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The seatbelt law q3

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

Title produced by software: Multiple Regression

Date of computation: Thu, 22 Nov 2007 09:59:43 -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/22/t11957513350njysa5uza3bn5y.htm/, Retrieved Thu, 22 Nov 2007 18:09:05 +0100

User-defined keywords:

Dataseries X:

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7.8 1 7.4 1 7.4 0 7.5 0 7.4 0 7.4 0 7 0 6.9 0 6.9 0 7.6 0 7.7 0 7.6 0 8.2 0 8 0 8.1 0 8.3 0 8.2 0 8.1 1 7.7 1 7.6 1 7.7 1 8.2 1 8.4 1 8.4 1 8.6 1 8.4 1 8.5 1 8.7 1 8.7 1 8.6 1 7.4 1 7.3 1 7.4 1 9 1 9.2 1 9.2 1 8.5 1 8.3 1 8.3 1 8.6 1 8.6 1 8.5 1 8.1 1 8.1 1 8 1 8.6 1 8.7 1 8.7 1 8.6 1 8.4 1 8.4 1 8.7 1 8.7 1 8.5 1 8.3 1 8.3 0 8.3 0 8.1 1 8.2 1 8.1 0 8.1 0

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] = + 7.68021390374331 + 0.363636363636362x[t] -0.0545751633986933M1[t] -0.233392751039809M2[t] -0.134598930481283M3[t] + 0.0714676173499709M4[t] + 0.0175341651812232M5[t] -0.169126559714794M6[t] -0.70306001188354M7[t] -0.704266191325014M8[t] -0.69819964349376M9[t] -0.14486036838978M10[t] -0.0187938205585262M11[t] + 0.0139334521687463t + 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) 7.68021390374331 0.177372 43.3 0 0 x 0.363636363636362 0.10566 3.4416 0.001224 0.000612 M1 -0.0545751633986933 0.20579 -0.2652 0.792016 0.396008 M2 -0.233392751039809 0.218064 -1.0703 0.289953 0.144977 M3 -0.134598930481283 0.215556 -0.6244 0.535368 0.267684 M4 0.0714676173499709 0.215256 0.332 0.741356 0.370678 M5 0.0175341651812232 0.21499 0.0816 0.935344 0.467672 M6 -0.169126559714794 0.216485 -0.7812 0.43858 0.21929 M7 -0.70306001188354 0.216177 -3.2522 0.002122 0.001061 M8 -0.704266191325014 0.214404 -3.2848 0.001933 0.000966 M9 -0.69819964349376 0.21428 -3.2584 0.002085 0.001043 M10 -0.14486036838978 0.215461 -0.6723 0.504668 0.252334 M11 -0.0187938205585262 0.215293 -0.0873 0.930809 0.465404 t 0.0139334521687463 0.002761 5.0472 7e-06 4e-06 Multiple Linear Regression - Regression Statistics Multiple R 0.832574434891245 R-squared 0.693180189634476 Adjusted R-squared 0.608315135703587 F-TEST (value) 8.1680286234069 F-TEST (DF numerator) 13 F-TEST (DF denominator) 47 p-value 3.14613436414035e-08 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.338552981283977 Sum Squared Residuals 5.38705169340464 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 7.8 8.00320855614973 -0.203208556149734 2 7.4 7.83832442067736 -0.438324420677364 3 7.4 7.58741532976827 -0.187415329768271 4 7.5 7.80741532976827 -0.307415329768272 5 7.4 7.76741532976827 -0.36741532976827 6 7.4 7.594688057041 -0.194688057040999 7 7 7.074688057041 -0.0746880570409974 8 6.9 7.08741532976827 -0.187415329768271 9 6.9 7.10741532976827 -0.207415329768272 10 7.6 7.674688057041 -0.0746880570409988 11 7.7 7.814688057041 -0.114688057040998 12 7.6 7.84741532976827 -0.247415329768271 13 8.2 7.80677361853832 0.393226381461676 14 8 7.64188948306595 0.358110516934046 15 8.1 7.75461675579323 0.345383244206773 16 8.3 7.97461675579323 0.325383244206774 17 8.2 7.93461675579323 0.265383244206773 18 8.1 8.12552584670232 -0.0255258467023171 19 7.7 7.60552584670232 0.0944741532976826 20 7.6 7.61825311942959 -0.0182531194295898 21 7.7 7.63825311942959 0.0617468805704104 22 8.2 8.20552584670232 -0.00552584670231735 23 8.4 8.34552584670232 0.0544741532976839 24 8.4 8.37825311942959 0.0217468805704113 25 8.6 8.33761140819964 0.262388591800357 26 8.4 8.17272727272727 0.227272727272728 27 8.5 8.28545454545455 0.214545454545455 28 8.7 8.50545454545454 0.194545454545454 29 8.7 8.46545454545454 0.234545454545455 30 8.6 8.29272727272727 0.307272727272727 31 7.4 7.77272727272727 -0.372727272727273 32 7.3 7.78545454545455 -0.485454545454545 33 7.4 7.80545454545455 -0.405454545454545 34 9 8.37272727272727 0.627272727272728 35 9.2 8.51272727272727 0.687272727272727 36 9.2 8.54545454545454 0.654545454545454 37 8.5 8.5048128342246 -0.00481283422459798 38 8.3 8.33992869875223 -0.0399286987522274 39 8.3 8.4526559714795 -0.152655971479500 40 8.6 8.6726559714795 -0.0726559714795008 41 8.6 8.6326559714795 -0.0326559714795006 42 8.5 8.45992869875223 0.040071301247772 43 8.1 7.93992869875223 0.160071301247771 44 8.1 7.9526559714795 0.147344028520499 45 8 7.9726559714795 0.0273440285204990 46 8.6 8.53992869875223 0.0600713012477719 47 8.7 8.67992869875223 0.0200713012477715 48 8.7 8.7126559714795 -0.0126559714795011 49 8.6 8.67201426024955 -0.072014260249554 50 8.4 8.50713012477718 -0.107130124777183 51 8.4 8.61985739750446 -0.219857397504456 52 8.7 8.83985739750446 -0.139857397504457 53 8.7 8.79985739750446 -0.0998573975044566 54 8.5 8.62713012477718 -0.127130124777184 55 8.3 8.10713012477718 0.192869875222816 56 8.3 7.75622103386809 0.543778966131907 57 8.3 7.7762210338681 0.523778966131907 58 8.1 8.70713012477718 -0.607130124777184 59 8.2 8.84713012477718 -0.647130124777184 60 8.1 8.5162210338681 -0.416221033868093 61 8.1 8.47557932263815 -0.375579322638147

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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