ws77777

*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: Fri, 20 Nov 2009 05:28:48 -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/20/t1258720196sm5uhx6m9of3rzz.htm/, Retrieved Fri, 20 Nov 2009 13:30:09 +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/20/t1258720196sm5uhx6m9of3rzz.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:

Dataseries X:

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101,8612953 1 118,1540031 105,5073942 95,84395716 100 109,8419174 1 101,8612953 118,1540031 105,5073942 95,84395716 105,6348802 1 109,8419174 101,8612953 118,1540031 105,5073942 112,927078 1 105,6348802 109,8419174 101,8612953 118,1540031 133,0698623 1 112,927078 105,6348802 109,8419174 101,8612953 125,6756757 1 133,0698623 112,927078 105,6348802 109,8419174 146,736359 1 125,6756757 133,0698623 112,927078 105,6348802 142,5803162 1 146,736359 125,6756757 133,0698623 112,927078 106,1448241 1 142,5803162 146,736359 125,6756757 133,0698623 126,5170831 1 106,1448241 142,5803162 146,736359 125,6756757 132,7893932 1 126,5170831 106,1448241 142,5803162 146,736359 121,2391637 1 132,7893932 126,5170831 106,1448241 142,5803162 114,5079041 1 121,2391637 132,7893932 126,5170831 106,1448241 146,1499235 1 114,5079041 121,2391637 132,7893932 126,5170831 146,1244263 1 146,1499235 114,5079041 121,2391637 132,7893932 128,5058644 1 146,1244263 146,1499235 114,5079041 121,2391637 155,5838858 1 128,5058644 146,1244 etc...

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 Y[t] = + 53.8696872319329 + 15.8488814290603X[t] + 0.133329923008086Y1[t] + 0.0532221071152637Y2[t] + 0.273745155025843Y3[t] + 0.0670592193928907Y4[t] -18.6035909016196M1[t] -3.10158370166338M2[t] -11.8809514270766M3[t] -7.94282530553286M4[t] + 3.99151966561568M5[t] -10.0326693378833M6[t] -3.40836044891388M7[t] + 0.564263857054042M8[t] -18.5636243442575M9[t] -9.04511375520523M10[t] -9.35771026063743M11[t] -0.174195328979543t + 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) 53.8696872319329 22.794464 2.3633 0.023333 0.011666 X 15.8488814290603 5.162977 3.0697 0.003943 0.001971 Y1 0.133329923008086 0.142827 0.9335 0.356451 0.178226 Y2 0.0532221071152637 0.133863 0.3976 0.693159 0.34658 Y3 0.273745155025843 0.131522 2.0814 0.04419 0.022095 Y4 0.0670592193928907 0.141487 0.474 0.638241 0.31912 M1 -18.6035909016196 8.435979 -2.2053 0.033559 0.016779 M2 -3.10158370166338 8.170224 -0.3796 0.706341 0.35317 M3 -11.8809514270766 8.303704 -1.4308 0.16066 0.08033 M4 -7.94282530553286 7.447672 -1.0665 0.292934 0.146467 M5 3.99151966561568 8.380269 0.4763 0.636588 0.318294 M6 -10.0326693378833 7.867426 -1.2752 0.209974 0.104987 M7 -3.40836044891388 8.056909 -0.423 0.674654 0.337327 M8 0.564263857054042 8.458629 0.0667 0.947163 0.473582 M9 -18.5636243442575 8.116399 -2.2872 0.027844 0.013922 M10 -9.04511375520523 8.747493 -1.034 0.307661 0.153831 M11 -9.35771026063743 8.863449 -1.0558 0.297742 0.148871 t -0.174195328979543 0.126072 -1.3817 0.175129 0.087564 Multiple Linear Regression - Regression Statistics Multiple R 0.829265907056123 R-squared 0.687681944605614 Adjusted R-squared 0.547960709297599 F-TEST (value) 4.92181408996007 F-TEST (DF numerator) 17 F-TEST (DF denominator) 38 p-value 2.20257367186116e-05 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 10.7884149852318 Sum Squared Residuals 4422.81611995582 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 101.8612953 105.252313252722 -3.39101795272242 2 109.8419174 121.447516902636 -11.6055995026361 3 105.6348802 116.800847797100 -11.1659675971001 4 112.927078 116.816622066248 -3.88954406624821 5 133.0698623 130.417212862257 2.65264943774267 6 125.6756757 118.676088779866 6.99958692013424 7 146.736359 126.926460620036 19.8098983799643 8 142.5803162 139.142373391638 3.43794280836247 9 106.1448241 119.733695571768 -13.5888714717678 10 126.5170831 129.268287753776 -2.75120465377585 11 132.7893932 129.833170381390 2.95622281860982 12 121.2391637 130.684486067153 -9.44532236715297 13 114.5079041 113.834005726355 0.673898373644709 14 146.1499235 130.732774007966 15.4171494920339 15 146.1244263 122.898583998578 23.2258423014216 16 128.5058644 125.725971120480 2.77989327952023 17 155.5838858 143.346138737976 12.2377470620241 18 125.0382458 133.935277311324 -8.89703151132393 19 136.8944416 132.929186616325 3.9652549836753 20 142.2233554 142.913688100608 -0.690332700608349 21 117.7715451 118.407229980460 -0.635684880459542 22 120.627231 125.972212659928 -5.34498165992803 23 127.7664457 126.818623909367 0.947821790632525 24 135.1096379 130.769783606576 4.3398542934241 25 105.7113717 112.493039544058 -6.7816678440582 26 117.9245283 126.437828509954 -8.51330020995356 27 120.754717 120.036920464059 0.71779653594113 28 107.572667 117.273005825247 -9.70033882524707 29 130.4436512 128.798090025921 1.64556117407938 30 107.2157063 118.541270971202 -11.3255646712015 31 105.0739419 119.692914321110 -14.6189724211104 32 130.1121877 127.346384976435 2.76580272356536 33 109.6379398 106.443832586220 3.19410721378048 34 116.7261601 112.246960669281 4.47919943071924 35 97.11881693 102.477150087142 -5.35833315714248 36 140.8975013 121.346869965567 19.5506313344331 37 108.2865885 107.929927116026 0.356661383973961 38 97.65425803 100.498756218487 -2.8444981884867 39 112.0346762 114.910194908369 -2.87551870836887 40 123.0494646 114.034275737134 9.01518886286626 41 112.4171341 122.930971115977 -10.5138370159773 42 116.4966854 111.124783244252 5.3719021557483 43 104.6914839 121.532532607381 -16.8410487073806 44 122.2335543 121.802191444423 0.431362855576731 45 99.79602244 88.7655733015532 11.0304491384468 46 96.71086181 93.0938749270153 3.61698688298465 47 112.3151453 110.860856752100 1.45428854790014 48 102.5497195 116.994882760704 -14.4451632607043 49 104.5385008 95.396374760838 9.14212603916197 50 122.0805711 114.534322690958 7.54624840904241 51 80.64762876 90.5497812918938 -9.90215253189376 52 91.40744518 89.6126444308912 1.7948007491088 53 99.51555329 105.537673947869 -6.02212065786882 54 106.527282 98.676174893357 7.85110710664293 55 98.49566548 90.8107977151485 7.68486776485149 56 106.7567568 112.701532486896 -5.94477568689619 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.928239601615206 0.143520796769588 0.0717603983847939 22 0.928767890427032 0.142464219145937 0.0712321095729685 23 0.878340022418805 0.243319955162390 0.121659977581195 24 0.82777064227862 0.344458715442759 0.172229357721379 25 0.811051026809998 0.377897946380003 0.188948973190002 26 0.752190062655804 0.495619874688392 0.247809937344196 27 0.658220725469022 0.683558549061955 0.341779274530978 28 0.594333300686514 0.811333398626973 0.405666699313486 29 0.48837974109318 0.97675948218636 0.51162025890682 30 0.446401505846252 0.892803011692504 0.553598494153748 31 0.47124142380337 0.94248284760674 0.52875857619663 32 0.45479924784171 0.90959849568342 0.54520075215829 33 0.439264208038213 0.878528416076427 0.560735791961787 34 0.348294809685982 0.696589619371965 0.651705190314018 35 0.232739428589462 0.465478857178924 0.767260571410538 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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