WS 7 Model 6

*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, 23 Nov 2009 09:53:08 -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/23/t1258996566mp6z1eg2jm2747c.htm/, Retrieved Mon, 23 Nov 2009 18:16:18 +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/23/t1258996566mp6z1eg2jm2747c.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:

WS 7 Model 6

Dataseries X:

» Textbox « » Textfile « » CSV «

277128 0 277915 277103 0 277128 275037 0 277103 270150 0 275037 267140 0 270150 264993 0 267140 287259 0 264993 291186 0 287259 292300 0 291186 288186 0 292300 281477 0 288186 282656 0 281477 280190 0 282656 280408 0 280190 276836 0 280408 275216 0 276836 274352 0 275216 271311 0 274352 289802 0 271311 290726 0 289802 292300 0 290726 278506 0 292300 269826 0 278506 265861 0 269826 269034 0 265861 264176 0 269034 255198 0 264176 253353 0 255198 246057 0 253353 235372 0 246057 258556 0 235372 260993 0 258556 254663 0 260993 250643 0 254663 243422 0 250643 247105 0 243422 248541 0 247105 245039 0 248541 237080 0 245039 237085 0 237080 225554 0 237085 226839 1 225554 247934 1 226839 248333 1 247934 246969 1 248333 245098 1 246969 246263 1 245098 255765 1 246263 264319 1 255765 268347 1 264319 273046 1 268347 273963 1 273046 267430 1 273963 271993 1 267430 292710 1 271993 295881 1 292710

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 nwwmb[t] = + 6488.09269370416 + 6674.20303615999dummy_variable[t] + 0.988129051900833`y[t-1]`[t] -628.655938595416M1[t] -3332.67722537028M2[t] -6007.65350211412M3[t] -3878.64402166556M4[t] -8174.83375644826M5[t] -5655.03092893379M6[t] + 17559.0183142201M7[t] -1086.65351682104M8[t] -3948.87269678224M9[t] -8579.72869423567M10[t] -7979.60737359601M11[t] -82.2504940926742t + 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) 6488.09269370416 10361.027297 0.6262 0.534654 0.267327 dummy_variable 6674.20303615999 1763.128503 3.7854 0.000492 0.000246 `y[t-1]` 0.988129051900833 0.035945 27.4898 0 0 M1 -628.655938595416 2380.00936 -0.2641 0.792995 0.396498 M2 -3332.67722537028 2382.569038 -1.3988 0.1694 0.0847 M3 -6007.65350211412 2380.775222 -2.5234 0.015594 0.007797 M4 -3878.64402166556 2374.587875 -1.6334 0.110043 0.055021 M5 -8174.83375644826 2373.873537 -3.4437 0.001336 0.000668 M6 -5655.03092893379 2396.370695 -2.3598 0.023125 0.011562 M7 17559.0183142201 2397.254211 7.3246 0 0 M8 -1086.65351682104 2438.242907 -0.4457 0.65818 0.32909 M9 -3948.87269678224 2530.405254 -1.5606 0.126312 0.063156 M10 -8579.72869423567 2526.299992 -3.3962 0.001529 0.000765 M11 -7979.60737359601 2506.550104 -3.1835 0.002777 0.001388 t -82.2504940926742 55.23241 -1.4892 0.144095 0.072048 Multiple Linear Regression - Regression Statistics Multiple R 0.985713337178518 R-squared 0.97163078309161 Adjusted R-squared 0.961943733415575 F-TEST (value) 100.302033703338 F-TEST (DF numerator) 14 F-TEST (DF denominator) 41 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3536.77348711924 Sum Squared Residuals 512859434.666773 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 277128 280393.071720036 -3265.0717200356 2 277103 276829.142375323 273.857624677456 3 275037 274047.212378189 989.787621811412 4 270150 274052.496743317 -3902.49674331729 5 267140 264845.069837803 2294.93016219744 6 264993 264308.353725003 684.646274997167 7 287259 285318.639399633 1940.36060036708 8 291186 288592.398544123 2593.60145587690 9 292300 289528.311656884 2771.68834311621 10 288186 285915.980929155 2270.01907084478 11 281477 282368.688836182 -891.688836182172 12 282656 283636.687906483 -980.687906482825 13 280190 284090.785625986 -3900.78562598582 14 280408 278867.787603131 1540.21239686918 15 276836 276325.972965609 510.027034391299 16 275216 274843.134978575 372.865021425208 17 274352 268863.92568562 5488.07431437992 18 271311 270447.734518200 863.265481800446 19 289802 290574.63282043 -772.632820430293 20 290726 290118.204793995 607.795206005168 21 292300 288086.766363897 4213.23363610268 22 278506 284928.975000043 -6422.97500004313 23 269826 271816.59368467 -1990.59368467002 24 265861 271136.990393674 -5275.99039367413 25 269034 266508.152270199 2525.84772980077 26 264176 266857.213971013 -2681.21397101304 27 255198 259299.656266042 -4101.65626604228 28 253353 252474.992624432 878.007375567527 29 246057 246273.4542948 -216.454294800073 30 235372 241501.617065553 -6129.61706555339 31 258556 254075.256895054 4480.74310494585 32 260993 258256.118509189 2736.88149081069 33 254663 257719.719334618 -3056.71933461776 34 250643 246751.755944539 3891.24405546063 35 243422 243297.347982445 124.65201755499 36 247105 244059.424978172 3045.57502182757 37 248541 246987.797843635 1553.20215636489 38 245039 245620.479381297 -581.479381297165 39 237080 239402.824670704 -2322.82467070394 40 237085 233585.064532981 3499.93546701892 41 225554 229211.564949365 -3657.56494936523 42 226839 226929.204221479 -90.2042214785065 43 247934 251330.748802232 -3396.74880223226 44 248333 253447.408826947 -5114.40882694657 45 246969 250897.202644601 -3928.20264460112 46 245098 244836.288126262 261.711873737726 47 246263 243505.369496703 2757.6305032972 48 255765 252553.896721671 3211.10327832938 49 264319 261232.192540144 3086.80745985576 50 268347 266898.376669236 1448.62333076357 51 273046 268121.333719456 4924.66628054352 52 273963 274811.311120694 -848.311120694364 53 267430 271338.985232412 -3908.98523241206 54 271993 267321.090469766 4671.90953023428 55 292710 294961.722082650 -2251.72208265039 56 295881 296704.869325746 -823.869325746182 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 18 0.0993617772457425 0.198723554491485 0.900638222754257 19 0.0601449020684734 0.120289804136947 0.939855097931527 20 0.0580113038513331 0.116022607702666 0.941988696148667 21 0.0477403803622359 0.0954807607244717 0.952259619637764 22 0.313191229855641 0.626382459711282 0.686808770144359 23 0.214426337364735 0.42885267472947 0.785573662635265 24 0.190185693773838 0.380371387547677 0.809814306226162 25 0.325927952115075 0.65185590423015 0.674072047884925 26 0.290669230272357 0.581338460544714 0.709330769727643 27 0.306874014398059 0.613748028796118 0.693125985601941 28 0.254820822726585 0.509641645453169 0.745179177273415 29 0.227943739128197 0.455887478256395 0.772056260871803 30 0.497829875638679 0.995659751277359 0.502170124361321 31 0.669453065829806 0.661093868340387 0.330546934170194 32 0.798798480852974 0.402403038294053 0.201201519147026 33 0.764161346789607 0.471677306420785 0.235838653210393 34 0.864975360206128 0.270049279587743 0.135024639793872 35 0.776209705921172 0.447580588157655 0.223790294078828 36 0.762911867104131 0.474176265791738 0.237088132895869 37 0.730003355701021 0.539993288597958 0.269996644298979 38 0.870449982017531 0.259100035964937 0.129550017982469 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 1 0.0476190476190476 OK

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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