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R Software Module: rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Mon, 24 Nov 2008 11:30:03 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Nov/24/t1227551461u0vqex6t58qe3v8.htm/, Retrieved Mon, 24 Nov 2008 18:31:10 +0000

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/2008/Nov/24/t1227551461u0vqex6t58qe3v8.htm/}, year = {2008}, } @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 = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

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Dataseries X:

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12300.00 0.00 12092.80 0.00 12380.80 0.00 12196.90 0.00 9455.00 0.00 13168.00 0.00 13427.90 0.00 11980.50 0.00 11884.80 0.00 11691.70 0.00 12233.80 0.00 14341.40 0.00 13130.70 0.00 12421.10 0.00 14285.80 0.00 12864.60 0.00 11160.20 0.00 14316.20 0.00 14388.70 0.00 14013.90 0.00 13419.00 0.00 12769.60 0.00 13315.50 0.00 15332.90 0.00 14243.00 0.00 13824.40 0.00 14962.90 0.00 13202.90 0.00 12199.00 0.00 15508.90 0.00 14199.80 0.00 15169.60 0.00 14058.00 0.00 13786.20 0.00 14147.90 0.00 16541.70 0.00 13587.50 0.00 15582.40 0.00 15802.80 0.00 14130.50 0.00 12923.20 0.00 15612.20 1.00 16033.70 1.00 16036.60 1.00 14037.80 1.00 15330.60 1.00 15038.30 1.00 17401.80 1.00 14992.50 1.00 16043.70 1.00 16929.60 1.00 15921.30 1.00 14417.20 1.00 15961.00 1.00 17851.90 1.00 16483.90 1.00 14215.50 1.00 17429.70 1.00 17839.50 1.00 17629.20 1.00

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 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation x[t] = + 13325.2037950664 + 16.9434535104332y[t] -1703.83777988615M1[t] -1442.73719165085M2[t] -644.276603415561M3[t] -1934.45601518026M4[t] -3647.81542694497M5[t] -849.903529411764M6[t] -663.802941176471M7[t] -1188.34235294117M8[t] -2483.26176470588M9[t] -1885.76117647059M10[t] -1653.36058823529M11[t] + 81.039411764706t + 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) 13325.2037950664 339.127633 39.2926 0 0 y 16.9434535104332 292.054931 0.058 0.953988 0.476994 M1 -1703.83777988615 390.608938 -4.362 7.2e-05 3.6e-05 M2 -1442.73719165085 389.903157 -3.7002 0.000574 0.000287 M3 -644.276603415561 389.353331 -1.6547 0.104787 0.052393 M4 -1934.45601518026 388.960123 -4.9734 1e-05 5e-06 M5 -3647.81542694497 388.724008 -9.3841 0 0 M6 -849.903529411764 389.923412 -2.1797 0.034438 0.017219 M7 -663.802941176471 389.059097 -1.7062 0.094719 0.04736 M8 -1188.34235294117 388.350499 -3.06 0.003687 0.001843 M9 -2483.26176470588 387.798473 -6.4035 0 0 M10 -1885.76117647059 387.403687 -4.8677 1.4e-05 7e-06 M11 -1653.36058823529 387.166622 -4.2704 9.7e-05 4.8e-05 t 81.039411764706 7.823544 10.3584 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.9542519941186 R-squared 0.910596868279325 Adjusted R-squared 0.885330765836525 F-TEST (value) 36.0402586960473 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 612.039183841238 Sum Squared Residuals 17231230.2776242 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 12300 11702.405426945 597.594573054989 2 12092.8 12044.5454269450 48.2545730550292 3 12380.8 12924.0454269450 -543.245426944971 4 12196.9 11714.9054269450 481.994573055034 5 9455 10082.5854269450 -627.585426944965 6 13168 12961.5367362429 206.463263757115 7 13427.9 13228.6767362429 199.223263757114 8 11980.5 12785.1767362429 -804.676736242883 9 11884.8 11571.2967362429 313.503263757121 10 11691.7 12249.8367362429 -558.136736242882 11 12233.8 12563.2767362429 -329.476736242883 12 14341.4 14297.6767362429 43.7232637571157 13 13130.7 12674.8783681214 455.82163187857 14 12421.1 13017.0183681214 -595.918368121441 15 14285.8 13896.5183681214 389.28163187856 16 12864.6 12687.3783681214 177.221631878559 17 11160.2 11055.0583681214 105.141631878559 18 14316.2 13934.0096774194 382.190322580647 19 14388.7 14201.1496774194 187.550322580647 20 14013.9 13757.6496774194 256.250322580645 21 13419 12543.7696774194 875.230322580645 22 12769.6 13222.3096774194 -452.709677419354 23 13315.5 13535.7496774194 -220.249677419354 24 15332.9 15270.1496774194 62.7503225806468 25 14243 13647.3513092979 595.648690702097 26 13824.4 13989.4913092979 -165.091309297913 27 14962.9 14868.9913092979 93.9086907020875 28 13202.9 13659.8513092979 -456.951309297914 29 12199 12027.5313092979 171.468690702085 30 15508.9 14906.4826185958 602.417381404173 31 14199.8 15173.6226185958 -973.822618595827 32 15169.6 14730.1226185958 439.477381404173 33 14058 13516.2426185958 541.757381404172 34 13786.2 14194.7826185958 -408.582618595827 35 14147.9 14508.2226185958 -360.322618595827 36 16541.7 16242.6226185958 299.077381404175 37 13587.5 14619.8242504744 -1032.32425047438 38 15582.4 14961.9642504744 620.435749525614 39 15802.8 15841.4642504744 -38.6642504743856 40 14130.5 14632.3242504744 -501.824250474387 41 12923.2 13000.0042504744 -76.804250474387 42 15612.2 15895.8990132827 -283.69901328273 43 16033.7 16163.0390132827 -129.339013282731 44 16036.6 15719.5390132827 317.060986717268 45 14037.8 14505.6590132827 -467.859013282734 46 15330.6 15184.1990132827 146.400986717268 47 15038.3 15497.6390132827 -459.339013282732 48 17401.8 17232.0390132827 169.760986717268 49 14992.5 15609.2406451613 -616.740645161281 50 16043.7 15951.3806451613 92.3193548387102 51 16929.6 16830.8806451613 98.7193548387087 52 15921.3 15621.7406451613 299.559354838707 53 14417.2 13989.4206451613 427.779354838708 54 15961 16868.3719544592 -907.371954459204 55 17851.9 17135.5119544592 716.388045540797 56 16483.9 16692.0119544592 -208.111954459204 57 14215.5 15478.1319544592 -1262.63195445921 58 17429.7 16156.6719544592 1273.02804554080 59 17839.5 16470.1119544592 1369.38804554080 60 17629.2 18204.5119544592 -575.311954459204 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.44225143605972 0.88450287211944 0.55774856394028 18 0.277006389721742 0.554012779443485 0.722993610278257 19 0.159072779215257 0.318145558430514 0.840927220784743 20 0.17069767944704 0.34139535889408 0.82930232055296 21 0.134034607184641 0.268069214369283 0.865965392815359 22 0.0831425497042519 0.166285099408504 0.916857450295748 23 0.0462800939528835 0.0925601879057671 0.953719906047116 24 0.0244326389856867 0.0488652779713734 0.975567361014313 25 0.0223327101132939 0.0446654202265878 0.977667289886706 26 0.0117800198245673 0.0235600396491346 0.988219980175433 27 0.00550299456241831 0.0110059891248366 0.994497005437582 28 0.0125419693823914 0.0250839387647828 0.987458030617609 29 0.00697165519667867 0.0139433103933573 0.993028344803321 30 0.00692988539233636 0.0138597707846727 0.993070114607664 31 0.0376790766276324 0.0753581532552649 0.962320923372368 32 0.0334662524010653 0.0669325048021306 0.966533747598935 33 0.0721997833845172 0.144399566769034 0.927800216615483 34 0.0598529598874147 0.119705919774829 0.940147040112585 35 0.0444360818149352 0.0888721636298703 0.955563918185065 36 0.0370474325466691 0.0740948650933382 0.96295256745333 37 0.110616733451491 0.221233466902983 0.889383266548509 38 0.130114196364363 0.260228392728726 0.869885803635637 39 0.0851129226377037 0.170225845275407 0.914887077362296 40 0.0554282482483351 0.110856496496670 0.944571751751665 41 0.0281064533189419 0.0562129066378839 0.971893546681058 42 0.0197155492128057 0.0394310984256114 0.980284450787194 43 0.0115817181577184 0.0231634363154367 0.988418281842282 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 9 0.333333333333333 NOK 10% type I error level 15 0.555555555555556 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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