*Unverified author*

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

Title produced by software: Multiple Regression

Date of computation: Wed, 18 Nov 2009 11:34:33 -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/18/t12585693528z8czs1zb1qugh9.htm/, Retrieved Wed, 18 Nov 2009 19:36:04 +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/18/t12585693528z8czs1zb1qugh9.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:

» Textbox « » Textfile « » CSV «

902.2 0 891.9 0 874 0 930.9 0 944.2 0 935.9 0 937.1 0 885.1 0 892.4 0 987.3 0 946.3 0 799.6 0 875.4 0 846.2 0 880.6 0 885.7 0 868.9 0 882.5 0 789.6 0 773.3 0 804.3 0 817.8 0 836.7 0 721.8 0 760.8 0 841.4 0 1045.6 0 949.2 1 850.1 1 957.4 0 851.8 0 913.9 0 888 0 973.8 0 927.6 1 833 1 879.5 1 797.3 1 834.5 1 735.1 1 835 1 892.8 1 697.2 1 821.1 1 732.7 1 797.6 1 866.3 1 826.3 1 778.6 1 779.2 1 951 1 692.3 1 841.4 1 857.3 1 760.7 1 841.2 0 810.3 0 1007.4 1 931.3 0 931.2 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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 879.344444444444 -48.3777777777777X[t] + 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) 879.344444444444 12.212258 72.0051 0 0 X -48.3777777777777 19.309275 -2.5054 0.01506 0.00753 Multiple Linear Regression - Regression Statistics Multiple R 0.312501253514239 R-squared 0.0976570334479704 Adjusted R-squared 0.0820993960936252 F-TEST (value) 6.27711208480472 F-TEST (DF numerator) 1 F-TEST (DF denominator) 58 p-value 0.0150603190912271 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 73.2735477299609 Sum Squared Residuals 311402.742222222 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 902.2 879.344444444447 22.8555555555531 2 891.9 879.344444444444 12.5555555555556 3 874 879.344444444444 -5.34444444444436 4 930.9 879.344444444444 51.5555555555556 5 944.2 879.344444444444 64.8555555555557 6 935.9 879.344444444444 56.5555555555556 7 937.1 879.344444444444 57.7555555555557 8 885.1 879.344444444444 5.75555555555566 9 892.4 879.344444444444 13.0555555555556 10 987.3 879.344444444444 107.955555555556 11 946.3 879.344444444444 66.9555555555556 12 799.6 879.344444444444 -79.7444444444443 13 875.4 879.344444444444 -3.94444444444439 14 846.2 879.344444444444 -33.1444444444443 15 880.6 879.344444444444 1.25555555555566 16 885.7 879.344444444444 6.35555555555568 17 868.9 879.344444444444 -10.4444444444444 18 882.5 879.344444444444 3.15555555555564 19 789.6 879.344444444444 -89.7444444444443 20 773.3 879.344444444444 -106.044444444444 21 804.3 879.344444444444 -75.0444444444444 22 817.8 879.344444444444 -61.5444444444444 23 836.7 879.344444444444 -42.6444444444443 24 721.8 879.344444444444 -157.544444444444 25 760.8 879.344444444444 -118.544444444444 26 841.4 879.344444444444 -37.9444444444444 27 1045.6 879.344444444444 166.255555555556 28 949.2 830.966666666667 118.233333333333 29 850.1 830.966666666667 19.1333333333334 30 957.4 879.344444444444 78.0555555555556 31 851.8 879.344444444444 -27.5444444444444 32 913.9 879.344444444444 34.5555555555556 33 888 879.344444444444 8.65555555555564 34 973.8 879.344444444444 94.4555555555556 35 927.6 830.966666666667 96.6333333333334 36 833 830.966666666667 2.03333333333333 37 879.5 830.966666666667 48.5333333333333 38 797.3 830.966666666667 -33.6666666666667 39 834.5 830.966666666667 3.53333333333333 40 735.1 830.966666666667 -95.8666666666666 41 835 830.966666666667 4.03333333333333 42 892.8 830.966666666667 61.8333333333333 43 697.2 830.966666666667 -133.766666666667 44 821.1 830.966666666667 -9.86666666666665 45 732.7 830.966666666667 -98.2666666666666 46 797.6 830.966666666667 -33.3666666666666 47 866.3 830.966666666667 35.3333333333333 48 826.3 830.966666666667 -4.66666666666672 49 778.6 830.966666666667 -52.3666666666666 50 779.2 830.966666666667 -51.7666666666666 51 951 830.966666666667 120.033333333333 52 692.3 830.966666666667 -138.666666666667 53 841.4 830.966666666667 10.4333333333333 54 857.3 830.966666666667 26.3333333333333 55 760.7 830.966666666667 -70.2666666666666 56 841.2 879.344444444444 -38.1444444444443 57 810.3 879.344444444444 -69.0444444444444 58 1007.4 830.966666666667 176.433333333333 59 931.3 879.344444444444 51.9555555555556 60 931.2 879.344444444444 51.8555555555557 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.0980985137088883 0.196197027417777 0.901901486291112 6 0.0469888077638944 0.0939776155277887 0.953011192236106 7 0.0214353527312179 0.0428707054624358 0.978564647268782 8 0.0115113682628098 0.0230227365256195 0.98848863173719 9 0.00477060494822676 0.00954120989645351 0.995229395051773 10 0.0176590143833917 0.0353180287667834 0.982340985616608 11 0.0104423785991855 0.0208847571983710 0.989557621400814 12 0.0755150520699445 0.151030104139889 0.924484947930055 13 0.051109310716038 0.102218621432076 0.948890689283962 14 0.0468557965292793 0.0937115930585585 0.95314420347072 15 0.0287073368630036 0.0574146737260073 0.971292663136996 16 0.0165585742754063 0.0331171485508126 0.983441425724594 17 0.0102840854893288 0.0205681709786576 0.989715914510671 18 0.0056140901780003 0.0112281803560006 0.994385909822 19 0.0165242118682728 0.0330484237365455 0.983475788131727 20 0.0444531436397962 0.0889062872795925 0.955546856360204 21 0.0510155193055026 0.102031038611005 0.948984480694497 22 0.047126285803272 0.094252571606544 0.952873714196728 23 0.0356882356907258 0.0713764713814515 0.964311764309274 24 0.155293396571060 0.310586793142119 0.84470660342894 25 0.250992789027719 0.501985578055438 0.749007210972281 26 0.215153165109709 0.430306330219417 0.784846834890291 27 0.485489228371542 0.970978456743084 0.514510771628458 28 0.501465507016909 0.997068985966183 0.498534492983091 29 0.466191671723719 0.932383343447439 0.53380832827628 30 0.465507534394849 0.931015068789698 0.534492465605151 31 0.40687328950342 0.81374657900684 0.59312671049658 32 0.345854966333339 0.691709932666677 0.654145033666661 33 0.279273538792405 0.55854707758481 0.720726461207595 34 0.311545053420367 0.623090106840735 0.688454946579633 35 0.32077923435525 0.6415584687105 0.67922076564475 36 0.278644721307343 0.557289442614686 0.721355278692657 37 0.240516552686317 0.481033105372635 0.759483447313683 38 0.215118266769451 0.430236533538903 0.784881733230549 39 0.167981553116445 0.335963106232889 0.832018446883555 40 0.211152495010323 0.422304990020645 0.788847504989677 41 0.158979308496635 0.31795861699327 0.841020691503365 42 0.144444429413793 0.288888858827586 0.855555570586207 43 0.256084898815458 0.512169797630915 0.743915101184542 44 0.192916444132741 0.385832888265483 0.807083555867259 45 0.227122308435387 0.454244616870774 0.772877691564613 46 0.176385914960700 0.352771829921401 0.8236140850393 47 0.131579403099512 0.263158806199025 0.868420596900488 48 0.087904118397873 0.175808236795746 0.912095881602127 49 0.0690131439615766 0.138026287923153 0.930986856038423 50 0.0553692991456853 0.110738598291371 0.944630700854315 51 0.0823732437347665 0.164746487469533 0.917626756265234 52 0.241046553808561 0.482093107617121 0.75895344619144 53 0.162748818340156 0.325497636680312 0.837251181659844 54 0.0972365135065442 0.194473027013088 0.902763486493456 55 0.517536135177893 0.964927729644213 0.482463864822107 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 1 0.0196078431372549 NOK 5% type I error level 9 0.176470588235294 NOK 10% type I error level 15 0.294117647058824 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No 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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