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 08:47:24 -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/t12278011858nz9qs322j7ym0r.htm/, Retrieved Thu, 27 Nov 2008 15:53:15 +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/t12278011858nz9qs322j7ym0r.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 «

119.5 0 125 0 145 0 105.3 0 116.9 0 120.1 0 88.9 0 78.4 0 114.6 0 113.3 0 117 0 99.6 0 99.4 0 101.9 0 115.2 0 108.5 0 113.8 0 121 0 92.2 0 90.2 0 101.5 0 126.6 0 93.9 0 89.8 0 93.4 0 101.5 0 110.4 0 105.9 0 108.4 0 113.9 0 86.1 0 69.4 0 101.2 0 100.5 0 98 0 106.6 0 90.1 0 96.9 0 125.9 0 112 0 100 0 123.9 0 79.8 0 83.4 0 113.6 0 112.9 0 104 0 109.9 0 99 0 106.3 0 128.9 0 111.1 0 102.9 0 130 0 87 0 87.5 0 117.6 0 103.4 0 110.8 0 112.6 0 102.5 0 112.4 0 135.6 0 105.1 0 127.7 0 137 0 91 0 90.5 0 122.4 1 123.3 1 124.3 1 120 1 118.1 1 119 1 142.7 1 123.6 1 129.6 1 151.6 1 110.4 1 99.2 1 130.5 1 136.2 1 129.7 1 128 1 121.6 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 y[t] = + 106.532352941176 + 18.7735294117647x[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) 106.532352941176 1.743906 61.0884 0 0 x 18.7735294117647 3.899492 4.8144 7e-06 3e-06 Multiple Linear Regression - Regression Statistics Multiple R 0.467219128896478 R-squared 0.218293714406784 Adjusted R-squared 0.208875566387588 F-TEST (value) 23.1779872180681 F-TEST (DF numerator) 1 F-TEST (DF denominator) 83 p-value 6.54887524531578e-06 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 14.3806170734493 Sum Squared Residuals 17164.5782352941 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 119.5 106.532352941177 12.9676470588229 2 125 106.532352941176 18.4676470588235 3 145 106.532352941176 38.4676470588235 4 105.3 106.532352941176 -1.23235294117646 5 116.9 106.532352941176 10.3676470588235 6 120.1 106.532352941176 13.5676470588235 7 88.9 106.532352941176 -17.6323529411765 8 78.4 106.532352941176 -28.1323529411765 9 114.6 106.532352941176 8.06764705882353 10 113.3 106.532352941176 6.76764705882354 11 117 106.532352941176 10.4676470588235 12 99.6 106.532352941176 -6.93235294117647 13 99.4 106.532352941176 -7.13235294117646 14 101.9 106.532352941176 -4.63235294117646 15 115.2 106.532352941176 8.66764705882354 16 108.5 106.532352941176 1.96764705882354 17 113.8 106.532352941176 7.26764705882354 18 121 106.532352941176 14.4676470588235 19 92.2 106.532352941176 -14.3323529411765 20 90.2 106.532352941176 -16.3323529411765 21 101.5 106.532352941176 -5.03235294117646 22 126.6 106.532352941176 20.0676470588235 23 93.9 106.532352941176 -12.6323529411765 24 89.8 106.532352941176 -16.7323529411765 25 93.4 106.532352941176 -13.1323529411765 26 101.5 106.532352941176 -5.03235294117646 27 110.4 106.532352941176 3.86764705882354 28 105.9 106.532352941176 -0.632352941176456 29 108.4 106.532352941176 1.86764705882354 30 113.9 106.532352941176 7.36764705882354 31 86.1 106.532352941176 -20.4323529411765 32 69.4 106.532352941176 -37.1323529411765 33 101.2 106.532352941176 -5.33235294117646 34 100.5 106.532352941176 -6.03235294117646 35 98 106.532352941176 -8.53235294117646 36 106.6 106.532352941176 0.0676470588235327 37 90.1 106.532352941176 -16.4323529411765 38 96.9 106.532352941176 -9.63235294117646 39 125.9 106.532352941176 19.3676470588235 40 112 106.532352941176 5.46764705882354 41 100 106.532352941176 -6.53235294117646 42 123.9 106.532352941176 17.3676470588235 43 79.8 106.532352941176 -26.7323529411765 44 83.4 106.532352941176 -23.1323529411765 45 113.6 106.532352941176 7.06764705882353 46 112.9 106.532352941176 6.36764705882354 47 104 106.532352941176 -2.53235294117646 48 109.9 106.532352941176 3.36764705882354 49 99 106.532352941176 -7.53235294117646 50 106.3 106.532352941176 -0.232352941176464 51 128.9 106.532352941176 22.3676470588235 52 111.1 106.532352941176 4.56764705882353 53 102.9 106.532352941176 -3.63235294117646 54 130 106.532352941176 23.4676470588235 55 87 106.532352941176 -19.5323529411765 56 87.5 106.532352941176 -19.0323529411765 57 117.6 106.532352941176 11.0676470588235 58 103.4 106.532352941176 -3.13235294117646 59 110.8 106.532352941176 4.26764705882354 60 112.6 106.532352941176 6.06764705882353 61 102.5 106.532352941176 -4.03235294117646 62 112.4 106.532352941176 5.86764705882354 63 135.6 106.532352941176 29.0676470588235 64 105.1 106.532352941176 -1.43235294117647 65 127.7 106.532352941176 21.1676470588235 66 137 106.532352941176 30.4676470588235 67 91 106.532352941176 -15.5323529411765 68 90.5 106.532352941176 -16.0323529411765 69 122.4 125.305882352941 -2.90588235294117 70 123.3 125.305882352941 -2.00588235294118 71 124.3 125.305882352941 -1.00588235294118 72 120 125.305882352941 -5.30588235294117 73 118.1 125.305882352941 -7.20588235294118 74 119 125.305882352941 -6.30588235294117 75 142.7 125.305882352941 17.3941176470588 76 123.6 125.305882352941 -1.70588235294118 77 129.6 125.305882352941 4.29411764705882 78 151.6 125.305882352941 26.2941176470588 79 110.4 125.305882352941 -14.9058823529412 80 99.2 125.305882352941 -26.1058823529412 81 130.5 125.305882352941 5.19411764705883 82 136.2 125.305882352941 10.8941176470588 83 129.7 125.305882352941 4.39411764705882 84 128 125.305882352941 2.69411764705883 85 121.6 125.305882352941 -3.70588235294118

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No 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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