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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 03:39:05 -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/t11954690264rlncllihx77s8y.htm/, Retrieved Mon, 19 Nov 2007 11:43:56 +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] = + 97.7056407447974 + 8.0907447973713`x `[t] + 5.02100697160936M1[t] + 1.57139119247554M2[t] + 9.9516690137172M3[t] + 3.97348180601192M4[t] + 3.32386602687806M5[t] + 5.61710739060135M6[t] + 1.73892018289609M7[t] -1.12498131052348M8[t] + 3.96826005319980M9[t] + 5.75161251064865M10[t] + 1.05913958865765M11[t] + 0.0924729219909944t + 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) 97.7056407447974 2.213221 44.1463 0 0 `x ` 8.0907447973713 1.986865 4.0721 0.000126 6.3e-05 M1 5.02100697160936 2.709545 1.8531 0.068275 0.034137 M2 1.57139119247554 2.709179 0.58 0.563843 0.281922 M3 9.9516690137172 2.714515 3.6661 0.000488 0.000244 M4 3.97348180601192 2.71195 1.4652 0.14755 0.073775 M5 3.32386602687806 2.709962 1.2265 0.22429 0.112145 M6 5.61710739060135 2.708552 2.0738 0.041941 0.02097 M7 1.73892018289609 2.707721 0.6422 0.52293 0.261465 M8 -1.12498131052348 2.70747 -0.4155 0.679096 0.339548 M9 3.96826005319980 2.707797 1.4655 0.147464 0.073732 M10 5.75161251064865 2.810199 2.0467 0.044614 0.022307 M11 1.05913958865765 2.809362 0.377 0.707362 0.353681 t 0.0924729219909944 0.039612 2.3345 0.022577 0.011288 Multiple Linear Regression - Regression Statistics Multiple R 0.820315320336834 R-squared 0.672917224779323 Adjusted R-squared 0.609453402721579 F-TEST (value) 10.6031626044687 F-TEST (DF numerator) 13 F-TEST (DF denominator) 67 p-value 9.47952827345944e-12 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4.86547326729879 Sum Squared Residuals 1586.07961769155 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 102.3 102.819120638398 -0.519120638397901 2 98.7 99.4619777812548 -0.761977781254835 3 104.4 107.934728524488 -3.53472852448757 4 97.6 102.049014238773 -4.44901423877329 5 102.7 101.491871381630 1.20812861836959 6 103 103.877585667345 -0.87758566734472 7 92.9 100.091871381630 -7.1918713816304 8 96.1 97.3204428102018 -1.22044281020183 9 94.9 102.506157095916 -7.60615709591612 10 99.9 104.381982475356 -4.48198247535596 11 96.3 99.781982475356 -3.48198247535597 12 89.5 98.8153158086893 -9.3153158086893 13 104.6 103.928795702290 0.67120429771035 14 101.5 100.571652845147 0.928347154853177 15 109.8 109.044403588379 0.755596411620518 16 112.1 103.158689302665 8.9413106973348 17 110.1 102.601546445522 7.49845355447765 18 107.1 104.987260731237 2.11273926876337 19 108.1 101.201546445522 6.89845355447764 20 99 98.4301178740938 0.569882125906226 21 104 103.615832159808 0.384167840191943 22 106.7 105.491657539248 1.20834246075210 23 101.1 100.891657539248 0.208342460752099 24 97.8 99.9249908725812 -2.12499087258124 25 113.8 105.038470766182 8.76152923381842 26 107.1 101.681327909039 5.41867209096124 27 117.5 118.244823449643 -0.74482344964272 28 113.7 112.359109163928 1.34089083607157 29 106.6 111.801966306786 -5.20196630678559 30 109.8 114.187680592500 -4.38768059249987 31 108.8 110.401966306786 -1.60196630678559 32 102 107.630537735357 -5.63053773535701 33 114.5 112.816252021071 1.68374797892870 34 116.5 114.692077400511 1.80792259948886 35 108.6 110.092077400511 -1.49207740051114 36 113.9 109.125410733844 4.77458926615553 37 109.3 114.238890627445 -4.93889062744482 38 112.5 110.881747770302 1.61825222969800 39 123.4 119.354498513535 4.04550148646535 40 115.2 113.468784227820 1.73121577217964 41 110.8 112.911641370678 -2.11164137067752 42 120.4 115.297355656392 5.10264434360821 43 117.6 111.511641370678 6.08835862932247 44 111.2 108.740212799249 2.45978720075106 45 131.1 113.925927084963 17.1740729150368 46 118.9 115.801752464403 3.09824753559694 47 115.7 111.201752464403 4.49824753559694 48 119.6 110.235085797736 9.3649142022636 49 113.1 115.348565691337 -2.24856569133675 50 106.4 111.991422834194 -5.59142283419392 51 115.5 120.464173577427 -4.96417357742659 52 111.8 114.578459291712 -2.7784592917123 53 109.6 114.021316434569 -4.42131643456946 54 121.5 116.407030720284 5.09296927971627 55 109.5 112.621316434569 -3.12131643456945 56 109 109.849887863141 -0.84988786314088 57 113.4 115.035602148855 -1.63560214885516 58 112.7 116.911427528295 -4.211427528295 59 114.4 112.311427528295 2.08857247170501 60 109.2 111.344760861628 -2.14476086162834 61 116.2 116.458240755229 -0.258240755228678 62 113.8 113.101097898086 0.698902101914137 63 123.6 121.573848641319 2.02615135868148 64 112.6 115.688134355604 -3.08813435560424 65 117.7 115.130991498461 2.56900850153862 66 113.3 117.516705784176 -4.21670578417566 67 110.7 113.730991498461 -3.03099149846138 68 114.7 110.959562927033 3.74043707296719 69 116.9 116.145277212747 0.754722787252912 70 120.6 118.021102592187 2.57889740781306 71 111.6 113.421102592187 -1.82110259218694 72 111.9 112.454435925520 -0.554435925520266 73 116.1 117.567915819121 -1.46791581912062 74 111.9 114.210772961978 -2.31077296197779 75 125.1 122.683523705210 2.41647629478954 76 115.1 116.797809419496 -1.69780941949617 77 116.7 116.240666562353 0.459333437646688 78 115.8 118.626380848068 -2.8263808480676 79 116.8 114.840666562353 1.95933343764668 80 113 112.069237990925 0.930762009075256 81 106.5 117.254952276639 -10.7549522766390

Charts produced by software:

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Parameters:

par1 = 1 ; 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')

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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