Q3 seatbelt trend + dummies

*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, 24 Nov 2008 12:37:49 -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/24/t1227555535mraqq5rhwaeavtp.htm/, Retrieved Mon, 24 Nov 2008 19:38:55 +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/24/t1227555535mraqq5rhwaeavtp.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)

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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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 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 6 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation y[t] = + 8.239 + 0.245000000000000x[t] + 0.0864444444444439M1[t] + 0.0793888888888892M2[t] -0.094333333333333M3[t] -0.251388888888889M4[t] -0.425111111111110M5[t] -0.648833333333333M6[t] -0.272555555555555M7[t] -0.246277777777777M8[t] -0.209833333333333M9[t] -0.143555555555555M10[t] -0.206277777777777M11[t] -0.0262777777777778t + 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) 8.239 0.223621 36.8436 0 0 x 0.245000000000000 0.219278 1.1173 0.268811 0.134406 M1 0.0864444444444439 0.265919 0.3251 0.746378 0.373189 M2 0.0793888888888892 0.265794 0.2987 0.766326 0.383163 M3 -0.094333333333333 0.265785 -0.3549 0.72403 0.362015 M4 -0.251388888888889 0.265894 -0.9454 0.348642 0.174321 M5 -0.425111111111110 0.26612 -1.5974 0.116003 0.058002 M6 -0.648833333333333 0.266463 -2.435 0.018226 0.009113 M7 -0.272555555555555 0.266922 -1.0211 0.311757 0.155878 M8 -0.246277777777777 0.267497 -0.9207 0.361314 0.180657 M9 -0.209833333333333 0.279024 -0.752 0.4553 0.22765 M10 -0.143555555555555 0.27951 -0.5136 0.609629 0.304814 M11 -0.206277777777777 0.277423 -0.7435 0.460373 0.230186 t -0.0262777777777778 0.005583 -4.7071 1.8e-05 9e-06 Multiple Linear Regression - Regression Statistics Multiple R 0.772605720789599 R-squared 0.596919599796816 Adjusted R-squared 0.499881725673827 F-TEST (value) 6.15140845975523 F-TEST (DF numerator) 13 F-TEST (DF denominator) 54 p-value 7.15354301350501e-07 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.438556132646075 Sum Squared Residuals 10.3859 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 7.8 8.29916666666667 -0.499166666666671 2 7.6 8.26583333333333 -0.665833333333333 3 7.5 8.06583333333333 -0.565833333333333 4 7.6 7.8825 -0.282500000000000 5 7.5 7.6825 -0.1825 6 7.3 7.4325 -0.132500000000000 7 7.6 7.7825 -0.1825 8 7.5 7.7825 -0.282500000000000 9 7.6 7.79266666666667 -0.192666666666667 10 7.9 7.83266666666667 0.0673333333333337 11 7.9 7.74366666666667 0.156333333333334 12 8.1 7.92366666666667 0.176333333333334 13 8.2 7.98383333333333 0.216166666666667 14 8 7.9505 0.0495000000000009 15 7.5 7.7505 -0.250500000000000 16 6.8 7.56716666666667 -0.767166666666667 17 6.5 7.36716666666667 -0.867166666666666 18 6.6 7.11716666666667 -0.517166666666667 19 7.6 7.46716666666667 0.132833333333333 20 8 7.46716666666667 0.532833333333334 21 8 7.47733333333333 0.522666666666667 22 7.7 7.51733333333333 0.182666666666667 23 7.5 7.42833333333333 0.0716666666666664 24 7.6 7.60833333333333 -0.00833333333333333 25 7.7 7.6685 0.0315000000000011 26 7.9 7.63516666666667 0.264833333333334 27 7.8 7.43516666666667 0.364833333333333 28 7.5 7.25183333333333 0.248166666666667 29 7.5 7.05183333333333 0.448166666666667 30 7.1 6.80183333333333 0.298166666666666 31 7.5 7.15183333333333 0.348166666666667 32 7.5 7.15183333333333 0.348166666666667 33 7.6 7.162 0.438 34 7.7 7.202 0.498 35 7.7 7.358 0.342000000000000 36 7.9 7.538 0.362000000000001 37 8.1 7.59816666666666 0.501833333333335 38 8.2 7.56483333333333 0.635166666666666 39 8.2 7.36483333333333 0.835166666666666 40 8.1 7.1815 0.9185 41 7.9 6.9815 0.9185 42 7.3 6.7315 0.5685 43 6.9 7.0815 -0.181499999999999 44 6.6 7.0815 -0.4815 45 6.7 7.09166666666667 -0.391666666666667 46 6.9 7.13166666666667 -0.231666666666667 47 7 7.04266666666667 -0.0426666666666671 48 7.1 7.22266666666667 -0.122666666666667 49 7.2 7.28283333333333 -0.0828333333333322 50 7.1 7.2495 -0.149500000000000 51 6.9 7.0495 -0.149500000000000 52 7 6.86616666666667 0.133833333333333 53 6.8 6.66616666666667 0.133833333333333 54 6.4 6.41616666666667 -0.0161666666666665 55 6.7 6.76616666666667 -0.0661666666666667 56 6.7 6.76616666666667 -0.0661666666666668 57 6.4 6.77633333333333 -0.376333333333333 58 6.3 6.81633333333333 -0.516333333333334 59 6.2 6.72733333333333 -0.527333333333334 60 6.5 6.90733333333333 -0.407333333333333 61 6.8 6.9675 -0.167499999999999 62 6.8 6.93416666666667 -0.134166666666667 63 6.5 6.73416666666667 -0.234166666666667 64 6.3 6.55083333333333 -0.250833333333334 65 5.9 6.35083333333333 -0.450833333333333 66 5.9 6.10083333333333 -0.200833333333333 67 6.4 6.45083333333333 -0.0508333333333334 68 6.4 6.45083333333333 -0.0508333333333333

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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