MLR

*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: Wed, 26 Nov 2008 11:25:12 -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/26/t1227723952ojt12ys9pek2fni.htm/, Retrieved Wed, 26 Nov 2008 18:26:01 +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/26/t1227723952ojt12ys9pek2fni.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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User-defined keywords:

MLR

Dataseries X:

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147768 0 137507 0 136919 0 136151 0 133001 0 125554 0 119647 0 114158 0 116193 0 152803 0 161761 0 160942 0 149470 0 139208 0 134588 0 130322 0 126611 0 122401 0 117352 0 112135 0 112879 0 148729 0 157230 0 157221 0 146681 0 136524 0 132111 1 125326 1 122716 1 116615 1 113719 1 110737 1 112093 1 143565 1 149946 1 149147 1 134339 1 122683 1 115614 1 116566 1 111272 1 104609 1 101802 1 94542 1 93051 1 124129 1 130374 1 123946 1 114971 1 105531 1 104919 0 104782 0 101281 0 94545 0 93248 0 84031 0 87486 0 115867 0 120327 0 117008 0 108811 0

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 jonger_dan_25[t] = + 167547.677641278 + 3044.85012285012plan[t] -11542.1457821457M1[t] -20893.5382473383M2[t] -23600.8044226044M3[t] -25048.4705978706M4[t] -27948.5367731368M5[t] -33426.8029484030M6[t] -36264.8691236691M7[t] -41544.7352989353M8[t] -39571.8014742015M9[t] -6140.46764946765M10[t] + 1521.66617526617M11[t] -753.133824733826t + 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) 167547.677641278 2597.099576 64.5134 0 0 plan 3044.85012285012 1396.763574 2.1799 0.034306 0.017153 M1 -11542.1457821457 3027.959204 -3.8119 4e-04 2e-04 M2 -20893.5382473383 3181.007092 -6.5682 0 0 M3 -23600.8044226044 3176.391658 -7.4301 0 0 M4 -25048.4705978706 3172.256368 -7.8961 0 0 M5 -27948.5367731368 3168.6031 -8.8205 0 0 M6 -33426.8029484030 3165.433524 -10.5599 0 0 M7 -36264.8691236691 3162.749095 -11.4662 0 0 M8 -41544.7352989353 3160.551047 -13.1448 0 0 M9 -39571.8014742015 3158.840397 -12.5273 0 0 M10 -6140.46764946765 3157.617937 -1.9447 0.057815 0.028907 M11 1521.66617526617 3156.884234 0.482 0.632032 0.316016 t -753.133824733826 39.297885 -19.1647 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.972916930982472 R-squared 0.946567354592352 Adjusted R-squared 0.931788112245556 F-TEST (value) 64.0470825486901 F-TEST (DF numerator) 13 F-TEST (DF denominator) 47 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4991.08548841622 Sum Squared Residuals 1170813914.57591 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 147768 155252.398034398 -7484.39803439766 2 137507 145147.871744472 -7640.87174447174 3 136919 141687.471744472 -4768.47174447178 4 136151 139486.671744472 -3335.67174447176 5 133001 135833.471744472 -2832.47174447177 6 125554 129602.071744472 -4048.0717444718 7 119647 126010.871744472 -6363.8717444717 8 114158 119977.871744472 -5819.87174447178 9 116193 121197.671744472 -5004.67174447175 10 152803 153875.871744472 -1072.87174447176 11 161761 160784.871744472 976.128255528244 12 160942 158510.071744472 2431.92825552822 13 149470 146214.792137592 3255.20786240776 14 139208 136110.265847666 3097.73415233414 15 134588 132649.865847666 1938.13415233414 16 130322 130449.065847666 -127.06584766586 17 126611 126795.865847666 -184.865847665857 18 122401 120564.465847666 1836.53415233415 19 117352 116973.265847666 378.734152334127 20 112135 110940.265847666 1194.73415233415 21 112879 112160.065847666 718.934152334142 22 148729 144838.265847666 3890.73415233414 23 157230 151747.265847666 5482.73415233414 24 157221 149472.465847666 7748.53415233414 25 146681 137177.186240786 9503.81375921367 26 136524 127072.65995086 9451.34004914004 27 132111 126657.11007371 5453.88992628993 28 125326 124456.31007371 869.689926289923 29 122716 120803.11007371 1912.88992628993 30 116615 114571.71007371 2043.28992628994 31 113719 110980.51007371 2738.48992628991 32 110737 104947.51007371 5789.48992628993 33 112093 106167.31007371 5925.68992628993 34 143565 138845.51007371 4719.48992628993 35 149946 145754.51007371 4191.48992628993 36 149147 143479.71007371 5667.28992628993 37 134339 131184.430466831 3154.56953316946 38 122683 121079.904176904 1603.09582309583 39 115614 117619.504176904 -2005.50417690416 40 116566 115418.704176904 1147.29582309583 41 111272 111765.504176904 -493.504176904163 42 104609 105534.104176904 -925.104176904158 43 101802 101942.904176904 -140.904176904178 44 94542 95909.9041769042 -1367.90417690416 45 93051 97129.7041769042 -4078.70417690417 46 124129 129807.904176904 -5678.90417690417 47 130374 136716.904176904 -6342.90417690417 48 123946 134442.104176904 -10496.1041769042 49 114971 122146.824570025 -7175.82457002464 50 105531 112042.298280098 -6511.29828009826 51 104919 105537.048157248 -618.04815724813 52 104782 103336.248157248 1445.75184275186 53 101281 99683.0481572481 1597.95184275186 54 94545 93451.6481572481 1093.35184275187 55 93248 89860.4481572481 3387.55184275185 56 84031 83827.4481572481 203.551842751858 57 87486 85047.2481572481 2438.75184275185 58 115867 117725.448157248 -1858.44815724815 59 120327 124634.448157248 -4307.44815724814 60 117008 122359.648157248 -5351.64815724814 61 108811 110064.368550369 -1253.36855036860 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.391964278192348 0.783928556384695 0.608035721807652 18 0.24791615883684 0.49583231767368 0.75208384116316 19 0.173804535195291 0.347609070390582 0.826195464804709 20 0.131452561229753 0.262905122459505 0.868547438770247 21 0.146787579619812 0.293575159239624 0.853212420380188 22 0.135675361531110 0.271350723062220 0.86432463846889 23 0.121894414622521 0.243788829245042 0.878105585377479 24 0.0830739549435725 0.166147909887145 0.916926045056428 25 0.0798565806582654 0.159713161316531 0.920143419341735 26 0.103083729561833 0.206167459123666 0.896916270438167 27 0.0633933182598389 0.126786636519678 0.936606681740161 28 0.127688771932574 0.255377543865147 0.872311228067426 29 0.150565442020736 0.301130884041472 0.849434557979264 30 0.197084188764035 0.39416837752807 0.802915811235965 31 0.49520335411382 0.99040670822764 0.50479664588618 32 0.57186009778743 0.85627980442514 0.42813990221257 33 0.607334805467866 0.785330389064267 0.392665194532133 34 0.547120253605851 0.905759492788299 0.452879746394149 35 0.557225547231698 0.885548905536604 0.442774452768302 36 0.893362378283061 0.213275243433879 0.106637621716939 37 0.92017626893806 0.15964746212388 0.07982373106194 38 0.932903739065233 0.134192521869533 0.0670962609347665 39 0.973617748628462 0.0527645027430763 0.0263822513715381 40 0.980237635421983 0.039524729156034 0.019762364578017 41 0.972954628539688 0.0540907429206243 0.0270453714603121 42 0.963243897959447 0.0735122040811052 0.0367561020405526 43 0.917628222371783 0.164743555256434 0.0823717776282168 44 0.910224259537202 0.179551480925596 0.0897757404627982 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 1 0.0357142857142857 OK 10% type I error level 4 0.142857142857143 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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