seatbelt law q3

*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, 27 Nov 2008 02:16:09 -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/t1227777505fa50lu7psybwly6.htm/, Retrieved Thu, 27 Nov 2008 09:18:25 +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/t1227777505fa50lu7psybwly6.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}, }

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

jenske_cole@hotmail.com

Dataseries X:

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98,6 0 98 0 106,8 0 96,6 0 100,1 0 107,7 0 91,5 0 97,8 0 107,4 1 117,5 1 105,6 1 97,4 1 99,5 1 98 1 104,3 1 100,6 1 101,1 1 103,9 1 96,9 1 95,5 1 108,4 1 117 1 103,8 1 100,8 1 110,6 1 104 1 112,6 1 107,3 1 98,9 1 109,8 1 104,9 1 102,2 1 123,9 1 124,9 1 112,7 1 121,9 1 100,6 1 104,3 1 120,4 1 107,5 1 102,9 1 125,6 1 107,5 1 108,8 1 128,4 1 121,1 1 119,5 1 128,7 1 108,7 1 105,5 1 119,8 1 111,3 1 110,6 1 120,1 1 97,5 1 107,7 1 127,3 1 117,2 1 119,8 1 116,2 1 111 1 112,4 1 130,6 1 109,1 1 118,8 1 123,9 1 101,6 1 112,8 1 128 1 129,6 1 125,8 1 119,5 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 7 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation x[t] = + 105.493333333333 + 8.58999999999997y[t] -7.8183333333333M1[t] -8.95166666666667M2[t] + 3.09833333333333M3[t] -7.25166666666668M4[t] -7.25166666666667M5[t] + 2.51499999999999M6[t] -12.6683333333333M7[t] -8.51833333333334M8[t] + 6.48333333333334M9[t] + 7.13333333333333M10[t] + 0.449999999999998M11[t] + 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) 105.493333333333 4.23982 24.8816 0 0 y 8.58999999999997 2.918044 2.9438 0.004631 0.002316 M1 -7.8183333333333 4.377066 -1.7862 0.079205 0.039602 M2 -8.95166666666667 4.377066 -2.0451 0.04531 0.022655 M3 3.09833333333333 4.377066 0.7079 0.481822 0.240911 M4 -7.25166666666668 4.377066 -1.6567 0.102881 0.05144 M5 -7.25166666666667 4.377066 -1.6567 0.102881 0.05144 M6 2.51499999999999 4.377066 0.5746 0.567756 0.283878 M7 -12.6683333333333 4.377066 -2.8943 0.005319 0.00266 M8 -8.51833333333334 4.377066 -1.9461 0.056407 0.028203 M9 6.48333333333334 4.349963 1.4904 0.141437 0.070719 M10 7.13333333333333 4.349963 1.6399 0.106356 0.053178 M11 0.449999999999998 4.349963 0.1034 0.917957 0.458979 Multiple Linear Regression - Regression Statistics Multiple R 0.735545441109676 R-squared 0.541027095937227 Adjusted R-squared 0.447676674771918 F-TEST (value) 5.79565779332853 F-TEST (DF numerator) 12 F-TEST (DF denominator) 59 p-value 1.69699007579460e-06 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 7.53435746251008 Sum Squared Residuals 3349.226 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 98.6 97.6749999999998 0.92500000000019 2 98 96.5416666666667 1.45833333333331 3 106.8 108.591666666667 -1.79166666666669 4 96.6 98.2416666666667 -1.64166666666669 5 100.1 98.2416666666667 1.8583333333333 6 107.7 108.008333333333 -0.308333333333358 7 91.5 92.825 -1.32500000000003 8 97.8 96.975 0.824999999999976 9 107.4 120.566666666667 -13.1666666666667 10 117.5 121.216666666667 -3.71666666666667 11 105.6 114.533333333333 -8.93333333333334 12 97.4 114.083333333333 -16.6833333333333 13 99.5 106.265 -6.76500000000003 14 98 105.131666666667 -7.13166666666666 15 104.3 117.181666666667 -12.8816666666667 16 100.6 106.831666666667 -6.23166666666666 17 101.1 106.831666666667 -5.73166666666666 18 103.9 116.598333333333 -12.6983333333333 19 96.9 101.415 -4.51499999999999 20 95.5 105.565 -10.065 21 108.4 120.566666666667 -12.1666666666667 22 117 121.216666666667 -4.21666666666667 23 103.8 114.533333333333 -10.7333333333333 24 100.8 114.083333333333 -13.2833333333333 25 110.6 106.265 4.33499999999996 26 104 105.131666666667 -1.13166666666666 27 112.6 117.181666666667 -4.58166666666666 28 107.3 106.831666666667 0.468333333333339 29 98.9 106.831666666667 -7.93166666666665 30 109.8 116.598333333333 -6.79833333333333 31 104.9 101.415 3.48500000000001 32 102.2 105.565 -3.36499999999999 33 123.9 120.566666666667 3.33333333333334 34 124.9 121.216666666667 3.68333333333334 35 112.7 114.533333333333 -1.83333333333333 36 121.9 114.083333333333 7.81666666666668 37 100.6 106.265 -5.66500000000004 38 104.3 105.131666666667 -0.831666666666666 39 120.4 117.181666666667 3.21833333333335 40 107.5 106.831666666667 0.668333333333341 41 102.9 106.831666666667 -3.93166666666665 42 125.6 116.598333333333 9.00166666666667 43 107.5 101.415 6.085 44 108.8 105.565 3.23500000000000 45 128.4 120.566666666667 7.83333333333333 46 121.1 121.216666666667 -0.116666666666671 47 119.5 114.533333333333 4.96666666666667 48 128.7 114.083333333333 14.6166666666667 49 108.7 106.265 2.43499999999997 50 105.5 105.131666666667 0.368333333333337 51 119.8 117.181666666667 2.61833333333334 52 111.3 106.831666666667 4.46833333333334 53 110.6 106.831666666667 3.76833333333333 54 120.1 116.598333333333 3.50166666666667 55 97.5 101.415 -3.91499999999999 56 107.7 105.565 2.13500000000001 57 127.3 120.566666666667 6.73333333333333 58 117.2 121.216666666667 -4.01666666666666 59 119.8 114.533333333333 5.26666666666667 60 116.2 114.083333333333 2.11666666666667 61 111 106.265 4.73499999999996 62 112.4 105.131666666667 7.26833333333335 63 130.6 117.181666666667 13.4183333333333 64 109.1 106.831666666667 2.26833333333334 65 118.8 106.831666666667 11.9683333333333 66 123.9 116.598333333333 7.30166666666668 67 101.6 101.415 0.184999999999998 68 112.8 105.565 7.235 69 128 120.566666666667 7.43333333333333 70 129.6 121.216666666667 8.38333333333332 71 125.8 114.533333333333 11.2666666666667 72 119.5 114.083333333333 5.41666666666667 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.0231735591743929 0.0463471183487859 0.976826440825607 17 0.00498859725810238 0.00997719451620476 0.995011402741898 18 0.00457049504713111 0.00914099009426223 0.995429504952869 19 0.00467362626904947 0.00934725253809894 0.99532637373095 20 0.00233847683846664 0.00467695367693328 0.997661523161533 21 0.00123712771141443 0.00247425542282886 0.998762872288586 22 0.000394152748365319 0.000788305496730638 0.999605847251635 23 0.000239868498533244 0.000479736997066489 0.999760131501467 24 0.00053555727041671 0.00107111454083342 0.999464442729583 25 0.0261634088398168 0.0523268176796336 0.973836591160183 26 0.0254582809643027 0.0509165619286055 0.974541719035697 27 0.040180296553214 0.080360593106428 0.959819703446786 28 0.0546241466661683 0.109248293332337 0.945375853333832 29 0.0614661688970903 0.122932337794181 0.93853383110291 30 0.0869965783331037 0.173993156666207 0.913003421666896 31 0.142791465577585 0.285582931155170 0.857208534422415 32 0.142702427873292 0.285404855746585 0.857297572126708 33 0.434428675962179 0.868857351924358 0.565571324037821 34 0.431699431629077 0.863398863258154 0.568300568370923 35 0.51891385038668 0.96217229922664 0.48108614961332 36 0.844150637877912 0.311698724244176 0.155849362122088 37 0.856516539241267 0.286966921517465 0.143483460758733 38 0.825075211260107 0.349849577479786 0.174924788739893 39 0.84615621031596 0.307687579368082 0.153843789684041 40 0.805456731513834 0.389086536972332 0.194543268486166 41 0.868428899370689 0.263142201258622 0.131571100629311 42 0.912755355404674 0.174489289190652 0.087244644595326 43 0.926706144095154 0.146587711809692 0.073293855904846 44 0.904768768159592 0.190462463680817 0.0952312318404083 45 0.905699450052024 0.188601099895951 0.0943005499479756 46 0.862379887314373 0.275240225371254 0.137620112685627 47 0.845398743636205 0.30920251272759 0.154601256363795 48 0.945552322915553 0.108895354168893 0.0544476770844466 49 0.912992051911103 0.174015896177793 0.0870079480888967 50 0.892609477710368 0.214781044579263 0.107390522289632 51 0.92268539530586 0.154629209388280 0.0773146046941399 52 0.873686388495625 0.252627223008750 0.126313611504375 53 0.872481818301553 0.255036363396894 0.127518181698447 54 0.803167546128952 0.393664907742097 0.196832453871048 55 0.703410776513221 0.593178446973558 0.296589223486779 56 0.585265378345286 0.829469243309428 0.414734621654714 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 8 0.195121951219512 NOK 5% type I error level 9 0.219512195121951 NOK 10% type I error level 12 0.292682926829268 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No 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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