multiple regression, include monthly dummies

*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 11:13:01 -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/t1258654490xyi942icxr69vjp.htm/, Retrieved Thu, 19 Nov 2009 19:15:02 +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/t1258654490xyi942icxr69vjp.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:

Y= aantal bouwvergunningen X= rente

Dataseries X:

» Textbox « » Textfile « » CSV «

2360 2 2214 2 2825 2 2355 2 2333 2 3016 2 2155 2 2172 2 2150 2 2533 2 2058 2 2160 2 2260 2 2498 2 2695 2 2799 2 2947 2 2930 2 2318 2 2540 2 2570 2 2669 2 2450 2 2842 2 3440 2 2678 2 2981 2 2260 2.21 2844 2.25 2546 2.25 2456 2.45 2295 2.5 2379 2.5 2479 2.64 2057 2.75 2280 2.93 2351 3 2276 3.17 2548 3.25 2311 3.39 2201 3.5 2725 3.5 2408 3.65 2139 3.75 1898 3.75 2537 3.9 2069 4 2063 4 2524 4 2437 4 2189 4 2793 4 2074 4 2622 4 2278 4 2144 4 2427 4 2139 4 1828 4.18 2072 4.25 1800 4.25

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 Y[t] = + 2718.53693396615 -143.325735825476X[t] + 149.357889865432M1[t] + 79.583054198158M2[t] + 308.876265971366M3[t] + 174.909067479149M4[t] + 155.408839553913M5[t] + 443.408839553913M6[t] + 8.6416410616967M7[t] -52.0585868635391M8[t] -25.2585868635390M9[t] + 169.654305814339M10[t] -198.166286791274M11[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) 2718.53693396615 165.418184 16.4343 0 0 X -143.325735825476 38.433263 -3.7292 0.000507 0.000254 M1 149.357889865432 158.881256 0.9401 0.351894 0.175947 M2 79.583054198158 166.538384 0.4779 0.634915 0.317457 M3 308.876265971366 166.482461 1.8553 0.069699 0.034849 M4 174.909067479149 166.264321 1.052 0.29807 0.149035 M5 155.408839553913 166.184078 0.9352 0.354386 0.177193 M6 443.408839553913 166.184078 2.6682 0.01037 0.005185 M7 8.6416410616967 166.027835 0.052 0.958705 0.479353 M8 -52.0585868635391 165.974178 -0.3137 0.755142 0.377571 M9 -25.2585868635390 165.974178 -0.1522 0.87968 0.43984 M10 169.654305814339 165.893118 1.0227 0.311589 0.155795 M11 -198.166286791274 165.831295 -1.195 0.237963 0.118982 Multiple Linear Regression - Regression Statistics Multiple R 0.677027504049389 R-squared 0.458366241239345 Adjusted R-squared 0.322957801549182 F-TEST (value) 3.38506404983442 F-TEST (DF numerator) 12 F-TEST (DF denominator) 48 p-value 0.00125516766011968 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 262.184694437486 Sum Squared Residuals 3299559.07186933 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 2360 2581.24335218062 -221.243352180622 2 2214 2511.46851651335 -297.468516513352 3 2825 2740.76172828656 84.23827171344 4 2355 2606.79452979434 -251.794529794343 5 2333 2587.29430186911 -254.294301869108 6 3016 2875.29430186911 140.705698130893 7 2155 2440.52710337689 -285.527103376891 8 2172 2379.82687545165 -207.826875451655 9 2150 2406.62687545165 -256.626875451655 10 2533 2601.53976812953 -68.5397681295326 11 2058 2233.71917552392 -175.71917552392 12 2160 2431.88546231519 -271.885462315194 13 2260 2581.24335218063 -321.243352180626 14 2498 2511.46851651335 -13.4685165133519 15 2695 2740.76172828656 -45.7617282865597 16 2799 2606.79452979434 192.205470205657 17 2947 2587.29430186911 359.705698130893 18 2930 2875.29430186911 54.7056981308925 19 2318 2440.52710337689 -122.527103376891 20 2540 2379.82687545165 160.173124548345 21 2570 2406.62687545165 163.373124548345 22 2669 2601.53976812953 67.4602318704673 23 2450 2233.71917552392 216.280824476080 24 2842 2431.88546231519 410.114537684806 25 3440 2581.24335218063 858.756647819374 26 2678 2511.46851651335 166.531483486648 27 2981 2740.76172828656 240.238271713440 28 2260 2576.69612527099 -316.696125270993 29 2844 2551.46286791274 292.537132087262 30 2546 2839.46286791274 -293.462867912738 31 2456 2376.03052225543 79.9694777445737 32 2295 2308.16400753892 -13.1640075389167 33 2379 2334.96400753892 44.0359924610832 34 2479 2509.81129720123 -30.8112972012277 35 2057 2126.22487365481 -69.2248736548125 36 2280 2298.5925279975 -18.5925279975007 37 2351 2437.91761635515 -86.9176163551494 38 2276 2343.77740559754 -67.7774055975444 39 2548 2561.60455850471 -13.6045585047140 40 2311 2407.57175699693 -96.5717569969307 41 2201 2372.30569813089 -171.305698130893 42 2725 2660.30569813089 64.6943018691073 43 2408 2204.03963926485 203.960360735145 44 2139 2129.00683775707 9.9931622429289 45 1898 2155.80683775707 -257.806837757071 46 2537 2329.22087006113 207.779129938873 47 2069 1947.06770387297 121.932296127033 48 2063 2145.23399066424 -82.2339906642408 49 2524 2294.59188052967 229.408119470327 50 2437 2224.8170448624 212.182955137601 51 2189 2454.11025663561 -265.110256635607 52 2793 2320.14305814339 472.85694185661 53 2074 2300.64283021815 -226.642830218154 54 2622 2588.64283021815 33.3571697818456 55 2278 2153.87563172594 124.124368274062 56 2144 2093.1754038007 50.824596199298 57 2427 2119.9754038007 307.024596199298 58 2139 2314.88829647858 -175.888296478580 59 1828 1921.26907142438 -93.2690714243812 60 2072 2109.40255670787 -37.4025567078717 61 1800 2258.76044657330 -458.760446573304 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.473008451142425 0.94601690228485 0.526991548857575 17 0.696647234174036 0.606705531651929 0.303352765825964 18 0.561486930091036 0.877026139817928 0.438513069908964 19 0.473286422109878 0.946572844219755 0.526713577890122 20 0.450255996155234 0.900511992310467 0.549744003844766 21 0.450911106048382 0.901822212096764 0.549088893951618 22 0.350202486683407 0.700404973366814 0.649797513316593 23 0.336242730367431 0.672485460734862 0.663757269632569 24 0.496316087284258 0.992632174568516 0.503683912715742 25 0.97483569161869 0.0503286167626209 0.0251643083813104 26 0.964367321088165 0.0712653578236699 0.0356326789118350 27 0.964416677022926 0.0711666459541487 0.0355833229770743 28 0.966604763403013 0.0667904731939735 0.0333952365969867 29 0.983555442586086 0.0328891148278272 0.0164445574139136 30 0.981332000788403 0.037335998423194 0.018667999211597 31 0.972852252736674 0.0542954945266524 0.0271477472633262 32 0.952903453957414 0.0941930920851721 0.0470965460425861 33 0.923372004897764 0.153255990204472 0.076627995102236 34 0.880164326957626 0.239671346084749 0.119835673042374 35 0.82319537435589 0.353609251288219 0.176804625644109 36 0.751349077168062 0.497301845663876 0.248650922831938 37 0.67053439752496 0.658931204950079 0.329465602475039 38 0.596532193966851 0.806935612066298 0.403467806033149 39 0.534210602351874 0.931578795296253 0.465789397648126 40 0.614490732838302 0.771018534323397 0.385509267161698 41 0.504602856183196 0.990794287633608 0.495397143816804 42 0.390842871997775 0.78168574399555 0.609157128002225 43 0.292795325839024 0.585590651678047 0.707204674160976 44 0.189023960671303 0.378047921342606 0.810976039328697 45 0.515444256287256 0.969111487425488 0.484555743712744 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 0.0666666666666667 NOK 10% type I error level 8 0.266666666666667 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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