Multiple Regression - ref.17

*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: Mon, 22 Dec 2008 09:54:43 -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/Dec/22/t1229966743zl9t6b89647tbwg.htm/, Retrieved Mon, 22 Dec 2008 18:25:52 +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/2008/Dec/22/t1229966743zl9t6b89647tbwg.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}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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101,1 103 100,7 102,4 100 102 100 101,8 100,8 101,6 101,9 101,4 102,7 101,3 103,1 101,4 103,5 101,7 103,9 102,4 104,4 103,1 105,2 103,8 106 104,4 107 105 108,2 105,7 109 106,4 109,1 107,1 109,3 107,9 110,1 108,8 110,7 109,6 110,8 110,3 110,7 110,8 110,9 111,2 111,3 111,7 111,6 112,3 111,8 112,8 112,1 113,1 112,3 113,1 112,5 113,1 113 113,2 113,6 113,1 114,4 112,8 114,9 112,5 115,2 112,3 116 112,5 117 112,9 118 113,5 119,4 114,1 121,1 114,6 123,1 114,9 125 115,4 126,3 115,7 127,4 116,1 129 116,5 131 117,1 133,3 117,5 135,9 117,7 138,4 117,7 140,3 117,7 141,7 117,6 143,1 117,5 144,5 117,6 146 117,9 147,7 118,2 149 118,5 149,7 118,7 150,2 118,8 150,5 118,9 150,7 119 150,9 119

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 Transportmiddelen[t] = + 117.173226126416 -0.169843653424947Machines[t] + 0.481241096237379t + 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) 117.173226126416 3.153979 37.1509 0 0 Machines -0.169843653424947 0.03383 -5.0205 5e-06 3e-06 t 0.481241096237379 0.031615 15.2217 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.978222902425695 R-squared 0.956920046830152 Adjusted R-squared 0.955408469525946 F-TEST (value) 633.060607729425 F-TEST (DF numerator) 2 F-TEST (DF denominator) 57 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.25524473150456 Sum Squared Residuals 89.8114421502871 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 103 100.483273861391 2.51672613860910 2 102.4 101.032452418998 1.36754758100175 3 102 101.632584072633 0.367415927366901 4 101.8 102.113825168870 -0.313825168870486 5 101.6 102.459191342368 -0.85919134236791 6 101.4 102.753604419838 -1.35360441983783 7 101.3 103.098970593335 -1.79897059333526 8 101.4 103.512274228203 -2.11227422820266 9 101.7 103.92557786307 -2.22557786307006 10 102.4 104.338881497937 -1.93888149793746 11 103.1 104.735200767462 -1.63520076746237 12 103.8 105.080566940960 -1.28056694095979 13 104.4 105.425933114457 -1.02593311445721 14 105 105.737330557270 -0.737330557269643 15 105.7 106.014759269397 -0.314759269397083 16 106.4 106.360125442895 0.0398745571054983 17 107.1 106.824382173789 0.275617826210601 18 107.9 107.271654539342 0.628345460658224 19 108.8 107.617020712839 1.18297928716079 20 109.6 107.996355617022 1.60364438297838 21 110.3 108.460612347916 1.8393876520835 22 110.8 108.958837809496 1.84116219050363 23 111.2 109.406110175049 1.79388982495124 24 111.7 109.819413809916 1.88058619008384 25 112.3 110.249701810126 2.05029818987394 26 112.8 110.696974175678 2.10302582432155 27 113.1 111.127262175888 1.97273782411165 28 113.1 111.574534541441 1.52546545855926 29 113.1 112.021806906993 1.07819309300687 30 113.2 112.418126176518 0.781873823481977 31 113.1 112.797461080700 0.302538919299557 32 112.8 113.142827254198 -0.342827254197859 33 112.5 113.539146523723 -1.03914652372276 34 112.3 113.969434523933 -1.66943452393266 35 112.5 114.31480069743 -1.81480069743008 36 112.9 114.626198140243 -1.72619814024251 37 113.5 114.937595583055 -1.43759558305494 38 114.1 115.181055564497 -1.08105556449740 39 114.6 115.373562449912 -0.773562449912372 40 114.9 115.515116239300 -0.615116239299846 41 115.4 115.673654394030 -0.273654394029825 42 115.7 115.934098740815 -0.234098740814776 43 116.1 116.228511818285 -0.128511818284721 44 116.5 116.438003069042 0.0619969309578202 45 117.1 116.579556858430 0.520443141570329 46 117.5 116.670157551790 0.829842448210336 47 117.7 116.709805149122 0.990194850877821 48 117.7 116.766437111797 0.93356288820281 49 117.7 116.924975266527 0.77502473347283 50 117.6 117.168435247970 0.431564752030364 51 117.5 117.411895229412 0.08810477058792 52 117.6 117.655355210855 -0.0553552108545395 53 117.9 117.881830826954 0.0181691730455138 54 118.2 118.074337712369 0.125662287630539 55 118.5 118.334782059154 0.16521794084559 56 118.7 118.697132597994 0.00286740200567781 57 118.8 119.093451867519 -0.293451867519234 58 118.9 119.523739867729 -0.62373986772912 59 119 119.971012233282 -0.971012233281516 60 119 120.418284598834 -1.41828459883390 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 6 0.000791955385131138 0.00158391077026228 0.999208044614869 7 5.92443941399347e-05 0.000118488788279869 0.99994075560586 8 6.94457919729656e-05 0.000138891583945931 0.999930554208027 9 0.000500105660326429 0.00100021132065286 0.999499894339674 10 0.00910276895932344 0.0182055379186469 0.990897231040677 11 0.0544744189905396 0.108948837981079 0.94552558100946 12 0.142435556412979 0.284871112825958 0.857564443587021 13 0.235938221963752 0.471876443927503 0.764061778036248 14 0.298726349103131 0.597452698206262 0.701273650896869 15 0.330727129737959 0.661454259475919 0.66927287026204 16 0.386397236283468 0.772794472566936 0.613602763716532 17 0.594846252380178 0.810307495239643 0.405153747619822 18 0.87327817564397 0.253443648712059 0.126721824356029 19 0.966593738586445 0.0668125228271103 0.0334062614135551 20 0.991935310969433 0.0161293780611345 0.00806468903056726 21 0.998885297262653 0.00222940547469483 0.00111470273734742 22 0.999874685117892 0.000250629764215283 0.000125314882107642 23 0.999968937510578 6.21249788447151e-05 3.10624894223575e-05 24 0.999982639878872 3.47202422565339e-05 1.73601211282669e-05 25 0.999981927925865 3.61441482704791e-05 1.80720741352395e-05 26 0.999973210363093 5.357927381512e-05 2.678963690756e-05 27 0.999953852807957 9.22943840860695e-05 4.61471920430347e-05 28 0.999909510087933 0.000180979824134642 9.04899120673208e-05 29 0.99982693147334 0.000346137053320798 0.000173068526660399 30 0.999707073165905 0.0005858536681893 0.00029292683409465 31 0.999525887213714 0.000948225572571417 0.000474112786285708 32 0.999402245252293 0.00119550949541401 0.000597754747707003 33 0.999602458814862 0.000795082370275189 0.000397541185137594 34 0.999896580750422 0.000206838499155109 0.000103419249577555 35 0.999985543868387 2.89122632262049e-05 1.44561316131025e-05 36 0.999998562792783 2.87441443481216e-06 1.43720721740608e-06 37 0.9999997204257 5.59148599762295e-07 2.79574299881148e-07 38 0.99999988039073 2.39218541045185e-07 1.19609270522593e-07 39 0.999999915468964 1.69062071741215e-07 8.45310358706073e-08 40 0.999999962920472 7.41590551243336e-08 3.70795275621668e-08 41 0.999999969883057 6.02338856723597e-08 3.01169428361798e-08 42 0.99999998268819 3.46236207927009e-08 1.73118103963504e-08 43 0.999999989276716 2.14465687918203e-08 1.07232843959102e-08 44 0.999999994653192 1.06936168358571e-08 5.34680841792854e-09 45 0.999999979841897 4.03162054839925e-08 2.01581027419963e-08 46 0.999999869365753 2.61268494856938e-07 1.30634247428469e-07 47 0.999999645234896 7.09530208072671e-07 3.54765104036336e-07 48 0.999999592808755 8.14382490774342e-07 4.07191245387171e-07 49 0.999999898232014 2.03535972924754e-07 1.01767986462377e-07 50 0.99999999731291 5.37418169393698e-09 2.68709084696849e-09 51 0.999999999366722 1.26655543400117e-09 6.33277717000587e-10 52 0.999999976872282 4.62554367379689e-08 2.31277183689844e-08 53 0.999999702239375 5.95521250052183e-07 2.97760625026091e-07 54 0.999984592177364 3.08156452716122e-05 1.54078226358061e-05 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 38 0.775510204081633 NOK 5% type I error level 40 0.816326530612245 NOK 10% type I error level 41 0.836734693877551 NOK

Charts produced by software:

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Parameters (Session):

par1 = 12 ;

Parameters (R input):

par1 = 2 ; par2 = Do not include Seasonal 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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