701 9877.2845404529 -176.284540452890 49 9049 9081.82356900593 -32.8235690059256 50 10190 10063.9764025058 126.023597494212 51 9706 9639.06473357331 66.9352664266856 52 9765 9857.57505114765 -92.5750511476481 53 9893 9836.2584518436 56.7415481563922 54 9994 10397.1696571260 -403.169657126049 55 10433 10208.6771054769 224.322894523107 56 10073 10011.6559673793 61.3440326206819 57 10112 10058.9506532890 53.0493467110276 58 9266 9388.1510580412 -122.151058041191 59 9820 9789.3681376426 30.6318623573906 60 10097 10047.7482476848 49.2517523151726 61 9115 9198.39733567584 -83.3973356758363 62 10411 10171.8528242650 239.147175734971 63 9678 9833.15293953952 -155.152939539525 64 10408 9997.89159020202 410.108409797981 65 10153 10036.7113131168 116.288686883222 66 10368 10609.3076486863 -241.30764868626 67 10581 10520.1163369137 60.883663086272 68 10597 10261.7065990714 335.293400928575 69 10680 10322.8374969625 357.162503037491 70 9738 9671.46469987878 66.5353001212155 71 9556 10145.6741377919 -589.674137791875 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 20 0.833340761229101 0.333318477541798 0.166659238770899 21 0.726781058746 0.546437882507999 0.273218941254000 22 0.627578872527312 0.744842254945377 0.372421127472688 23 0.654168596707194 0.691662806585613 0.345831403292806 24 0.622606621870514 0.754786756258972 0.377393378129486 25 0.545221904467923 0.909556191064154 0.454778095532077 26 0.502840871755862 0.994318256488276 0.497159128244138 27 0.729201928198364 0.541596143603272 0.270798071801636 28 0.690055144068788 0.619889711862425 0.309944855931212 29 0.632182711768666 0.735634576462669 0.367817288231334 30 0.800990961641634 0.398018076716731 0.199009038358366 31 0.784536011742289 0.430927976515422 0.215463988257711 32 0.773204549526251 0.453590900947498 0.226795450473749 33 0.70707883591435 0.585842328171301 0.292921164085650 34 0.703058280876658 0.593883438246684 0.296941719123342 35 0.701482337227175 0.59703532554565 0.298517662772825 36 0.684558439295633 0.630883121408733 0.315441560704367 37 0.678045717784136 0.643908564431727 0.321954282215864 38 0.59700549907631 0.805989001847379 0.402994500923690 39 0.518059220163218 0.963881559673563 0.481940779836782 40 0.7352854894399 0.5294290211202 0.2647145105601 41 0.818262772849163 0.363474454301673 0.181737227150837 42 0.807858594729152 0.384282810541696 0.192141405270848 43 0.794064815488617 0.411870369022767 0.205935184511383 44 0.751217668895695 0.497564662208611 0.248782331104305 45 0.690320390660296 0.619359218679409 0.309679609339704 46 0.606908280419936 0.786183439160128 0.393091719580064 47 0.839260333677683 0.321479332644634 0.160739666322317 48 0.74941961119965 0.5011607776007 0.25058038880035 49 0.924069118314058 0.151861763371884 0.0759308816859418 50 0.849205886449405 0.301588227101189 0.150794113550595 51 0.751897709602831 0.496204580794338 0.248102290397169 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 = No 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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