The seatbelt law - Q3

*Unverified author*

R Software Module: rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Thu, 27 Nov 2008 07:40:26 -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/Nov/27/t12277976242ykw1ofbq35be28.htm/, Retrieved Thu, 27 Nov 2008 14:53:59 +0000

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/Nov/27/t12277976242ykw1ofbq35be28.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}, }

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

Feedback Forum:

2008-11-27 13:41:43 [a2386b643d711541400692649981f2dc]  [reply]  test Post a new message

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

110.40 0 96.40 0 101.90 0 106.20 0 81.00 0 94.70 0 101.00 1 109.40 1 102.30 1 90.70 1 96.20 1 96.10 1 106.00 1 103.10 1 102.00 1 104.70 1 86.00 1 92.10 1 106.90 1 112.60 1 101.70 1 92.00 1 97.40 1 97.00 1 105.40 1 102.70 1 98.10 1 104.50 1 87.40 1 89.90 1 109.80 1 111.70 1 98.60 1 96.90 1 95.10 1 97.00 1 112.70 1 102.90 1 97.40 1 111.40 1 87.40 1 96.80 1 114.10 1 110.30 1 103.90 1 101.60 1 94.60 1 95.90 1 104.70 1 102.80 1 98.10 1 113.90 1 80.90 1 95.70 1 113.20 1 105.90 1 108.80 1 102.30 1 99.00 1 100.70 1 115.50 1

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 IP[t] = + 95.5952173913044 -1.72989130434785D[t] + 11.9709450483092M1[t] + 4.85920893719807M2[t] + 2.6826902173913M3[t] + 11.2261714975845M4[t] -12.4703472222222M5[t] -3.26686594202899M6[t] + 12.1425935990338M7[t] + 13.0260748792271M8[t] + 6.00955615942029M9[t] -0.446962560386476M10[t] -0.783481280193239M11[t] + 0.0965187198067633t + 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) 95.5952173913044 2.089692 45.7461 0 0 D -1.72989130434785 1.720911 -1.0052 0.319939 0.15997 M1 11.9709450483092 1.994786 6.0011 0 0 M2 4.85920893719807 2.091302 2.3235 0.024526 0.012263 M3 2.6826902173913 2.090074 1.2835 0.205596 0.102798 M4 11.2261714975845 2.089218 5.3734 2e-06 1e-06 M5 -12.4703472222222 2.088736 -5.9703 0 0 M6 -3.26686594202899 2.088626 -1.5641 0.124498 0.062249 M7 12.1425935990338 2.07205 5.8602 0 0 M8 13.0260748792271 2.070356 6.2917 0 0 M9 6.00955615942029 2.069038 2.9045 0.00559 0.002795 M10 -0.446962560386476 2.068095 -0.2161 0.829827 0.414914 M11 -0.783481280193239 2.06753 -0.3789 0.706435 0.353217 t 0.0965187198067633 0.027922 3.4567 0.001171 0.000585 Multiple Linear Regression - Regression Statistics Multiple R 0.93371807006284 R-squared 0.871829434361873 Adjusted R-squared 0.83637800131303 F-TEST (value) 24.5922198169169 F-TEST (DF numerator) 13 F-TEST (DF denominator) 47 p-value 1.11022302462516e-16 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.26875370300229 Sum Squared Residuals 502.183286231885 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 110.4 107.662681159420 2.73731884057980 2 96.4 100.647463768116 -4.24746376811595 3 101.9 98.567463768116 3.33253623188406 4 106.2 107.207463768116 -1.00746376811597 5 81 83.607463768116 -2.60746376811595 6 94.7 92.907463768116 1.79253623188403 7 101 106.683550724638 -5.68355072463771 8 109.4 107.663550724638 1.73644927536232 9 102.3 100.743550724638 1.55644927536233 10 90.7 94.3835507246377 -3.68355072463768 11 96.2 94.1435507246377 2.05644927536232 12 96.1 95.0235507246377 1.07644927536231 13 106 107.091014492754 -1.09101449275364 14 103.1 100.075797101449 3.02420289855072 15 102 97.9957971014493 4.00420289855072 16 104.7 106.635797101449 -1.93579710144927 17 86 83.0357971014493 2.96420289855072 18 92.1 92.3357971014493 -0.235797101449276 19 106.9 107.841775362319 -0.941775362318826 20 112.6 108.821775362319 3.77822463768115 21 101.7 101.901775362319 -0.201775362318840 22 92 95.5417753623188 -3.54177536231884 23 97.4 95.3017753623188 2.09822463768117 24 97 96.1817753623188 0.818224637681158 25 105.4 108.249239130435 -2.84923913043479 26 102.7 101.234021739130 1.46597826086957 27 98.1 99.1540217391304 -1.05402173913044 28 104.5 107.794021739130 -3.29402173913043 29 87.4 84.1940217391304 3.20597826086957 30 89.9 93.4940217391304 -3.59402173913042 31 109.8 109 0.800000000000007 32 111.7 109.98 1.72 33 98.6 103.06 -4.46000000000001 34 96.9 96.7 0.200000000000007 35 95.1 96.46 -1.36000000000000 36 97 97.34 -0.340000000000001 37 112.7 109.407463768116 3.29253623188404 38 102.9 102.392246376812 0.507753623188416 39 97.4 100.312246376812 -2.91224637681159 40 111.4 108.952246376812 2.44775362318842 41 87.4 85.3522463768116 2.04775362318841 42 96.8 94.6522463768116 2.14775362318841 43 114.1 110.158224637681 3.94177536231885 44 110.3 111.138224637681 -0.838224637681164 45 103.9 104.218224637681 -0.318224637681156 46 101.6 97.8582246376812 3.74177536231884 47 94.6 97.6182246376812 -3.01822463768116 48 95.9 98.4982246376812 -2.59822463768115 49 104.7 110.565688405797 -5.86568840579712 50 102.8 103.550471014493 -0.750471014492751 51 98.1 101.470471014493 -3.37047101449276 52 113.9 110.110471014493 3.78952898550726 53 80.9 86.5104710144928 -5.61047101449275 54 95.7 95.8104710144927 -0.110471014492744 55 113.2 111.316449275362 1.88355072463769 56 105.9 112.296449275362 -6.39644927536232 57 108.8 105.376449275362 3.42355072463768 58 102.3 99.0164492753623 3.28355072463768 59 99 98.7764492753623 0.223550724637683 60 100.7 99.6564492753623 1.04355072463768 61 115.5 111.723913043478 3.77608695652172 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.712813548618823 0.574372902762353 0.287186451381177 18 0.620139303927786 0.759721392144428 0.379860696072214 19 0.4796739157821 0.9593478315642 0.5203260842179 20 0.408942835392447 0.817885670784893 0.591057164607553 21 0.375910833518141 0.751821667036282 0.624089166481859 22 0.317636628294935 0.63527325658987 0.682363371705065 23 0.244537823779528 0.489075647559057 0.755462176220472 24 0.172510505315216 0.345021010630432 0.827489494684784 25 0.198077005758755 0.396154011517511 0.801922994241245 26 0.143775637018902 0.287551274037804 0.856224362981098 27 0.171386198005633 0.342772396011266 0.828613801994367 28 0.164136062498893 0.328272124997785 0.835863937501107 29 0.179010242092838 0.358020484185676 0.820989757907162 30 0.199721519431378 0.399443038862756 0.800278480568622 31 0.201559693366651 0.403119386733302 0.798440306633349 32 0.203576590199478 0.407153180398955 0.796423409800522 33 0.283539937548908 0.567079875097817 0.716460062451092 34 0.299905339786385 0.59981067957277 0.700094660213615 35 0.240448951915625 0.48089790383125 0.759551048084375 36 0.167920768593041 0.335841537186082 0.83207923140696 37 0.183347250075460 0.366694500150919 0.81665274992454 38 0.124236241891067 0.248472483782135 0.875763758108933 39 0.104359862325904 0.208719724651808 0.895640137674096 40 0.0852183142025827 0.170436628405165 0.914781685797417 41 0.153870320519724 0.307740641039448 0.846129679480276 42 0.125700190020091 0.251400380040183 0.874299809979909 43 0.126245503251593 0.252491006503186 0.873754496748407 44 0.378802858479767 0.757605716959534 0.621197141520233 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 = 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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