Q3 seatbelt law dummy

*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 15:25:22 -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/t1228170382gyf5ccef43gq775.htm/, Retrieved Mon, 01 Dec 2008 22:26:32 +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/t1228170382gyf5ccef43gq775.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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation y[t] = + 7.9589090909091 -0.664848484848485x[t] + 0.00684848484848708M1[t] -0.109818181818181M2[t] -0.259818181818182M3[t] -0.543151515151516M4[t] -0.776484848484849M5[t] -0.793151515151515M6[t] -0.559818181818181M7[t] -0.472969696969696M8[t] -0.412969696969697M9[t] -0.26M10[t] -0.180000000000000M11[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) 7.9589090909091 0.239188 33.2747 0 0 x -0.664848484848485 0.125026 -5.3177 2e-06 1e-06 M1 0.00684848484848708 0.307777 0.0223 0.982329 0.491165 M2 -0.109818181818181 0.307777 -0.3568 0.722624 0.361312 M3 -0.259818181818182 0.307777 -0.8442 0.402295 0.201147 M4 -0.543151515151516 0.307777 -1.7648 0.083259 0.04163 M5 -0.776484848484849 0.307777 -2.5229 0.014618 0.007309 M6 -0.793151515151515 0.307777 -2.577 0.01273 0.006365 M7 -0.559818181818181 0.307777 -1.8189 0.074472 0.037236 M8 -0.472969696969696 0.322169 -1.4681 0.147884 0.073942 M9 -0.412969696969697 0.322169 -1.2818 0.205374 0.102687 M10 -0.26 0.321197 -0.8095 0.421796 0.210898 M11 -0.180000000000000 0.321197 -0.5604 0.577522 0.288761 Multiple Linear Regression - Regression Statistics Multiple R 0.674729792914137 R-squared 0.455260293445954 Adjusted R-squared 0.334207025322833 F-TEST (value) 3.76082612641995 F-TEST (DF numerator) 12 F-TEST (DF denominator) 54 p-value 0.000371990161561309 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.507857010373402 Sum Squared Residuals 13.9276121212121 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 7.8 7.96575757575756 -0.165757575757563 2 7.6 7.8490909090909 -0.249090909090909 3 7.5 7.69909090909091 -0.199090909090909 4 7.6 7.41575757575758 0.184242424242423 5 7.5 7.18242424242424 0.317575757575757 6 7.3 7.16575757575757 0.134242424242425 7 7.6 7.39909090909091 0.200909090909091 8 7.5 7.4859393939394 0.0140606060606061 9 7.6 7.5459393939394 0.0540606060606054 10 7.9 7.69890909090909 0.201090909090909 11 7.9 7.77890909090909 0.121090909090909 12 8.1 7.95890909090909 0.141090909090909 13 8.2 7.96575757575758 0.234242424242421 14 8 7.84909090909091 0.150909090909091 15 7.5 7.69909090909091 -0.199090909090909 16 6.8 7.41575757575758 -0.615757575757576 17 6.5 7.18242424242424 -0.682424242424242 18 6.6 7.16575757575758 -0.565757575757577 19 7.6 7.39909090909091 0.200909090909090 20 8 7.4859393939394 0.514060606060606 21 8 7.5459393939394 0.454060606060606 22 7.7 7.69890909090909 0.00109090909090900 23 7.5 7.77890909090909 -0.278909090909091 24 7.6 7.9589090909091 -0.358909090909091 25 7.7 7.96575757575758 -0.265757575757578 26 7.9 7.84909090909091 0.0509090909090912 27 7.8 7.69909090909091 0.100909090909091 28 7.5 7.41575757575758 0.0842424242424244 29 7.5 7.18242424242424 0.317575757575758 30 7.1 7.16575757575758 -0.0657575757575765 31 7.5 7.39909090909091 0.100909090909091 32 7.5 7.4859393939394 0.0140606060606057 33 7.6 7.5459393939394 0.0540606060606058 34 7.7 7.0340606060606 0.665939393939394 35 7.9 7.1140606060606 0.785939393939394 36 8.1 7.2940606060606 0.805939393939394 37 8.2 7.30090909090909 0.899090909090906 38 8.2 7.18424242424242 1.01575757575758 39 8.1 7.03424242424242 1.06575757575758 40 7.9 6.75090909090909 1.14909090909091 41 7.3 6.51757575757576 0.782424242424242 42 6.9 6.50090909090909 0.399090909090909 43 6.6 6.73424242424242 -0.134242424242425 44 6.7 6.82109090909091 -0.121090909090909 45 6.9 6.88109090909091 0.0189090909090916 46 7 7.0340606060606 -0.034060606060606 47 7.1 7.1140606060606 -0.0140606060606064 48 7.2 7.2940606060606 -0.0940606060606056 49 7.1 7.30090909090909 -0.200909090909093 50 6.9 7.18424242424242 -0.284242424242424 51 7 7.03424242424242 -0.0342424242424239 52 6.8 6.75090909090909 0.0490909090909093 53 6.4 6.51757575757576 -0.117575757575757 54 6.7 6.50090909090909 0.199090909090909 55 6.7 6.73424242424242 -0.034242424242424 56 6.4 6.82109090909091 -0.421090909090909 57 6.3 6.88109090909091 -0.581090909090909 58 6.2 7.0340606060606 -0.834060606060606 59 6.5 7.1140606060606 -0.614060606060606 60 6.8 7.2940606060606 -0.494060606060606 61 6.8 7.30090909090909 -0.500909090909093 62 6.5 7.18424242424242 -0.684242424242424 63 6.3 7.03424242424242 -0.734242424242424 64 5.9 6.75090909090909 -0.85090909090909 65 5.9 6.51757575757576 -0.617575757575757 66 6.4 6.50090909090909 -0.100909090909091 67 6.4 6.73424242424242 -0.334242424242424

Charts produced by software:

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Parameters (Session):

par1 = 0 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 0 ; par2 = Include Monthly 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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