Q3 seatbelt case

*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: Sun, 30 Nov 2008 14:48:04 -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/30/t1228081757wj8oc1lqbxs8mkx.htm/, Retrieved Sun, 30 Nov 2008 21:49:17 +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/30/t1228081757wj8oc1lqbxs8mkx.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 «

5.014 0 6.153 0 6.441 0 5.584 0 6.427 0 6.062 0 5.589 0 6.216 0 5.809 0 4.989 0 6.706 0 7.174 0 6.122 0 8.075 0 6.292 0 6.337 0 8.576 0 6.077 0 5.931 0 6.288 0 7.167 0 6.054 0 6.468 0 6.401 0 6.927 0 7.914 0 7.728 0 8.699 0 8.522 0 6.481 0 7.502 0 7.778 0 7.424 0 6.941 0 8.574 0 9.169 1 7.701 1 9.035 1 7.158 1 8.195 1 8.124 1 7.073 1 7.017 1 7.390 1 7.776 1 6.197 1 6.889 1 7.087 1 6.485 1 7.654 1 6.501 1 6.313 1 7.826 1 6.589 1 6.729 1 5.684 1 8.105 1 6.391 1 5.901 1 6.758 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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation y[t] = + 6.75548571428571 + 0.434394285714286x[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) 6.75548571428571 0.162438 41.5881 0 0 x 0.434394285714286 0.251648 1.7262 0.089635 0.044818 Multiple Linear Regression - Regression Statistics Multiple R 0.221054033711299 R-squared 0.048864885820036 Adjusted R-squared 0.0324660045410712 F-TEST (value) 2.97976947261126 F-TEST (DF numerator) 1 F-TEST (DF denominator) 58 p-value 0.0896350965108561 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.960995096536139 Sum Squared Residuals 53.5636713828572 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 5.014 6.75548571428572 -1.74148571428572 2 6.153 6.75548571428571 -0.602485714285714 3 6.441 6.75548571428571 -0.314485714285714 4 5.584 6.75548571428571 -1.17148571428571 5 6.427 6.75548571428571 -0.328485714285714 6 6.062 6.75548571428571 -0.693485714285714 7 5.589 6.75548571428571 -1.16648571428571 8 6.216 6.75548571428571 -0.539485714285714 9 5.809 6.75548571428571 -0.946485714285714 10 4.989 6.75548571428571 -1.76648571428571 11 6.706 6.75548571428571 -0.0494857142857135 12 7.174 6.75548571428571 0.418514285714286 13 6.122 6.75548571428571 -0.633485714285714 14 8.075 6.75548571428571 1.31951428571429 15 6.292 6.75548571428571 -0.463485714285714 16 6.337 6.75548571428571 -0.418485714285714 17 8.576 6.75548571428571 1.82051428571429 18 6.077 6.75548571428571 -0.678485714285714 19 5.931 6.75548571428571 -0.824485714285714 20 6.288 6.75548571428571 -0.467485714285714 21 7.167 6.75548571428571 0.411514285714286 22 6.054 6.75548571428571 -0.701485714285714 23 6.468 6.75548571428571 -0.287485714285714 24 6.401 6.75548571428571 -0.354485714285714 25 6.927 6.75548571428571 0.171514285714286 26 7.914 6.75548571428571 1.15851428571429 27 7.728 6.75548571428571 0.972514285714286 28 8.699 6.75548571428571 1.94351428571429 29 8.522 6.75548571428571 1.76651428571429 30 6.481 6.75548571428571 -0.274485714285714 31 7.502 6.75548571428571 0.746514285714286 32 7.778 6.75548571428571 1.02251428571429 33 7.424 6.75548571428571 0.668514285714286 34 6.941 6.75548571428571 0.185514285714286 35 8.574 6.75548571428571 1.81851428571429 36 9.169 7.18988 1.97912 37 7.701 7.18988 0.511119999999999 38 9.035 7.18988 1.84512 39 7.158 7.18988 -0.0318799999999998 40 8.195 7.18988 1.00512 41 8.124 7.18988 0.93412 42 7.073 7.18988 -0.116880000000000 43 7.017 7.18988 -0.172880000000000 44 7.39 7.18988 0.200120000000000 45 7.776 7.18988 0.58612 46 6.197 7.18988 -0.99288 47 6.889 7.18988 -0.30088 48 7.087 7.18988 -0.102880000000000 49 6.485 7.18988 -0.70488 50 7.654 7.18988 0.46412 51 6.501 7.18988 -0.68888 52 6.313 7.18988 -0.87688 53 7.826 7.18988 0.63612 54 6.589 7.18988 -0.60088 55 6.729 7.18988 -0.46088 56 5.684 7.18988 -1.50588 57 8.105 7.18988 0.91512 58 6.391 7.18988 -0.79888 59 5.901 7.18988 -1.28888 60 6.758 7.18988 -0.43188

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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This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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