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the seatbelt law

R Software Module: rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Mon, 19 Nov 2007 04:01:48 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2007/Nov/19/t1195469763yqp27qafvvu2sqv.htm/, Retrieved Mon, 19 Nov 2007 11:56:34 +0100

User-defined keywords:

Q3

Dataseries X:

» Textbox « » Textfile « » CSV «

102.3 0 98.7 0 104.4 0 97.6 0 102.7 0 103.0 0 92.9 0 96.1 0 94.9 0 99.9 0 96.3 0 89.5 0 104.6 0 101.5 0 109.8 0 112.1 0 110.1 0 107.1 0 108.1 0 99.0 0 104.0 0 106.7 0 101.1 0 97.8 0 113.8 0 107.1 0 117.5 1 113.7 1 106.6 1 109.8 1 108.8 1 102.0 1 114.5 1 116.5 1 108.6 1 113.9 1 109.3 1 112.5 1 123.4 1 115.2 1 110.8 1 120.4 1 117.6 1 111.2 1 131.1 1 118.9 1 115.7 1 119.6 1 113.1 1 106.4 1 115.5 1 111.8 1 109.6 1 121.5 1 109.5 1 109.0 1 113.4 1 112.7 1 114.4 1 109.2 1 116.2 1 113.8 1 123.6 1 112.6 1 117.7 1 113.3 1 110.7 1 114.7 1 116.9 1 120.6 1 111.6 1 111.9 1 116.1 1 111.9 1 125.1 1 115.1 1 116.7 1 115.8 1 116.8 1 113.0 1 106.5 1

Text written by user:

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 compuational 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] = + 102.35 + 11.91`x `[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) 102.35 1.068477 95.7905 0 0 `x ` 11.91 1.296661 9.1851 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.718627141240444 R-squared 0.516424968127414 Adjusted R-squared 0.510303765192318 F-TEST (value) 84.3665817982413 F-TEST (DF numerator) 1 F-TEST (DF denominator) 79 p-value 4.2410519540681e-14 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 5.44818748167159 Sum Squared Residuals 2344.937 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 102.3 102.350000000000 -0.0500000000001618 2 98.7 102.35 -3.64999999999991 3 104.4 102.35 2.05000000000001 4 97.6 102.35 -4.75 5 102.7 102.35 0.350000000000008 6 103 102.35 0.650000000000005 7 92.9 102.35 -9.44999999999999 8 96.1 102.35 -6.25 9 94.9 102.35 -7.44999999999999 10 99.9 102.35 -2.44999999999999 11 96.3 102.35 -6.05 12 89.5 102.35 -12.85 13 104.6 102.35 2.25 14 101.5 102.35 -0.849999999999995 15 109.8 102.35 7.45 16 112.1 102.35 9.75 17 110.1 102.35 7.75 18 107.1 102.35 4.75 19 108.1 102.35 5.75 20 99 102.35 -3.34999999999999 21 104 102.35 1.65000000000001 22 106.7 102.35 4.35000000000001 23 101.1 102.35 -1.25 24 97.8 102.35 -4.55 25 113.8 102.35 11.45 26 107.1 102.35 4.75 27 117.5 114.26 3.24 28 113.7 114.26 -0.559999999999997 29 106.6 114.26 -7.66 30 109.8 114.26 -4.46 31 108.8 114.26 -5.46 32 102 114.26 -12.26 33 114.5 114.26 0.24 34 116.5 114.26 2.24 35 108.6 114.26 -5.66 36 113.9 114.26 -0.359999999999994 37 109.3 114.26 -4.96 38 112.5 114.26 -1.76 39 123.4 114.26 9.14 40 115.2 114.26 0.940000000000003 41 110.8 114.26 -3.46 42 120.4 114.26 6.14000000000001 43 117.6 114.26 3.33999999999999 44 111.2 114.26 -3.06 45 131.1 114.26 16.84 46 118.9 114.26 4.64000000000001 47 115.7 114.26 1.44000000000000 48 119.6 114.26 5.34 49 113.1 114.26 -1.16000000000001 50 106.4 114.26 -7.86 51 115.5 114.26 1.24 52 111.8 114.26 -2.46000000000000 53 109.6 114.26 -4.66000000000001 54 121.5 114.26 7.24 55 109.5 114.26 -4.76 56 109 114.26 -5.26 57 113.4 114.26 -0.859999999999994 58 112.7 114.26 -1.56000000000000 59 114.4 114.26 0.140000000000006 60 109.2 114.26 -5.06 61 116.2 114.26 1.94000000000000 62 113.8 114.26 -0.460000000000003 63 123.6 114.26 9.34 64 112.6 114.26 -1.66000000000001 65 117.7 114.26 3.44 66 113.3 114.26 -0.960000000000003 67 110.7 114.26 -3.56 68 114.7 114.26 0.440000000000003 69 116.9 114.26 2.64000000000001 70 120.6 114.26 6.34 71 111.6 114.26 -2.66000000000001 72 111.9 114.26 -2.35999999999999 73 116.1 114.26 1.83999999999999 74 111.9 114.26 -2.35999999999999 75 125.1 114.26 10.84 76 115.1 114.26 0.839999999999994 77 116.7 114.26 2.44000000000000 78 115.8 114.26 1.54000000000000 79 116.8 114.26 2.54000000000000 80 113 114.26 -1.26 81 106.5 114.26 -7.76

Charts produced by software:

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Parameters:

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')

Copyright

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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