multiple regression toevoeging variabele uit het verleden

*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, 14 Dec 2009 12:53:55 -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/Dec/14/t12608204644l09yzvk59h7t43.htm/, Retrieved Mon, 14 Dec 2009 20:54:36 +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/Dec/14/t12608204644l09yzvk59h7t43.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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455 1802 462 452 449 441 461 1863 455 462 452 449 461 1989 461 455 462 452 463 2197 461 461 455 462 462 2409 463 461 461 455 456 2502 462 463 461 461 455 2593 456 462 463 461 456 2598 455 456 462 463 472 2053 456 455 456 462 472 2213 472 456 455 456 471 2238 472 472 456 455 465 2359 471 472 472 456 459 2151 465 471 472 472 465 2474 459 465 471 472 468 3079 465 459 465 471 467 2312 468 465 459 465 463 2565 467 468 465 459 460 1972 463 467 468 465 462 2484 460 463 467 468 461 2202 462 460 463 467 476 2151 461 462 460 463 476 1976 476 461 462 460 471 2012 476 476 461 462 453 2114 471 476 476 461 443 1772 453 471 476 476 442 1957 443 453 471 476 444 2070 442 443 453 471 438 1990 444 442 443 453 427 2182 438 444 442 443 424 2008 427 438 444 442 416 1916 424 427 438 444 406 2397 416 424 427 438 431 2114 406 416 424 427 434 1778 431 406 416 424 418 1641 434 431 406 416 412 2186 418 434 431 406 404 1773 412 418 434 431 409 1785 404 412 418 434 412 2217 409 404 412 418 406 2153 4 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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation wkl[t] = -17.3691385226585 + 0.00407364554764026bvg[t] + 1.10516982971292Y1[t] -0.0940382526645915Y2[t] + 0.289524027067878Y3[t] -0.317759264859482Y4[t] + 9.29743613448183M1[t] + 23.0351035992936M2[t] + 18.3512500276087M3[t] + 14.5008375862024M4[t] + 7.78279725801128M5[t] + 10.8214637131233M6[t] + 9.53156919044552M7[t] + 15.2481682777225M8[t] + 34.7976956423727M9[t] + 14.6136201071320M10[t] + 5.74174285239308M11[t] + 0.081710785331368t + 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) -17.3691385226585 22.861144 -0.7598 0.451962 0.225981 bvg 0.00407364554764026 0.003008 1.3541 0.183499 0.09175 Y1 1.10516982971292 0.135272 8.17 0 0 Y2 -0.0940382526645915 0.20943 -0.449 0.655902 0.327951 Y3 0.289524027067878 0.213059 1.3589 0.181989 0.090994 Y4 -0.317759264859482 0.13335 -2.3829 0.022146 0.011073 M1 9.29743613448183 4.160621 2.2346 0.031243 0.015622 M2 23.0351035992936 4.67632 4.9259 1.6e-05 8e-06 M3 18.3512500276087 5.075341 3.6158 0.000847 0.000424 M4 14.5008375862024 5.188928 2.7946 0.008019 0.004009 M5 7.78279725801128 3.947056 1.9718 0.055756 0.027878 M6 10.8214637131233 3.897096 2.7768 0.008393 0.004196 M7 9.53156919044552 4.323033 2.2048 0.033431 0.016715 M8 15.2481682777225 4.539136 3.3593 0.001757 0.000878 M9 34.7976956423727 4.540695 7.6635 0 0 M10 14.6136201071320 6.227325 2.3467 0.024114 0.012057 M11 5.74174285239308 5.510217 1.042 0.30382 0.15191 t 0.081710785331368 0.076214 1.0721 0.290254 0.145127 Multiple Linear Regression - Regression Statistics Multiple R 0.9889469010895 R-squared 0.978015973174527 Adjusted R-squared 0.968433192250602 F-TEST (value) 102.059723679253 F-TEST (DF numerator) 17 F-TEST (DF denominator) 39 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4.75490825023572 Sum Squared Residuals 881.756946258229 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 455 457.298341147422 -2.29834114742237 2 461 461.016138403663 -0.0161384036624990 3 461 466.158524179342 -5.15852417934163 4 463 457.468650443118 5.53134955688158 5 462 457.867732432208 4.13226756779218 6 456 458.167156784383 -2.16715678438277 7 455 451.371742120394 3.62825787960555 8 456 455.724437350229 0.275562649771210 9 472 472.915361861576 -0.91536186157618 10 472 472.67049098412 -0.670490984120429 11 471 463.084836902698 7.91516309730226 12 465 461.127171285414 3.87282871458585 13 459 458.037870967954 0.962129032046447 14 465 466.816723240627 -1.81672324062661 15 468 470.454999607313 -2.45499960731271 16 467 466.482503216099 0.517496783901395 17 463 463.133221160649 -0.133221160649257 18 460 458.473302017202 1.52669798279838 19 462 455.16866650012 6.83133349987969 20 461 461.470325902302 -0.470325902301687 21 476 480.003026772546 -4.00302677254582 22 476 477.391685598872 -1.39168559887205 23 471 466.412554022424 4.58744597757621 24 453 460.302804323534 -7.30280432353444 25 443 444.099509821653 -1.09950982165285 26 442 447.865882613603 -5.86588261360346 27 444 439.936638308142 4.06336169185815 28 438 440.970849417138 -2.97084941713812 29 427 431.185632957345 -4.18563295734549 30 424 422.90136458064 1.09863541935987 31 416 416.664654050956 -0.664654050956333 32 406 414.58493484368 -8.5849348436803 33 431 425.390718860118 5.60928113988209 34 434 431.126323053706 2.87367694629421 35 418 422.389454164993 -4.38945416499253 36 412 411.400420213286 0.599579786713967 37 404 406.895335045996 -2.89533504599635 38 409 406.900805693331 2.09919430666917 39 412 413.683637028784 -1.68363702878363 40 406 412.089903656090 -6.08990365608949 41 398 401.479134079882 -3.47913407988245 42 397 397.964872373148 -0.964872373147614 43 385 390.935176606929 -5.93517660692864 44 390 385.253777605295 4.74622239470486 45 413 412.744947121881 0.255052878119127 46 413 413.811500363302 -0.811500363301738 47 401 409.113154909886 -8.11315490988594 48 397 394.169604177765 2.83039582223463 49 397 391.668943016975 5.33105698302512 50 409 403.400450048777 5.59954995122339 51 419 413.76620087642 5.23379912357982 52 424 420.988093267555 3.01190673244464 53 428 424.334279369915 3.66572063008502 54 430 429.493304244628 0.506695755372136 55 424 427.8597607216 -3.85976072160027 56 433 428.966524298494 4.03347570150591 57 456 456.945945383879 -0.945945383879216 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.0296550638957149 0.0593101277914297 0.970344936104285 22 0.00672368760379788 0.0134473752075958 0.993276312396202 23 0.0451818827579995 0.090363765515999 0.954818117242 24 0.396762263500394 0.793524527000789 0.603237736499606 25 0.288865793102962 0.577731586205925 0.711134206897038 26 0.260616726846311 0.521233453692621 0.73938327315369 27 0.240634446580768 0.481268893161537 0.759365553419232 28 0.155254656022985 0.310509312045970 0.844745343977015 29 0.0931227406679645 0.186245481335929 0.906877259332036 30 0.167379785990644 0.334759571981287 0.832620214009356 31 0.233609336124058 0.467218672248117 0.766390663875941 32 0.332398550512587 0.664797101025174 0.667601449487413 33 0.797954968824963 0.404090062350073 0.202045031175037 34 0.889435529394024 0.221128941211952 0.110564470605976 35 0.904557938054877 0.190884123890245 0.0954420619451226 36 0.828676329887834 0.342647340224332 0.171323670112166 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 1 0.0625 NOK 10% type I error level 3 0.1875 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') }

Copyright

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.

Privacy Policy

We may request personal information to be submitted to our servers in order to be able to:

• personalize online software applications according to your needs
• enforce strict security rules with respect to the data that you upload (e.g. statistical data)
• manage user sessions of online applications
• alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

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