Q3 seatbelt law d+L

*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: Mon, 01 Dec 2008 15:29:17 -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/Dec/01/t122817062917i4ugtwfo3nsfy.htm/, Retrieved Mon, 01 Dec 2008 22:30:30 +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/Dec/01/t122817062917i4ugtwfo3nsfy.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 «

7.8 0 7.6 0 7.5 0 7.6 0 7.5 0 7.3 0 7.6 0 7.5 0 7.6 0 7.9 0 7.9 0 8.1 0 8.2 0 8.0 0 7.5 0 6.8 0 6.5 0 6.6 0 7.6 0 8.0 0 8.0 0 7.7 0 7.5 0 7.6 0 7.7 0 7.9 0 7.8 0 7.5 0 7.5 0 7.1 0 7.5 0 7.5 0 7.6 0 7.7 1 7.9 1 8.1 1 8.2 1 8.2 1 8.1 1 7.9 1 7.3 1 6.9 1 6.6 1 6.7 1 6.9 1 7.0 1 7.1 1 7.2 1 7.1 1 6.9 1 7.0 1 6.8 1 6.4 1 6.7 1 6.7 1 6.4 1 6.3 1 6.2 1 6.5 1 6.8 1 6.8 1 6.5 1 6.3 1 5.9 1 5.9 1 6.4 1 6.4 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 5 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Multiple Linear Regression - Estimated Regression Equation y[t] = + 8.38947368421052 + 0.262061403508772x[t] -0.0375036549707602M1[t] -0.126761695906432M2[t] -0.249353070175439M3[t] -0.505277777777778M4[t] -0.711202485380117M5[t] -0.70046052631579M6[t] -0.439718567251462M7[t] -0.397222222222222M8[t] -0.309813596491228M9[t] -0.314817251461988M10[t] -0.207408625730994M11[t] -0.0274086257309942t + 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) 8.38947368421052 0.216535 38.7441 0 0 x 0.262061403508772 0.211976 1.2363 0.221807 0.110903 M1 -0.0375036549707602 0.255961 -0.1465 0.884066 0.442033 M2 -0.126761695906432 0.255831 -0.4955 0.622302 0.311151 M3 -0.249353070175439 0.255817 -0.9747 0.334121 0.167061 M4 -0.505277777777778 0.25592 -1.9744 0.053562 0.026781 M5 -0.711202485380117 0.256139 -2.7766 0.007576 0.003788 M6 -0.70046052631579 0.256475 -2.7311 0.008553 0.004277 M7 -0.439718567251462 0.256926 -1.7115 0.092844 0.046422 M8 -0.397222222222222 0.268196 -1.4811 0.144504 0.072252 M9 -0.309813596491228 0.268559 -1.1536 0.253834 0.126917 M10 -0.314817251461988 0.267186 -1.1783 0.243953 0.121976 M11 -0.207408625730994 0.267019 -0.7768 0.440755 0.220378 t -0.0274086257309942 0.005463 -5.0169 6e-06 3e-06 Multiple Linear Regression - Regression Statistics Multiple R 0.794139183421726 R-squared 0.630657042645726 Adjusted R-squared 0.540063487068263 F-TEST (value) 6.96138967750829 F-TEST (DF numerator) 13 F-TEST (DF denominator) 53 p-value 1.34900312365183e-07 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.422105286890354 Sum Squared Residuals 9.44316228070175 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 7.8 8.32456140350877 -0.524561403508772 2 7.6 8.2078947368421 -0.607894736842105 3 7.5 8.0578947368421 -0.557894736842105 4 7.6 7.77456140350877 -0.174561403508772 5 7.5 7.54122807017544 -0.0412280701754385 6 7.3 7.52456140350877 -0.224561403508772 7 7.6 7.7578947368421 -0.157894736842106 8 7.5 7.77298245614035 -0.272982456140351 9 7.6 7.83298245614035 -0.232982456140351 10 7.9 7.8005701754386 0.0994298245614037 11 7.9 7.8805701754386 0.0194298245614038 12 8.1 8.0605701754386 0.0394298245614034 13 8.2 7.99565789473684 0.204342105263157 14 8 7.87899122807018 0.121008771929825 15 7.5 7.72899122807017 -0.228991228070175 16 6.8 7.44565789473684 -0.645657894736842 17 6.5 7.21232456140351 -0.712324561403509 18 6.6 7.19565789473684 -0.595657894736842 19 7.6 7.42899122807018 0.171008771929824 20 8 7.44407894736842 0.555921052631579 21 8 7.50407894736842 0.495921052631579 22 7.7 7.47166666666667 0.228333333333333 23 7.5 7.55166666666667 -0.0516666666666667 24 7.6 7.73166666666667 -0.131666666666667 25 7.7 7.66675438596491 0.0332456140350881 26 7.9 7.55008771929825 0.349912280701755 27 7.8 7.40008771929825 0.399912280701754 28 7.5 7.11675438596491 0.383245614035088 29 7.5 6.88342105263158 0.616578947368421 30 7.1 6.86675438596491 0.233245614035088 31 7.5 7.10008771929825 0.399912280701755 32 7.5 7.11517543859649 0.384824561403509 33 7.6 7.17517543859649 0.424824561403509 34 7.7 7.40482456140351 0.295175438596491 35 7.9 7.48482456140351 0.415175438596492 36 8.1 7.66482456140351 0.435175438596491 37 8.2 7.59991228070175 0.600087719298245 38 8.2 7.48324561403509 0.716754385964911 39 8.1 7.33324561403509 0.766754385964912 40 7.9 7.04991228070175 0.850087719298246 41 7.3 6.81657894736842 0.483421052631579 42 6.9 6.79991228070175 0.100087719298246 43 6.6 7.03324561403509 -0.433245614035088 44 6.7 7.04833333333333 -0.348333333333333 45 6.9 7.10833333333333 -0.208333333333333 46 7 7.07592105263158 -0.0759210526315792 47 7.1 7.15592105263158 -0.0559210526315794 48 7.2 7.33592105263158 -0.135921052631579 49 7.1 7.27100877192982 -0.171008771929825 50 6.9 7.15434210526316 -0.254342105263158 51 7 7.00434210526316 -0.00434210526315777 52 6.8 6.72100877192982 0.0789912280701753 53 6.4 6.48767543859649 -0.0876754385964908 54 6.7 6.47100877192982 0.228991228070176 55 6.7 6.70434210526316 -0.00434210526315763 56 6.4 6.7194298245614 -0.319429824561403 57 6.3 6.7794298245614 -0.479429824561404 58 6.2 6.74701754385965 -0.54701754385965 59 6.5 6.82701754385965 -0.327017543859649 60 6.8 7.00701754385965 -0.207017543859649 61 6.8 6.9421052631579 -0.142105263157895 62 6.5 6.82543859649123 -0.325438596491228 63 6.3 6.67543859649123 -0.375438596491228 64 5.9 6.3921052631579 -0.492105263157895 65 5.9 6.15877192982456 -0.258771929824562 66 6.4 6.1421052631579 0.257894736842105 67 6.4 6.37543859649123 0.0245614035087722

Charts produced by software:

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Parameters (Session):

par1 = 0 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 0 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

R code (references can be found in the software module):

library(lattice) 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)) 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$resid, main='Residual Normal Q-Q Plot') grid() dev.off() (myerror <- as.ts(mysum$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() 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')

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Software written by Ed van Stee & Patrick Wessa

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