*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: Tue, 07 Dec 2010 19:30:22 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/07/t1291750098hay6ffjtvdtiym3.htm/, Retrieved Tue, 07 Dec 2010 20:28:18 +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/2010/Dec/07/t1291750098hay6ffjtvdtiym3.htm/}, year = {2010}, } @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 = {2010}, 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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103,48 103,93 103,89 104,4 104,79 104,77 105,13 105,26 104,96 104,75 105,01 105,15 105,2 105,77 105,78 106,26 106,13 106,12 106,57 106,44 106,54 107,1 108,1 108,4 108,84 109,62 110,42 110,67 111,66 112,28 112,87 112,18 112,36 112,16 111,49 111,25 111,36 111,74 111,1 111,33 111,25 111,04 110,97 111,31 111,02 111,07 111,36 111,54 112,05 112,52 112,94 113,33 113,78 113,77 113,82 113,89 114,25 114,41

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 5 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation Consumptieindexprijs[t] = + 103.373409090909 + 0.0529318181817703M1[t] + 0.392545454545451M2[t] + 0.312159090909086M3[t] + 0.493772727272725M4[t] + 0.627386363636359M5[t] + 0.510999999999996M6[t] + 0.596613636363628M7[t] + 0.350227272727270M8[t] + 0.169840909090903M9[t] + 0.0514545454545356M10[t] + 0.0953863636363579M11[t] + 0.190386363636364t + 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) 103.373409090909 0.679554 152.1194 0 0 M1 0.0529318181817703 0.824423 0.0642 0.949092 0.474546 M2 0.392545454545451 0.823904 0.4764 0.636062 0.318031 M3 0.312159090909086 0.8235 0.3791 0.706423 0.353212 M4 0.493772727272725 0.823212 0.5998 0.55164 0.27582 M5 0.627386363636359 0.823039 0.7623 0.44987 0.224935 M6 0.510999999999996 0.822981 0.6209 0.537789 0.268895 M7 0.596613636363628 0.823039 0.7249 0.472271 0.236136 M8 0.350227272727270 0.823212 0.4254 0.672544 0.336272 M9 0.169840909090903 0.8235 0.2062 0.837532 0.418766 M10 0.0514545454545356 0.823904 0.0625 0.950479 0.47524 M11 0.0953863636363579 0.867553 0.1099 0.912939 0.456469 t 0.190386363636364 0.009748 19.5312 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.947165971215957 R-squared 0.897123377029467 Adjusted R-squared 0.869689610903991 F-TEST (value) 32.7014297973613 F-TEST (DF numerator) 12 F-TEST (DF denominator) 45 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.22682766565322 Sum Squared Residuals 67.7297754545456 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 103.48 103.616727272727 -0.136727272727445 2 103.93 104.146727272727 -0.216727272727259 3 103.89 104.256727272727 -0.366727272727266 4 104.4 104.628727272727 -0.228727272727262 5 104.79 104.952727272727 -0.162727272727259 6 104.77 105.026727272727 -0.256727272727271 7 105.13 105.302727272727 -0.172727272727268 8 105.26 105.246727272727 0.0132727272727364 9 104.96 105.256727272727 -0.296727272727272 10 104.75 105.328727272727 -0.578727272727262 11 105.01 105.563045454545 -0.553045454545445 12 105.15 105.658045454545 -0.508045454545449 13 105.2 105.901363636364 -0.70136363636359 14 105.77 106.431363636364 -0.661363636363637 15 105.78 106.541363636364 -0.761363636363631 16 106.26 106.913363636364 -0.65336363636363 17 106.13 107.237363636364 -1.10736363636364 18 106.12 107.311363636364 -1.19136363636363 19 106.57 107.587363636364 -1.01736363636364 20 106.44 107.531363636364 -1.09136363636364 21 106.54 107.541363636364 -1.00136363636363 22 107.1 107.613363636364 -0.513363636363634 23 108.1 107.847681818182 0.252318181818179 24 108.4 107.942681818182 0.457318181818184 25 108.84 108.186 0.654000000000048 26 109.62 108.716 0.904000000000005 27 110.42 108.826 1.59400000000000 28 110.67 109.198 1.472 29 111.66 109.522 2.13800000000000 30 112.28 109.596 2.684 31 112.87 109.872 2.99800000000001 32 112.18 109.816 2.36400000000000 33 112.36 109.826 2.534 34 112.16 109.898 2.262 35 111.49 110.132318181818 1.35768181818181 36 111.25 110.227318181818 1.02268181818181 37 111.36 110.470636363636 0.889363636363678 38 111.74 111.000636363636 0.739363636363628 39 111.1 111.110636363636 -0.0106363636363711 40 111.33 111.482636363636 -0.152636363636371 41 111.25 111.806636363636 -0.556636363636368 42 111.04 111.880636363636 -0.840636363636362 43 110.97 112.156636363636 -1.18663636363636 44 111.31 112.100636363636 -0.790636363636367 45 111.02 112.110636363636 -1.09063636363637 46 111.07 112.182636363636 -1.11263636363637 47 111.36 112.416954545455 -1.05695454545455 48 111.54 112.511954545455 -0.971954545454548 49 112.05 112.755272727273 -0.705272727272692 50 112.52 113.285272727273 -0.765272727272738 51 112.94 113.395272727273 -0.455272727272735 52 113.33 113.767272727273 -0.437272727272737 53 113.78 114.091272727273 -0.311272727272733 54 113.77 114.165272727273 -0.395272727272737 55 113.82 114.441272727273 -0.621272727272739 56 113.89 114.385272727273 -0.495272727272736 57 114.25 114.395272727273 -0.145272727272733 58 114.41 114.467272727273 -0.0572727272727344 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 7.30168962605973e-05 0.000146033792521195 0.99992698310374 17 0.000374024374560540 0.000748048749121081 0.99962597562544 18 0.000141988202878381 0.000283976405756761 0.999858011797122 19 3.22493177008497e-05 6.44986354016994e-05 0.9999677506823 20 2.45812555089469e-05 4.91625110178938e-05 0.999975418744491 21 8.11282689917961e-06 1.62256537983592e-05 0.9999918871731 22 6.12792521584869e-05 0.000122558504316974 0.999938720747842 23 0.0016377244469181 0.0032754488938362 0.998362275553082 24 0.00682588236301327 0.0136517647260265 0.993174117636987 25 0.0255723293274583 0.0511446586549167 0.974427670672542 26 0.0505123810050003 0.101024762010001 0.949487618995 27 0.118900980916420 0.237801961832839 0.88109901908358 28 0.132383534906900 0.264767069813799 0.8676164650931 29 0.205155081651326 0.410310163302652 0.794844918348674 30 0.34954619062035 0.6990923812407 0.65045380937965 31 0.558725808218555 0.88254838356289 0.441274191781445 32 0.596109971540002 0.807780056919996 0.403890028459998 33 0.702760721642858 0.594478556714284 0.297239278357142 34 0.806988810606245 0.386022378787510 0.193011189393755 35 0.874545551873577 0.250908896252847 0.125454448126423 36 0.926051792940868 0.147896414118264 0.073948207059132 37 0.963185290692964 0.0736294186140724 0.0368147093070362 38 0.995312496686628 0.0093750066267433 0.00468750331337165 39 0.996930856608685 0.00613828678262989 0.00306914339131495 40 0.99853645473261 0.0029270905347812 0.0014635452673906 41 0.996673916919879 0.00665216616024273 0.00332608308012136 42 0.987896329482582 0.0242073410348360 0.0121036705174180 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 12 0.444444444444444 NOK 5% type I error level 14 0.518518518518518 NOK 10% type I error level 16 0.592592592592593 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291750098hay6ffjtvdtiym3/10wtpt1291750214.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/07/t1291750098hay6ffjtvdtiym3/10wtpt1291750214.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/07/t1291750098hay6ffjtvdtiym3/1pssh1291750214.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/07/t1291750098hay6ffjtvdtiym3/1pssh1291750214.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/07/t1291750098hay6ffjtvdtiym3/2pssh1291750214.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/07/t1291750098hay6ffjtvdtiym3/2pssh1291750214.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/07/t1291750098hay6ffjtvdtiym3/301921291750214.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/07/t1291750098hay6ffjtvdtiym3/301921291750214.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/07/t1291750098hay6ffjtvdtiym3/401921291750214.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/07/t1291750098hay6ffjtvdtiym3/401921291750214.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/07/t1291750098hay6ffjtvdtiym3/501921291750214.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/07/t1291750098hay6ffjtvdtiym3/501921291750214.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/07/t1291750098hay6ffjtvdtiym3/6bs8n1291750214.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/07/t1291750098hay6ffjtvdtiym3/6bs8n1291750214.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/07/t1291750098hay6ffjtvdtiym3/74j8q1291750214.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/07/t1291750098hay6ffjtvdtiym3/74j8q1291750214.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/07/t1291750098hay6ffjtvdtiym3/84j8q1291750214.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/07/t1291750098hay6ffjtvdtiym3/84j8q1291750214.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/07/t1291750098hay6ffjtvdtiym3/94j8q1291750214.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/07/t1291750098hay6ffjtvdtiym3/94j8q1291750214.ps (open in new window)

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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