*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: Thu, 19 Nov 2009 12:58:46 -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/19/t1258660805ydsoorzq3q97gpa.htm/, Retrieved Thu, 19 Nov 2009 21:00:17 +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/19/t1258660805ydsoorzq3q97gpa.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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101.9 122.2 19 73 77.8 74.8 80.2 102 123.7 22 72 73 77.8 74.8 100.7 122.6 23 75.8 72 73 77.8 99 115.7 20 72.6 75.8 72 73 96.5 116.1 14 71.9 72.6 75.8 72 101.8 120.5 14 74.8 71.9 72.6 75.8 100.5 122.6 14 72.9 74.8 71.9 72.6 103.3 119.9 15 72.9 72.9 74.8 71.9 102.3 120.7 11 79.9 72.9 72.9 74.8 100.4 120.2 17 74 79.9 72.9 72.9 103 122.1 16 76 74 79.9 72.9 99 119.3 20 69.6 76 74 79.9 104.8 121.7 24 77.3 69.6 76 74 104.5 113.5 23 75.2 77.3 69.6 76 104.8 123.7 20 75.8 75.2 77.3 69.6 103.8 123.4 21 77.6 75.8 75.2 77.3 106.3 126.4 19 76.7 77.6 75.8 75.2 105.2 124.1 23 77 76.7 77.6 75.8 108.2 125.6 23 77.9 77 76.7 77.6 106.2 124.8 23 76.7 77.9 77 76.7 103.9 123 23 71.9 76.7 77.9 77 104.9 126.9 27 73.4 71.9 76.7 77.9 106.2 127.3 26 72.5 73.4 71.9 76.7 107.9 129 17 73.7 72.5 73.4 71.9 106.9 126.2 24 69.5 73.7 72.5 73.4 110.3 125.4 26 74.7 69.5 73.7 72.5 109.8 126.3 24 72.5 74.7 69.5 73.7 108.3 126.3 27 72.1 72.5 74.7 69.5 110.9 128.4 27 70.7 72.1 72.5 74.7 109.8 127.2 26 71.4 70.7 72.1 72.5 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 R Framework error message The field 'Names of X columns' contains a hard return which cannot be interpreted. Please, resubmit your request without hard returns in the 'Names of X columns'. Multiple Linear Regression - Estimated Regression Equation Y[t] = + 19.5447097642314 + 0.474153907672798totid[t] -0.087206661204238ndzcg[t] + 0.0461297131404523indc[t] + 0.163565208603853y1[t] + 0.115836079954216y2[t] -0.0837072924607436`y3 `[t] + 1.37117081963841M1[t] + 1.77995473905426M2[t] + 2.41301826429556M3[t] + 2.28548228718490M4[t] + 2.58505687122945M5[t] + 4.83378346325529M6[t] + 3.70223862569186M7[t] + 3.24366895236396M8[t] + 4.85075294798024M9[t] + 4.14558329093348M10[t] + 3.09304594699270M11[t] -0.158704064647780t + 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) 19.5447097642314 18.446578 1.0595 0.295876 0.147938 totid 0.474153907672798 0.184449 2.5707 0.014082 0.007041 ndzcg -0.087206661204238 0.2114 -0.4125 0.682218 0.341109 indc 0.0461297131404523 0.079521 0.5801 0.565188 0.282594 y1 0.163565208603853 0.158225 1.0338 0.307619 0.15381 y2 0.115836079954216 0.148703 0.779 0.440696 0.220348 `y3 ` -0.0837072924607436 0.144047 -0.5811 0.564509 0.282254 M1 1.37117081963841 2.058699 0.666 0.509308 0.254654 M2 1.77995473905426 2.13776 0.8326 0.410126 0.205063 M3 2.41301826429556 2.175475 1.1092 0.274141 0.13707 M4 2.28548228718490 2.145102 1.0654 0.293228 0.146614 M5 2.58505687122945 2.081456 1.2419 0.221673 0.110837 M6 4.83378346325529 2.072542 2.3323 0.02494 0.01247 M7 3.70223862569186 2.094088 1.7679 0.084892 0.042446 M8 3.24366895236396 2.091477 1.5509 0.129004 0.064502 M9 4.85075294798024 2.0226 2.3983 0.021355 0.010677 M10 4.14558329093348 2.060549 2.0119 0.051177 0.025589 M11 3.09304594699270 2.13337 1.4498 0.155098 0.077549 t -0.158704064647780 0.052286 -3.0353 0.004265 0.002133 Multiple Linear Regression - Regression Statistics Multiple R 0.900418032880322 R-squared 0.810752633936068 Adjusted R-squared 0.723407695752715 F-TEST (value) 9.28219368859303 F-TEST (DF numerator) 18 F-TEST (DF denominator) 39 p-value 4.30708124721235e-09 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.9653736316565 Sum Squared Residuals 342.944190237623 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 73 73.9698574161942 -0.969857416194245 2 72 74.2893464271969 -2.28934642719692 3 75.8 73.3186625785146 2.48133742148541 4 72.6 73.5972044331523 -0.99720443315227 5 71.9 72.241504968797 -0.341504968797058 6 74.8 75.6575750843153 -0.857575084315297 7 72.9 74.2289092984581 -1.32890929845814 8 72.9 75.3046000406006 -2.40460004060062 9 79.9 75.561702182322 4.33829781767805 10 74 75.4213179613963 -1.42131796139633 11 76 75.0768721722453 0.923127827754687 12 69.6 69.4149505321 0.185049467900048 13 77.3 73.0314606676266 4.26853933237341 14 75.2 74.1589458684483 1.04105413155168 15 75.8 74.8318319669672 0.968168033032772 16 77.6 73.3540669343484 4.24593306565155 17 76.7 74.8661471506606 1.83385284933938 18 77 76.8307664336278 0.169233566372159 19 77.9 76.6263132268217 1.27368677317832 20 76.7 75.3877930774082 1.31220692259180 21 71.9 75.7854530447928 -3.88545304479284 22 73.4 74.2406932441782 -0.840693244178151 23 72.5 73.3546229180205 -0.854622918020528 24 73.7 70.773856243112 2.92614375688805 25 69.5 72.0457205734595 -2.54572057345952 26 74.7 73.597314452583 1.10268554741705 27 72.5 73.9274303359548 -1.42743033595479 28 72.1 73.6624233572771 -1.56242335727708 29 70.7 74.0974166679575 -3.39741666795754 30 71.4 75.6332184965867 -4.2332184965867 31 69.5 73.8860726057638 -4.38607260576378 32 73.5 72.9243212208094 0.575678779190643 33 72.4 74.2354296972381 -1.83542969723809 34 74.5 74.149553085271 0.350446914729022 35 72.2 72.250321722223 -0.0503217222230579 36 73 70.0932477026869 2.90675229731315 37 73.3 70.8388611457942 2.46113885420577 38 71.3 70.8176749047772 0.482325095222791 39 73.6 73.9438274633004 -0.343827463300385 40 71.3 73.9145747245828 -2.61457472458277 41 71.2 70.6200221207626 0.579977879237361 42 81.4 75.2146104322073 6.18538956779272 43 76.1 74.5571219900001 1.54287800999987 44 71.1 73.2312931339398 -2.13129313393983 45 75.7 72.2029650424995 3.49703495750055 46 70 71.2621157876944 -1.26211578769439 47 68.5 68.5181831875111 -0.0181831875111015 48 56.7 62.7179455221013 -6.01794552210127 49 57.9 61.1141001969254 -3.21410019692541 50 58.8 59.1367183469946 -0.336718346994596 51 59.3 60.978247655263 -1.67824765526301 52 61.3 60.3717305506394 0.92826944936056 53 62.9 61.5749090918221 1.32509090817785 54 61.4 62.6638295532629 -1.26382955326288 55 64.5 61.6015828789563 2.89841712104373 56 63.8 61.151992527242 2.64800747275801 57 61.6 63.7144500331477 -2.11445003314766 58 64.7 61.5263199214601 3.17368007853985 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 22 0.665854023285714 0.668291953428572 0.334145976714286 23 0.534210096213425 0.93157980757315 0.465789903786575 24 0.463126610737488 0.926253221474975 0.536873389262512 25 0.422005942714747 0.844011885429494 0.577994057285253 26 0.314905449707632 0.629810899415263 0.685094550292368 27 0.334823666270497 0.669647332540993 0.665176333729503 28 0.283442596682463 0.566885193364925 0.716557403317537 29 0.251386965553277 0.502773931106555 0.748613034446723 30 0.195758530524326 0.391517061048653 0.804241469475674 31 0.248388918640582 0.496777837281165 0.751611081359418 32 0.201234190110752 0.402468380221503 0.798765809889249 33 0.159425690536585 0.318851381073171 0.840574309463414 34 0.174751971165059 0.349503942330118 0.825248028834941 35 0.385718076499658 0.771436152999317 0.614281923500342 36 0.274070415002665 0.548140830005331 0.725929584997335 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 = 4 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 4 ; 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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