model 4

*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 12:49:56 -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/t1258746707umoipc9f3yhphwh.htm/, Retrieved Fri, 20 Nov 2009 20:51:58 +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/t1258746707umoipc9f3yhphwh.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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12,8 23 20,3 13,2 15,7 12,6 8 20 12,8 20,3 13,2 15,7 0,9 20 8 12,8 20,3 13,2 3,6 15 0,9 8 12,8 20,3 14,1 17 3,6 0,9 8 12,8 21,7 16 14,1 3,6 0,9 8 24,5 15 21,7 14,1 3,6 0,9 18,9 10 24,5 21,7 14,1 3,6 13,9 13 18,9 24,5 21,7 14,1 11 10 13,9 18,9 24,5 21,7 5,8 19 11 13,9 18,9 24,5 15,5 21 5,8 11 13,9 18,9 22,4 17 15,5 5,8 11 13,9 31,7 16 22,4 15,5 5,8 11 30,3 17 31,7 22,4 15,5 5,8 31,4 14 30,3 31,7 22,4 15,5 20,2 18 31,4 30,3 31,7 22,4 19,7 17 20,2 31,4 30,3 31,7 10,8 14 19,7 20,2 31,4 30,3 13,2 15 10,8 19,7 20,2 31,4 15,1 16 13,2 10,8 19,7 20,2 15,6 11 15,1 13,2 10,8 19,7 15,5 15 15,6 15,1 13,2 10,8 12,7 13 15,5 15,6 15,1 13,2 10,9 17 12,7 15,5 15,6 15,1 10 16 10,9 12,7 15,5 15,6 9,1 9 10 10,9 12,7 15,5 10,3 17 9,1 10 10,9 12,7 16,9 15 10,3 9,1 10 10,9 22 12 16,9 10,3 9,1 10 27,6 12 22 16,9 10,3 9,1 28,9 12 27,6 22 16,9 10,3 31 12 28,9 27,6 22 16,9 32,9 4 31 28,9 27,6 22 38,1 7 32,9 31 28,9 27,6 28,8 4 38,1 32,9 31 28,9 29 3 28,8 38,1 32,9 31 21,8 3 29 28,8 38,1 32,9 28,8 0 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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = -3.14673253583627 + 0.159273111161314X[t] + 1.19239391388524Y1[t] + 0.0547489071340255Y2[t] -0.846957446955572Y3[t] + 0.51657962018494Y4[t] + 1.18489455307365M1[t] + 0.787703242296826M2[t] + 1.77623608216405M3[t] + 1.99845232381733M4[t] + 2.44382728416817M5[t] + 2.51934153446727M6[t] + 1.65025027547976M7[t] + 1.96425139545177M8[t] + 1.97878859140112M9[t] + 1.43407402510184M10[t] + 1.18187657202455M11[t] + 0.0360920857270811t + 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) -3.14673253583627 5.714127 -0.5507 0.585067 0.292534 X 0.159273111161314 0.204092 0.7804 0.439991 0.219996 Y1 1.19239391388524 0.138054 8.6371 0 0 Y2 0.0547489071340255 0.190013 0.2881 0.774812 0.387406 Y3 -0.846957446955572 0.18777 -4.5106 6e-05 3e-05 Y4 0.51657962018494 0.143438 3.6014 0.000903 0.000452 M1 1.18489455307365 3.044019 0.3893 0.699262 0.349631 M2 0.787703242296826 3.054939 0.2578 0.797917 0.398959 M3 1.77623608216405 3.13858 0.5659 0.574764 0.287382 M4 1.99845232381733 3.072049 0.6505 0.519266 0.259633 M5 2.44382728416817 3.047575 0.8019 0.427602 0.213801 M6 2.51934153446727 3.0586 0.8237 0.415255 0.207628 M7 1.65025027547976 3.069212 0.5377 0.593934 0.296967 M8 1.96425139545177 3.069922 0.6398 0.526117 0.263059 M9 1.97878859140112 3.215322 0.6154 0.541943 0.270971 M10 1.43407402510184 3.376825 0.4247 0.673464 0.336732 M11 1.18187657202455 3.206876 0.3685 0.714513 0.357256 t 0.0360920857270811 0.075509 0.478 0.635398 0.317699 Multiple Linear Regression - Regression Statistics Multiple R 0.92674741174573 R-squared 0.858860765177409 Adjusted R-squared 0.79571952854625 F-TEST (value) 13.6022164119855 F-TEST (DF numerator) 17 F-TEST (DF denominator) 38 p-value 2.89758217419944e-11 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4.52155480976008 Sum Squared Residuals 776.889400111252 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 12.8 19.8774889828420 -7.07748898284196 2 8 14.2031237507828 -6.20312375078278 3 0.9 1.78879416237584 -0.888794162375841 4 3.6 2.54184154660096 1.05815845339904 5 14.1 6.36364973583978 7.73635026416022 6 21.7 22.5177568022584 -0.81775680225839 7 24.5 25.2080413781786 -0.708041378178616 8 18.9 21.0182754626342 -2.11827546263423 9 13.9 14.0098245150921 -0.109824515092060 10 11 8.30934351358911 2.69065648641089 11 5.8 11.9843939002224 -6.18439390022245 12 15.5 6.13987681509788 9.36012318490212 13 22.4 17.8785761520897 4.5214238479103 14 31.7 29.0228840465195 2.6771159534805 15 30.3 30.7721116812019 -0.472111681201894 16 31.4 28.5592299638059 2.84077003619412 17 20.2 26.6004694124044 -6.40046941240445 18 19.7 19.2481454930598 0.451854506940208 19 10.8 15.0730776095617 -4.27307760956167 20 13.2 14.9969246273823 -1.79692462738228 21 15.1 12.2190941174582 2.88090588254176 22 15.6 20.5906833623952 -4.9906833623952 23 15.5 15.0816338278482 0.418366172151823 24 12.7 13.1560101206348 -0.45601012063484 25 10.9 12.2279339093623 -1.32793390936235 26 10 9.75094114297062 0.249058857029382 27 9.1 10.8087746245549 -1.70877462455487 28 10.3 11.2969397703106 -0.9969397703106 29 16.9 12.6738776602347 4.22612233976531 30 22 20.5405032270739 1.45949677292609 31 27.6 24.6687852071996 2.93121479280037 32 28.9 27.0054801513548 1.89451984864525 33 31 28.0027579147797 2.99724208522027 34 32.9 26.6867457033422 6.21325429665776 35 38.1 31.1207820028328 6.9792179971672 36 28.8 34.694592326443 -5.894592326443 37 29 24.4273348252194 4.57266517478059 38 21.8 20.3728721007827 1.42712789921731 39 28.8 22.9083095759946 5.89169042400536 40 25.6 26.9419667679022 -1.34196676790221 41 28.2 29.87387895928 -1.67387895928003 42 20.2 23.4217106857197 -3.22171068571968 43 17.9 19.3589554203169 -1.4589554203169 44 16.3 13.7883189984606 2.51168100153937 45 13.2 18.9683234526700 -5.76832345266998 46 8.1 12.0132274206734 -3.91322742067344 47 4.5 5.71319026909658 -1.21319026909658 48 -0.1 2.90952073782429 -3.00952073782429 49 0 0.688666130486581 -0.688666130486581 50 2.3 0.4501789589444 1.8498210410556 51 2.8 5.62200995587275 -2.82200995587275 52 2.9 4.46002195138034 -1.56002195138034 53 0.1 3.98812423224105 -3.88812423224105 54 3.5 1.37188379188822 2.12811620811178 55 8.6 5.09114038474318 3.50885961525682 56 13.8 14.2910007601681 -0.491000760168099 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.458371295529067 0.916742591058135 0.541628704470933 22 0.84455182567338 0.310896348653240 0.155448174326620 23 0.784215001147905 0.43156999770419 0.215784998852095 24 0.949137749583338 0.101724500833324 0.0508622504166618 25 0.939026004144066 0.121947991711868 0.060973995855934 26 0.929057403473308 0.141885193053385 0.0709425965266925 27 0.924993611196012 0.150012777607976 0.0750063888039879 28 0.991568167727073 0.0168636645458544 0.00843183227292722 29 0.980705718409128 0.0385885631817441 0.0192942815908721 30 0.957380372211167 0.085239255577666 0.042619627788833 31 0.934219080513254 0.131561838973492 0.0657809194867459 32 0.889307674284809 0.221384651430382 0.110692325715191 33 0.90302896528495 0.193942069430102 0.0969710347150508 34 0.896018662492057 0.207962675015886 0.103981337507943 35 0.874825637299067 0.250348725401867 0.125174362700933 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 2 0.133333333333333 NOK 10% type I error level 3 0.2 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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