multiple regression met 3 maanden minder, index van totale industriële productie & prijsindex van grondstoffen, incl. enerige

*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: Thu, 19 Nov 2009 08:54:48 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Nov/19/t12586461469p65xfi3hmu4u1s.htm/, Retrieved Thu, 19 Nov 2009 16:55:58 +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/2009/Nov/19/t12586461469p65xfi3hmu4u1s.htm/}, year = {2009}, } @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 = {2009}, 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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102.9 127.5 112.7 97 95.1 97.4 134.6 102.9 112.7 97 111.4 131.8 97.4 102.9 112.7 87.4 135.9 111.4 97.4 102.9 96.8 142.7 87.4 111.4 97.4 114.1 141.7 96.8 87.4 111.4 110.3 153.4 114.1 96.8 87.4 103.9 145 110.3 114.1 96.8 101.6 137.7 103.9 110.3 114.1 94.6 148.3 101.6 103.9 110.3 95.9 152.2 94.6 101.6 103.9 104.7 169.4 95.9 94.6 101.6 102.8 168.6 104.7 95.9 94.6 98.1 161.1 102.8 104.7 95.9 113.9 174.1 98.1 102.8 104.7 80.9 179 113.9 98.1 102.8 95.7 190.6 80.9 113.9 98.1 113.2 190 95.7 80.9 113.9 105.9 181.6 113.2 95.7 80.9 108.8 174.8 105.9 113.2 95.7 102.3 180.5 108.8 105.9 113.2 99 196.8 102.3 108.8 105.9 100.7 193.8 99 102.3 108.8 115.5 197 100.7 99 102.3 100.7 216.3 115.5 100.7 99 109.9 221.4 100.7 115.5 100.7 114.6 217.9 109.9 100.7 115.5 85.4 229.7 114.6 109.9 100.7 100.5 227.4 85.4 114.6 109.9 114.8 204.2 100.5 85.4 114.6 116.5 196.6 114.8 100.5 85.4 112.9 198.8 116.5 114.8 100.5 102 207.5 112.9 116.5 114.8 106 190.7 102 112.9 116.5 105.3 201.6 106 102 112.9 118.8 210.5 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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation tot.ind.prod.index[t] = + 136.369545246487 + 0.0530843258192137prijsindex.grondst.incl.energie[t] -0.0119367169882655`y(t-1)`[t] -0.301068823246038`y(t-2)`[t] -0.0891857427440547`y(t-3)`[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) 136.369545246487 27.046743 5.042 6e-06 3e-06 prijsindex.grondst.incl.energie 0.0530843258192137 0.019245 2.7583 0.007956 0.003978 `y(t-1)` -0.0119367169882655 0.141427 -0.0844 0.933055 0.466527 `y(t-2)` -0.301068823246038 0.134349 -2.2409 0.029243 0.014622 `y(t-3)` -0.0891857427440547 0.142868 -0.6243 0.53514 0.26757 Multiple Linear Regression - Regression Statistics Multiple R 0.411787166404869 R-squared 0.169568670415751 Adjusted R-squared 0.106894607805619 F-TEST (value) 2.70556372690508 F-TEST (DF numerator) 4 F-TEST (DF denominator) 53 p-value 0.039939568367107 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 8.63250883290268 Sum Squared Residuals 3949.57106375757 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 102.9 104.107288794034 -1.20728879403354 2 97.4 99.7049338976584 -2.30493389765837 3 111.4 101.172208035530 10.2277919644704 4 87.4 103.752638540298 -16.3526385402976 5 96.8 100.675651223234 -3.87565122323435 6 114.1 106.487413117214 7.6125868827864 7 110.3 106.212405412746 4.08759458725404 8 103.9 99.7650199764694 4.13498002353061 9 101.6 99.0550475655768 2.54495243442316 10 94.6 101.910942159536 -7.31094215953557 11 95.9 103.464775096176 -7.56477509617619 12 104.7 106.674916739216 -1.97491673921552 13 102.8 106.760316898052 -3.96031689805194 14 98.1 103.619517106553 -5.51951710655314 15 113.9 104.152912140068 9.74708785993245 16 80.9 105.808901588637 -24.9089015886372 17 95.7 102.480877012362 -6.78087701236248 18 113.2 110.798499437208 2.40150056279218 19 105.9 108.631009479544 -2.73100947954421 20 108.8 101.768520698570 7.03147930142977 21 102.3 102.673536788149 -0.3735367881489 22 99 103.394356294044 -4.3943562940439 23 100.7 104.972803179789 -4.27280317978902 24 115.5 106.695615048079 8.80438495192126 25 100.7 107.325975076500 -6.62597507650034 26 109.9 103.165934202898 6.7340657971016 27 114.6 106.006190857668 8.59380914233152 28 85.4 105.126599151239 -19.7265991512388 29 100.5 103.117525035410 -2.61752503541028 30 114.8 110.077760897769 4.72223910223102 31 116.5 107.561709425722 8.93829057427803 32 112.9 102.006213635791 10.8937863642094 33 102 100.723846330817 1.27615366918271 34 106 100.894371873247 5.10562812675257 35 105.3 105.027963003984 0.272036996015781 36 118.8 105.276618508593 13.5233814914069 37 106.1 105.659574270197 0.440425729802744 38 109.3 101.825096779793 7.47490322020669 39 117.2 104.799289824673 12.400710175327 40 92.5 105.553707829414 -13.0537078294138 41 104.2 102.691022428481 1.50897757151942 42 112.5 110.106002456415 2.39399754358519 43 122.4 109.510117369410 12.8898826305905 44 113.3 107.012146183619 6.28785381638108 45 100 103.171684692278 -3.17168469227807 46 110.7 105.829550809007 4.8704491909927 47 112.8 111.414758651721 1.38524134827921 48 109.8 110.495738520922 -0.695738520921836 49 117.3 109.682888824596 7.61711117540436 50 109.1 112.193773423741 -3.09377342374134 51 115.9 111.569910944011 4.33008905598881 52 96 113.633660666353 -17.633660666353 53 99.8 109.853264242650 -10.0532642426497 54 116.8 113.026870756607 3.77312924339306 55 115.7 109.075224439993 6.62477556000697 56 99.4 101.061997641420 -1.66199764142012 57 94.3 98.4100448091092 -4.11004480910918 58 91 103.672860207209 -12.6728602072093 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 8 0.826591883888339 0.346816232223323 0.173408116111661 9 0.709568496559929 0.580863006880141 0.290431503440071 10 0.723494137088191 0.553011725823618 0.276505862911809 11 0.682194129639952 0.635611740720095 0.317805870360048 12 0.567319197678659 0.865361604642682 0.432680802321341 13 0.456208420481885 0.91241684096377 0.543791579518115 14 0.362637029848000 0.725274059695999 0.637362970152 15 0.402005761966412 0.804011523932823 0.597994238033588 16 0.799173723408167 0.401652553183665 0.200826276591833 17 0.754486779092245 0.491026441815509 0.245513220907755 18 0.70326003325895 0.593479933482101 0.296739966741050 19 0.675412364869884 0.649175270260232 0.324587635130116 20 0.720073602558577 0.559852794882847 0.279926397441423 21 0.653109326011831 0.693781347976338 0.346890673988169 22 0.587297270683141 0.825405458633719 0.412702729316860 23 0.523962833243008 0.952074333513984 0.476037166756992 24 0.542439521477452 0.915120957045097 0.457560478522548 25 0.511216688357202 0.977566623285595 0.488783311642798 26 0.485624388135235 0.971248776270471 0.514375611864765 27 0.477039535453208 0.954079070906416 0.522960464546792 28 0.808995086211175 0.382009827577649 0.191004913788825 29 0.759992480103982 0.480015039792036 0.240007519896018 30 0.701172600629847 0.597654798740305 0.298827399370153 31 0.708390936555866 0.583218126888268 0.291609063444134 32 0.73134239670759 0.53731520658482 0.26865760329241 33 0.660659986858424 0.678680026283152 0.339340013141576 34 0.608764459797976 0.782471080404047 0.391235540202024 35 0.525238525086353 0.949522949827293 0.474761474913647 36 0.57577681481326 0.84844637037348 0.42422318518674 37 0.490250996256143 0.980501992512287 0.509749003743857 38 0.452238597237222 0.904477194474444 0.547761402762778 39 0.590567913250776 0.81886417349845 0.409432086749225 40 0.722157036865714 0.555685926268571 0.277842963134286 41 0.647256737111128 0.705486525777744 0.352743262888872 42 0.565788347113708 0.868423305772583 0.434211652886292 43 0.559109870110045 0.881780259779911 0.440890129889956 44 0.485324877131856 0.970649754263711 0.514675122868144 45 0.388797557889489 0.777595115778978 0.611202442110511 46 0.441013720856688 0.882027441713377 0.558986279143312 47 0.345326241848214 0.690652483696429 0.654673758151786 48 0.252277663899236 0.504555327798471 0.747722336100764 49 0.280358415580020 0.560716831160041 0.71964158441998 50 0.176237641491102 0.352475282982204 0.823762358508898 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):

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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