WS 7 Multiple regression 3

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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: Thu, 19 Nov 2009 12:43:57 -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/t1258659900vv9e67p8iy90w3m.htm/, Retrieved Thu, 19 Nov 2009 20:45:12 +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/19/t1258659900vv9e67p8iy90w3m.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:

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Dataseries X:

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108.01 102.9 101.21 97.4 119.93 111.4 94.76 87.4 95.26 96.8 117.96 114.1 115.86 110.3 111.44 103.9 108.16 101.6 108.77 94.6 109.45 95.9 124.83 104.7 115.31 102.8 109.49 98.1 124.24 113.9 92.85 80.9 98.42 95.7 120.88 113.2 111.72 105.9 116.1 108.8 109.37 102.3 111.65 99 114.29 100.7 133.68 115.5 114.27 100.7 126.49 109.9 131 114.6 104 85.4 108.88 100.5 128.48 114.8 132.44 116.5 128.04 112.9 116.35 102 120.93 106 118.59 105.3 133.1 118.8 121.05 106.1 127.62 109.3 135.44 117.2 114.88 92.5 114.34 104.2 128.85 112.5 138.9 122.4 129.44 113.3 114.96 100 127.98 110.7 127.03 112.8 128.75 109.8 137.91 117.3 128.37 109.1 135.9 115.9 122.19 96 113.08 99.8 136.2 116.8 138 115.7 115.24 99.4 110.95 94.3 99.23 91 102.39 93.2 112.67 103.1

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] = -24.6219614667864 + 1.31422861183913X[t] + 0.396153803546174M1[t] + 1.12802237964250M2[t] -1.30919291896518M3[t] + 9.3338218086357M4[t] -4.98132953523177M5[t] -4.23025703750864M6[t] -3.3337553621986M7[t] -2.29447514335494M8[t] -0.545258879251453M9[t] + 0.748405068033284M10[t] -0.519582457705025M11[t] + 0.17120575811066t + 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) -24.6219614667864 10.456775 -2.3546 0.022864 0.011432 X 1.31422861183913 0.096083 13.678 0 0 M1 0.396153803546174 2.346093 0.1689 0.86665 0.433325 M2 1.12802237964250 2.363136 0.4773 0.635379 0.31769 M3 -1.30919291896518 2.367355 -0.553 0.582928 0.291464 M4 9.3338218086357 3.082101 3.0284 0.004022 0.002011 M5 -4.98132953523177 2.515298 -1.9804 0.053656 0.026828 M6 -4.23025703750864 2.348809 -1.801 0.078257 0.039128 M7 -3.3337553621986 2.343343 -1.4226 0.161584 0.080792 M8 -2.29447514335494 2.316977 -0.9903 0.327214 0.163607 M9 -0.545258879251453 2.499253 -0.2182 0.828263 0.414131 M10 0.748405068033284 2.493823 0.3001 0.76545 0.382725 M11 -0.519582457705025 2.450689 -0.212 0.833032 0.416516 t 0.17120575811066 0.029137 5.876 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.962264891450104 R-squared 0.92595372131748 Adjusted R-squared 0.905027599081115 F-TEST (value) 44.2487007797554 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.64189471923847 Sum Squared Residuals 610.116268716785 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 108.01 111.179522253117 -3.16952225311654 2 101.21 104.854339222208 -3.64433922220817 3 119.93 120.987530247459 -1.05753024745896 4 94.76 100.260264049031 -5.50026404903146 5 95.26 98.4700674145624 -3.21006741456242 6 117.96 122.128500655213 -4.16850065521311 7 115.86 118.202139363645 -2.34213936364512 8 111.44 111.001562224829 0.438437775170948 9 108.16 109.899258439813 -1.73925843981319 10 108.77 102.164527862335 6.60547213766529 11 109.45 102.776243290098 6.67375670990207 12 124.83 115.032243290098 9.79775670990208 13 115.31 113.102568489260 2.20743151073959 14 109.49 107.828768347823 1.66123165217649 15 124.24 126.327570874385 -2.0875708743847 16 92.85 93.772247169405 -0.92224716940508 17 98.42 99.0788850388673 -0.658885038867318 18 120.88 123.000164001886 -2.12016400188582 19 111.72 114.474002568881 -2.75400256888090 20 116.1 119.495751520169 -3.39575152016868 21 109.37 112.873687565428 -3.5036875654285 22 111.65 110.001602851755 1.64839714824522 23 114.29 111.139009724254 3.15099027574635 24 133.68 131.280381395288 2.3996186047116 25 114.27 112.397157501726 1.87284249827382 26 126.49 125.391135064853 1.09886493514687 27 131 129.302 1.69800000000001 28 104 101.740745020009 2.25925497999095 29 108.88 107.441651473023 1.43834852697696 30 128.48 127.157398878156 1.32260112184365 31 132.44 130.459294951704 1.98070504829644 32 128.04 126.938557926037 1.10144207396297 33 116.35 114.533888079205 1.81611192079531 34 120.93 121.255672231957 -0.325672231956583 35 118.59 119.238930436042 -0.648930436041546 36 133.1 137.671804911685 -4.57180491168545 37 121.05 121.548461102985 -0.498461102985367 38 127.62 126.657066995078 0.962933004922446 39 135.44 134.773463488110 0.666536511890348 40 114.88 113.126237261395 1.75376273860523 41 114.34 114.358766434156 -0.0187664341557281 42 128.85 126.189142168254 2.66085783174573 43 138.9 140.267712858882 -1.36771285888232 44 129.44 129.518718468101 -0.078718468100583 45 114.96 113.959899952854 1.00010004714564 46 127.98 129.487015804928 -1.50701580492840 47 127.03 131.150114122163 -4.12011412216291 48 128.75 127.898216502461 0.851783497538777 49 137.91 138.322290652912 -0.412290652911507 50 128.37 128.448690370038 -0.0786903700376452 51 135.9 135.119435390047 0.780564609953298 52 122.19 119.780506500160 2.40949349984037 53 113.08 110.630629639391 2.44937036060851 54 136.2 133.894794296490 2.30520570350956 55 138 133.516850256888 4.48314974311191 56 115.24 113.305409860865 1.93459013913534 57 110.95 108.523265962699 2.42673403730075 58 99.23 105.651181249026 -6.42118124902553 59 102.39 107.445702427444 -5.05570242744397 60 112.67 121.147353900467 -8.47735390046699 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.292793070314049 0.585586140628098 0.707206929685951 18 0.183797476376682 0.367594952753364 0.816202523623318 19 0.259464128657442 0.518928257314883 0.740535871342558 20 0.365481685150644 0.730963370301287 0.634518314849357 21 0.457043150021585 0.914086300043169 0.542956849978415 22 0.453385716954363 0.906771433908725 0.546614283045637 23 0.432420180365512 0.864840360731024 0.567579819634488 24 0.445907366472363 0.891814732944727 0.554092633527637 25 0.359559005840081 0.719118011680162 0.640440994159919 26 0.70773598625288 0.58452802749424 0.29226401374712 27 0.64481626533171 0.71036746933658 0.35518373466829 28 0.628282612647919 0.743434774704162 0.371717387352081 29 0.56321033562707 0.87357932874586 0.43678966437293 30 0.501133948608053 0.997732102783893 0.498866051391947 31 0.508408052509954 0.983183894980093 0.491591947490046 32 0.420980634509848 0.841961269019696 0.579019365490152 33 0.33310628198934 0.66621256397868 0.66689371801066 34 0.354402848397587 0.708805696795174 0.645597151602413 35 0.454920832039858 0.909841664079716 0.545079167960142 36 0.60067610920617 0.798647781587661 0.399323890793830 37 0.507555248091256 0.984889503817487 0.492444751908744 38 0.407142607527302 0.814285215054605 0.592857392472698 39 0.296089619776318 0.592179239552637 0.703910380223682 40 0.219114401106056 0.438228802212112 0.780885598893944 41 0.151488906838398 0.302977813676796 0.848511093161602 42 0.0855601077920609 0.171120215584122 0.91443989220794 43 0.140141744315776 0.280283488631551 0.859858255684224 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 0 0 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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