Regression Analyse Nieuwbouw

*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: Mon, 20 Dec 2010 22:02:17 +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/Dec/20/t1292882794srjono6w8l2nf8z.htm/, Retrieved Mon, 20 Dec 2010 23:06:37 +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/Dec/20/t1292882794srjono6w8l2nf8z.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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4143 4429 5219 4929 5761 5592 4163 4962 5208 4755 4491 5732 5731 5040 6102 4904 5369 5578 4619 4731 5011 5299 4146 4625 4736 4219 5116 4205 4121 5103 4300 4578 3809 5657 4248 3830 4736 4839 4411 4570 4104 4801 3953 3828 4440 4026 4109 4785 3224 3552 3940 3913 3681 4309 3830 4143 4087 3818 3380 3430 3458 3970 5260 5024 5634 6549 4676

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 'RServer@AstonUniversity' @ vre.aston.ac.uk Multiple Linear Regression - Estimated Regression Equation nb[t] = + 5017.8 -217.03888888889M1[t] -198.611111111111M2[t] + 482.816666666667M3[t] + 80.5777777777779M4[t] + 283.005555555556M5[t] + 841.6M6[t] -208.638888888889M7[t] -91.711111111111M8[t] -14.1833333333332M9[t] + 200.744444444445M10[t] -420.527777777778M11[t] -14.9277777777778t + 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) 5017.8 309.379994 16.2189 0 0 M1 -217.03888888889 373.570937 -0.581 0.563668 0.281834 M2 -198.611111111111 373.386826 -0.5319 0.596965 0.298482 M3 482.816666666667 373.243566 1.2936 0.20132 0.10066 M4 80.5777777777779 373.141204 0.2159 0.829845 0.414922 M5 283.005555555556 373.079773 0.7586 0.451411 0.225705 M6 841.6 373.059294 2.2559 0.028147 0.014073 M7 -208.638888888889 373.079773 -0.5592 0.578314 0.289157 M8 -91.711111111111 389.961324 -0.2352 0.814959 0.407479 M9 -14.1833333333332 389.824155 -0.0364 0.97111 0.485555 M10 200.744444444445 389.726148 0.5151 0.608592 0.304296 M11 -420.527777777778 389.667332 -1.0792 0.285297 0.142648 t -14.9277777777778 3.909006 -3.8188 0.000348 0.000174 Multiple Linear Regression - Regression Statistics Multiple R 0.623207054194961 R-squared 0.388387032398361 Adjusted R-squared 0.252473039597996 F-TEST (value) 2.85759416227907 F-TEST (DF numerator) 12 F-TEST (DF denominator) 54 p-value 0.00413501323506293 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 616.087147114356 Sum Squared Residuals 20496422.1333333 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 4143 4785.83333333334 -642.833333333337 2 4429 4789.33333333333 -360.333333333333 3 5219 5455.83333333333 -236.833333333334 4 4929 5038.66666666667 -109.666666666667 5 5761 5226.16666666667 534.833333333334 6 5592 5769.83333333333 -177.833333333333 7 4163 4704.66666666667 -541.666666666667 8 4962 4806.66666666667 155.333333333333 9 5208 4869.26666666667 338.733333333333 10 4755 5069.26666666667 -314.266666666666 11 4491 4433.06666666667 57.9333333333332 12 5732 4838.66666666667 893.333333333334 13 5731 4606.7 1124.3 14 5040 4610.2 429.8 15 6102 5276.7 825.3 16 4904 4859.53333333333 44.4666666666668 17 5369 5047.03333333333 321.966666666667 18 5578 5590.7 -12.6999999999999 19 4619 4525.53333333333 93.466666666667 20 4731 4627.53333333333 103.466666666667 21 5011 4690.13333333333 320.866666666667 22 5299 4890.13333333333 408.866666666667 23 4146 4253.93333333333 -107.933333333333 24 4625 4659.53333333333 -34.5333333333332 25 4736 4427.56666666667 308.433333333334 26 4219 4431.06666666667 -212.066666666667 27 5116 5097.56666666667 18.4333333333333 28 4205 4680.4 -475.4 29 4121 4867.9 -746.9 30 5103 5411.56666666667 -308.566666666667 31 4300 4346.4 -46.3999999999999 32 4578 4448.4 129.6 33 3809 4511 -702 34 5657 4711 946 35 4248 4074.8 173.2 36 3830 4480.4 -650.4 37 4736 4248.43333333333 487.566666666668 38 4839 4251.93333333333 587.066666666667 39 4411 4918.43333333333 -507.433333333333 40 4570 4501.26666666667 68.7333333333333 41 4104 4688.76666666667 -584.766666666667 42 4801 5232.43333333333 -431.433333333333 43 3953 4167.26666666667 -214.266666666666 44 3828 4269.26666666667 -441.266666666667 45 4440 4331.86666666667 108.133333333333 46 4026 4531.86666666667 -505.866666666667 47 4109 3895.66666666667 213.333333333333 48 4785 4301.26666666667 483.733333333333 49 3224 4069.3 -845.299999999999 50 3552 4072.8 -520.8 51 3940 4739.3 -799.3 52 3913 4322.13333333333 -409.133333333333 53 3681 4509.63333333333 -828.633333333334 54 4309 5053.3 -744.3 55 3830 3988.13333333333 -158.133333333333 56 4143 4090.13333333333 52.8666666666665 57 4087 4152.73333333333 -65.7333333333335 58 3818 4352.73333333333 -534.733333333334 59 3380 3716.53333333333 -336.533333333334 60 3430 4122.13333333333 -692.133333333333 61 3458 3890.16666666667 -432.166666666666 62 3970 3893.66666666667 76.3333333333334 63 5260 4560.16666666667 699.833333333333 64 5024 4143 881 65 5634 4330.5 1303.5 66 6549 4874.16666666667 1674.83333333333 67 4676 3809 867 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.349214170503655 0.698428341007311 0.650785829496345 17 0.429918730662745 0.85983746132549 0.570081269337255 18 0.32714985370524 0.65429970741048 0.67285014629476 19 0.208513984203917 0.417027968407834 0.791486015796083 20 0.170639846478776 0.341279692957553 0.829360153521223 21 0.134160692029925 0.26832138405985 0.865839307970075 22 0.088034680053508 0.176069360107016 0.911965319946492 23 0.0712295378025196 0.142459075605039 0.92877046219748 24 0.138527242114939 0.277054484229878 0.861472757885061 25 0.112429641024936 0.224859282049871 0.887570358975064 26 0.092703420191913 0.185406840383826 0.907296579808087 27 0.0768626867551936 0.153725373510387 0.923137313244806 28 0.0639930107458384 0.127986021491677 0.936006989254162 29 0.106952487249069 0.213904974498138 0.893047512750931 30 0.071234205267273 0.142468410534546 0.928765794732727 31 0.0457926022243636 0.0915852044487272 0.954207397775636 32 0.0300561534722357 0.0601123069444715 0.969943846527764 33 0.0348793631799475 0.0697587263598949 0.965120636820053 34 0.081753794665685 0.16350758933137 0.918246205334315 35 0.0611380479283276 0.122276095856655 0.938861952071672 36 0.0650400269963617 0.130080053992723 0.934959973003638 37 0.10142920507558 0.202858410151159 0.89857079492442 38 0.170622690852541 0.341245381705082 0.82937730914746 39 0.147120847235874 0.294241694471748 0.852879152764126 40 0.123562219815662 0.247124439631325 0.876437780184337 41 0.0934102261069327 0.186820452213865 0.906589773893067 42 0.0605094866832076 0.121018973366415 0.939490513316792 43 0.0393389834073336 0.0786779668146672 0.960661016592666 44 0.0254182132893589 0.0508364265787178 0.97458178671064 45 0.0200378640361546 0.0400757280723092 0.979962135963845 46 0.0187557414782874 0.0375114829565748 0.981244258521713 47 0.0301051193967822 0.0602102387935645 0.969894880603218 48 0.362276138291642 0.724552276583283 0.637723861708358 49 0.493479900765518 0.986959801531035 0.506520099234482 50 0.619957549827779 0.760084900344441 0.380042450172221 51 0.468822388109059 0.937644776218117 0.531177611890941 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 2 0.0555555555555556 NOK 10% type I error level 8 0.222222222222222 NOK

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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