Multiple regression

*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, 21 Nov 2009 08:05:34 -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/21/t125881620082otl7sfmlihxdy.htm/, Retrieved Sat, 21 Nov 2009 16:10:12 +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/21/t125881620082otl7sfmlihxdy.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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562000 4814 561000 3908 555000 5250 544000 3937 537000 4004 543000 5560 594000 3922 611000 3759 613000 4138 611000 4634 594000 3996 595000 4308 591000 4143 589000 4429 584000 5219 573000 4929 567000 5755 569000 5592 621000 4163 629000 4962 628000 5208 612000 4755 595000 4491 597000 5732 593000 5731 590000 5040 580000 6102 574000 4904 573000 5369 573000 5578 620000 4619 626000 4731 620000 5011 588000 5299 566000 4146 557000 4625 561000 4736 549000 4219 532000 5116 526000 4205 511000 4121 499000 5103 555000 4300 565000 4578 542000 3809 527000 5526 510000 4247 514000 3830 517000 4394 508000 4826 493000 4409 490000 4569 469000 4106 478000 4794 528000 3914 534000 3793 518000 4405 506000 4022 502000 4100 516000 4788

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 werkloos[t] = + 381414.27936713 + 37.4491518775223bouw[t] + 4992.94074910514M1[t] + 10048.7439533093M2[t] -28068.8928462940M3[t] -8865.01535250223M4[t] -24939.2677870364M5[t] -48445.9927756869M6[t] + 45513.448838068M7[t] + 48135.1523482365M8[t] + 33732.7592273591M9[t] + 5862.19165214424M10[t] + 14849.0793547867M11[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) 381414.27936713 47610.143376 8.0112 0 0 bouw 37.4491518775223 9.613221 3.8956 0.000309 0.000154 M1 4992.94074910514 22950.216024 0.2176 0.828717 0.414359 M2 10048.7439533093 22986.83766 0.4372 0.664003 0.332002 M3 -28068.8928462940 23556.424575 -1.1916 0.239416 0.119708 M4 -8865.01535250223 22971.13704 -0.3859 0.701298 0.350649 M5 -24939.2677870364 22927.571402 -1.0877 0.282256 0.141128 M6 -48445.9927756869 23811.563426 -2.0346 0.047559 0.02378 M7 45513.448838068 23373.70454 1.9472 0.057499 0.028749 M8 48135.1523482365 23098.353978 2.0839 0.04263 0.021315 M9 33732.7592273591 22967.984604 1.4687 0.14858 0.07429 M10 5862.19165214424 23000.252547 0.2549 0.799932 0.399966 M11 14849.0793547867 23350.807696 0.6359 0.527918 0.263959 Multiple Linear Regression - Regression Statistics Multiple R 0.63694263876158 R-squared 0.405695925072565 Adjusted R-squared 0.253958714452794 F-TEST (value) 2.67367459448806 F-TEST (DF numerator) 12 F-TEST (DF denominator) 47 p-value 0.00801932413477702 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 36251.012655262 Sum Squared Residuals 61764388171.0023 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 562000 566687.437254627 -4687.43725462689 2 561000 537814.308857796 23185.6911422039 3 555000 549953.433877828 5046.56612217234 4 544000 519986.574956433 24013.4250435672 5 537000 506421.415697693 30578.5843023074 6 543000 541185.571030467 1814.42896953326 7 594000 573803.30186884 20196.6981311598 8 611000 570320.793622973 40679.2063770275 9 613000 570111.629063676 42888.3709363239 10 611000 560815.840819712 50184.1591802878 11 594000 545910.169624496 48089.8303755045 12 595000 542745.225655496 52254.7743445042 13 591000 541559.05634481 49440.9436551903 14 589000 557325.316985985 31674.6830140147 15 584000 548792.510169624 35207.4898303755 16 573000 557136.133618935 15863.8663810652 17 567000 571994.880635234 -4994.88063523412 18 569000 542383.943890547 26616.0561094526 19 621000 582828.547471323 38171.452528677 20 629000 615372.123331632 13627.8766683682 21 628000 610182.221572625 17817.7784273751 22 612000 565347.188196893 46652.8118031075 23 595000 564447.499803869 30552.5001961309 24 597000 596072.817929087 927.182070912546 25 593000 601028.309526315 -8028.30952631508 26 590000 580206.748783151 9793.25121684864 27 580000 581860.111277477 -1860.11127747666 28 574000 556199.904821997 17800.0951780032 29 573000 557539.508010511 15460.4919894895 30 573000 541859.655764262 31140.3442357379 31 620000 599905.360727473 20094.6392725268 32 626000 606721.369247924 19278.6307520758 33 620000 602804.738652753 17195.2613472469 34 588000 585719.526818265 2280.47318173545 35 566000 551527.542406124 14472.4575938761 36 557000 554616.60680067 2383.39319932969 37 561000 563766.40340818 -2766.40340818043 38 549000 549460.995091706 -460.995091705588 39 532000 544935.24752624 -12935.2475262397 40 526000 530022.947659609 -4022.94765960873 41 511000 510802.966467363 197.033532637253 42 499000 524071.308622439 -25071.3086224390 43 555000 587959.081278544 -32959.0812785436 44 565000 600991.649010663 -35991.6490106632 45 542000 557790.858095971 -15790.8580959713 46 527000 594220.484294462 -67220.4842944621 47 510000 555309.906745754 -45309.9067457536 48 514000 524844.53105804 -10844.5310580401 49 517000 550958.793466068 -33958.7934660678 50 508000 572192.630281362 -64192.6302813616 51 493000 518458.697148831 -25458.6971488315 52 490000 543654.438943027 -53654.4389430268 53 469000 510241.2291892 -41241.2291891999 54 478000 512499.520692285 -34499.5206922847 55 528000 573503.70865382 -45503.70865382 56 534000 571594.064786808 -37594.0647868083 57 518000 580110.552614975 -62110.5526149746 58 506000 537896.959870669 -31896.9598706686 59 502000 549804.881419758 -47804.8814197578 60 516000 560720.818556706 -44720.8185567064 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.288046793219582 0.576093586439164 0.711953206780418 17 0.150409140518005 0.300818281036009 0.849590859481995 18 0.105648284730644 0.211296569461287 0.894351715269356 19 0.0818409163060342 0.163681832612068 0.918159083693966 20 0.0403658389598566 0.0807316779197132 0.959634161040143 21 0.0189253116510783 0.0378506233021566 0.981074688348922 22 0.0155102152532617 0.0310204305065234 0.984489784746738 23 0.00959760917660232 0.0191952183532046 0.990402390823398 24 0.00557918541323486 0.0111583708264697 0.994420814586765 25 0.00233713583125221 0.00467427166250441 0.997662864168748 26 0.00109495876911036 0.00218991753822072 0.99890504123089 27 0.000412090494866829 0.000824180989733659 0.999587909505133 28 0.000221030095481153 0.000442060190962305 0.999778969904519 29 0.000116308024324342 0.000232616048648684 0.999883691975676 30 0.000128784730184185 0.000257569460368371 0.999871215269816 31 0.000110176814618500 0.000220353629237001 0.999889823185381 32 0.000105763181571909 0.000211526363143818 0.999894236818428 33 0.000195365574665702 0.000390731149331403 0.999804634425334 34 0.00192791056060857 0.00385582112121714 0.998072089439391 35 0.0133094432534573 0.0266188865069146 0.986690556746543 36 0.0375157340866798 0.0750314681733597 0.96248426591332 37 0.0552319645120968 0.110463929024194 0.944768035487903 38 0.145608404629387 0.291216809258775 0.854391595370613 39 0.217432369811554 0.434864739623108 0.782567630188446 40 0.382733895675101 0.765467791350201 0.617266104324899 41 0.649237061682482 0.701525876635036 0.350762938317518 42 0.695509928974383 0.608980142051233 0.304490071025617 43 0.75551842095044 0.48896315809912 0.24448157904956 44 0.801921623787821 0.396156752424357 0.198078376212179 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 10 0.344827586206897 NOK 5% type I error level 15 0.517241379310345 NOK 10% type I error level 17 0.586206896551724 NOK

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 = 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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