*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, 16 Dec 2009 07:12:18 -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/Dec/16/t1260972798kbe2dsfajgi1rr2.htm/, Retrieved Wed, 16 Dec 2009 15:13:30 +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/Dec/16/t1260972798kbe2dsfajgi1rr2.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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13807 0 19169 22782 20366 29743 0 13807 19169 22782 25591 0 29743 13807 19169 29096 0 25591 29743 13807 26482 0 29096 25591 29743 22405 0 26482 29096 25591 27044 0 22405 26482 29096 17970 0 27044 22405 26482 18730 0 17970 27044 22405 19684 0 18730 17970 27044 19785 0 19684 18730 17970 18479 0 19785 19684 18730 10698 0 18479 19785 19684 31956 0 10698 18479 19785 29506 0 31956 10698 18479 34506 0 29506 31956 10698 27165 0 34506 29506 31956 26736 0 27165 34506 29506 23691 0 26736 27165 34506 18157 0 23691 26736 27165 17328 0 18157 23691 26736 18205 0 17328 18157 23691 20995 0 18205 17328 18157 17382 0 20995 18205 17328 9367 0 17382 20995 18205 31124 0 9367 17382 20995 26551 0 31124 9367 17382 30651 0 26551 31124 9367 25859 0 30651 26551 31124 25100 0 25859 30651 26551 25778 0 25100 25859 30651 20418 0 25778 25100 25859 18688 0 20418 25778 25100 20424 0 18688 20418 25778 24776 0 20424 18688 20418 19814 0 24776 20424 18688 12738 0 19814 24776 20424 31566 0 12738 19814 24776 30 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 10 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 4707.37233564554 -889.595599244605X[t] + 0.153530771296594Y1[t] + 0.436558232697684Y2[t] + 0.0508654692781182Y3[t] -6720.22713821588M1[t] + 14266.9491999809M2[t] + 11667.1125103659M3[t] + 7644.99499046983M4[t] + 4714.7777808122M5[t] + 460.306602584105M6[t] + 3169.10551863843M7[t] -1444.75317412772M8[t] -2090.70678676465M9[t] + 2356.44218947412M10[t] + 5209.20853962815M11[t] + 14.0026261095115t + 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) 4707.37233564554 3579.149132 1.3152 0.195926 0.097963 X -889.595599244605 889.524958 -1.0001 0.323284 0.161642 Y1 0.153530771296594 0.15948 0.9627 0.341483 0.170742 Y2 0.436558232697684 0.143608 3.0399 0.00416 0.00208 Y3 0.0508654692781182 0.15997 0.318 0.752162 0.376081 M1 -6720.22713821588 1491.209035 -4.5066 5.6e-05 2.8e-05 M2 14266.9491999809 2354.156582 6.0603 0 0 M3 11667.1125103659 2236.842751 5.2159 6e-06 3e-06 M4 7644.99499046983 2523.660912 3.0293 0.00428 0.00214 M5 4714.7777808122 2035.268652 2.3165 0.025735 0.012867 M6 460.306602584105 1983.605589 0.2321 0.817678 0.408839 M7 3169.10551863843 2204.852622 1.4373 0.158401 0.0792 M8 -1444.75317412772 1755.2875 -0.8231 0.415339 0.20767 M9 -2090.70678676465 1833.958534 -1.14 0.261068 0.130534 M10 2356.44218947412 2051.721378 1.1485 0.257576 0.128788 M11 5209.20853962815 1359.892516 3.8306 0.000441 0.000221 t 14.0026261095115 24.084759 0.5814 0.56424 0.28212 Multiple Linear Regression - Regression Statistics Multiple R 0.966482294440936 R-squared 0.934088025467816 Adjusted R-squared 0.907723235654942 F-TEST (value) 35.4293750148430 F-TEST (DF numerator) 16 F-TEST (DF denominator) 40 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1786.11048781796 Sum Squared Residuals 127607626.987733 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 13807 11925.7749831604 1881.22501683961 2 29743 30649.3280308136 -906.328030813608 3 25591 27985.5581544637 -2394.55815446371 4 29096 30024.2348482547 -928.23484825475 5 26482 26644.1479543565 -162.147954356516 6 22405 23321.2931432313 -916.293143231263 7 27044 24455.2699803669 2588.73001963306 8 17970 18654.8329103538 -684.832910353758 9 18730 18447.5588283187 282.441171681305 10 19684 19300.0293253348 383.970674665202 11 19785 22183.4976460359 -2398.49764603589 12 18479 17458.9326510632 1020.06734893684 13 10698 10644.8149908372 53.1850091627691 14 31956 29886.3633841787 2069.63661582131 15 29506 27100.9965453982 2405.00345460179 16 34506 31601.3019561694 2904.69804383064 17 27165 29464.4717049091 -2299.47170490913 18 26736 26155.1045244593 580.895475540727 19 23691 25861.5947258938 -2170.59472589377 20 18157 20233.5505688410 -2076.55056884103 21 17328 17400.8191890735 -72.8191890734954 22 18205 19163.8951683160 -958.895168316047 23 20995 21521.9143491152 -526.91434911522 24 17382 17095.7533835584 286.246616441618 25 9367 11097.4286805409 -1730.42868054086 26 31124 29432.6882774542 1691.31172254578 27 26551 26504.4320294749 46.5679705251251 28 30651 30884.7316510884 -233.731651088411 29 25859 27708.2924468138 -1849.29244681385 30 25100 24289.3854016936 810.61459830635 31 25778 25012.2184613964 765.78153860364 32 20418 19941.3612302805 476.638769719473 33 18688 18743.8649001903 -55.8649001902982 34 20424 20633.9429291065 -209.94292910645 35 24776 22739.3566664432 2036.64333355682 36 19814 18882.1844997193 931.815500280656 37 12738 13402.3441838064 -664.344183806407 38 31566 31372.3039820705 193.696017929485 39 30111 28335.6667674104 1775.33323258962 40 30019 31963.7589460073 -1944.75894600734 41 31934 28466.3267592486 3467.67324075139 42 25826 24405.6970189552 1420.30298104484 43 26835 27022.0620024819 -187.062002481873 44 20205 20008.0281724136 196.971827586355 45 17789 18487.9691426310 -698.969142631017 46 20520 19735.1325772427 784.867422757295 47 22518 21629.2313384057 888.768661594281 48 15572 17810.1294656591 -2238.12946565911 49 11509 11048.6371616551 460.362838344891 50 25447 28495.3163254830 -3048.31632548296 51 24090 25922.3465032528 -1832.34650325282 52 27786 27583.9725984801 202.027401519862 53 26195 25351.7611346719 843.238865328108 54 20516 22411.5199116607 -1895.51991166066 55 22759 23755.8548298611 -996.85482986105 56 19028 16940.2271181110 2087.77288188896 57 16971 16425.7879397865 545.212060213505 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 20 0.909121855315953 0.181756289368093 0.0908781446840466 21 0.860275762944488 0.279448474111024 0.139724237055512 22 0.87122683975094 0.25754632049812 0.12877316024906 23 0.824165683322474 0.351668633355053 0.175834316677526 24 0.758401090187357 0.483197819625285 0.241598909812643 25 0.787089033908096 0.425821932183808 0.212910966091904 26 0.772563768371864 0.454872463256272 0.227436231628136 27 0.673245012282214 0.653509975435571 0.326754987717786 28 0.624544464574429 0.750911070851142 0.375455535425571 29 0.842517244145238 0.314965511709525 0.157482755854762 30 0.780293636601265 0.43941272679747 0.219706363398735 31 0.69240743453583 0.61518513092834 0.30759256546417 32 0.639034900735557 0.721930198528885 0.360965099264443 33 0.539816943555905 0.92036611288819 0.460183056444095 34 0.45264395528209 0.90528791056418 0.54735604471791 35 0.426483185229102 0.852966370458204 0.573516814770898 36 0.291847511579805 0.58369502315961 0.708152488420195 37 0.233085331138173 0.466170662276346 0.766914668861827 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 = 0 ; par2 = 36 ;

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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