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seatbelt law Q3

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

Title produced by software: Multiple Regression

Date of computation: Sun, 18 Nov 2007 07:20:30 -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/18/t1195395354qz1l6mnqojidngq.htm/, Retrieved Sun, 18 Nov 2007 15:16:04 +0100

User-defined keywords:

s0650062 s0650550

Dataseries X:

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8,2 0 8 0 8,1 0 8,3 0 8,2 0 8,1 0 7,7 0 7,6 0 7,7 0 8,2 0 8,4 0 8,4 0 8,6 0 8,4 0 8,5 0 8,7 0 8,7 0 8,6 0 7,4 0 7,3 0 7,4 0 9 0 9,2 0 9,2 0 8,5 0 8,3 0 8,3 0 8,6 0 8,6 0 8,5 0 8,1 0 8,1 0 8 0 8,6 0 8,7 0 8,7 0 8,6 0 8,4 0 8,4 0 8,7 0 8,7 0 8,5 0 8,3 0 8,3 0 8,3 0 8,1 0 8,2 0 8,1 0 8,1 0 7,9 0 7,7 0 8,1 1 8 1 7,7 1 7,8 1 7,6 1 7,4 1 7,7 1 7,8 1 7,5 1 7,2 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] = + 8.42344370860927 -0.729470198675496x[t] -0.190086460632817M1[t] -0.297435614422368M2[t] -0.300281456953642M3[t] + 0.122766740250184M4[t] + 0.079920897718911M5[t] -0.0829249448123618M6[t] -0.505770787343634M7[t] -0.588616629874908M8[t] -0.61146247240618M9[t] -0.0543083149374538M10[t] + 0.0828458425312732M11[t] + 0.00284584253127298t + 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) 8.42344370860927 0.18182 46.3284 0 0 x -0.729470198675496 0.15582 -4.6815 2.4e-05 1.2e-05 M1 -0.190086460632817 0.205811 -0.9236 0.360413 0.180206 M2 -0.297435614422368 0.216195 -1.3758 0.175412 0.087706 M3 -0.300281456953642 0.216029 -1.39 0.171075 0.085538 M4 0.122766740250184 0.216074 0.5682 0.572623 0.286312 M5 0.079920897718911 0.215704 0.3705 0.712666 0.356333 M6 -0.0829249448123618 0.215384 -0.385 0.701967 0.350984 M7 -0.505770787343634 0.215113 -2.3512 0.022959 0.011479 M8 -0.588616629874908 0.21489 -2.7391 0.008676 0.004338 M9 -0.61146247240618 0.214717 -2.8478 0.00651 0.003255 M10 -0.0543083149374538 0.214593 -0.2531 0.801314 0.400657 M11 0.0828458425312732 0.214519 0.3862 0.701096 0.350548 t 0.00284584253127298 0.003259 0.8731 0.387034 0.193517 Multiple Linear Regression - Regression Statistics Multiple R 0.753786602111772 R-squared 0.568194241523211 Adjusted R-squared 0.448758606199844 F-TEST (value) 4.75732590181187 F-TEST (DF numerator) 13 F-TEST (DF denominator) 47 p-value 3.49705896813823e-05 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.339145514015531 Sum Squared Residuals 5.40592494481236 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 8.2 8.23620309050772 -0.0362030905077201 2 8 8.13169977924945 -0.131699779249448 3 8.1 8.13169977924945 -0.0316997792494489 4 8.3 8.55759381898455 -0.257593818984547 5 8.2 8.51759381898455 -0.317593818984548 6 8.1 8.35759381898455 -0.257593818984548 7 7.7 7.93759381898455 -0.237593818984548 8 7.6 7.85759381898455 -0.257593818984548 9 7.7 7.83759381898455 -0.137593818984548 10 8.2 8.39759381898455 -0.197593818984548 11 8.4 8.53759381898455 -0.137593818984547 12 8.4 8.45759381898455 -0.0575938189845468 13 8.6 8.270353200883 0.329646799116996 14 8.4 8.16584988962473 0.234150110375276 15 8.5 8.16584988962472 0.334150110375276 16 8.7 8.59174392935982 0.108256070640176 17 8.7 8.55174392935982 0.148256070640176 18 8.6 8.39174392935982 0.208256070640176 19 7.4 7.97174392935982 -0.571743929359823 20 7.3 7.89174392935982 -0.591743929359824 21 7.4 7.87174392935982 -0.471743929359823 22 9 8.43174392935982 0.568256070640177 23 9.2 8.57174392935982 0.628256070640176 24 9.2 8.49174392935982 0.708256070640176 25 8.5 8.30450331125828 0.195496688741721 26 8.3 8.2 0.1 27 8.3 8.2 0.100000000000000 28 8.6 8.6258940397351 -0.0258940397350993 29 8.6 8.5858940397351 0.0141059602649008 30 8.5 8.4258940397351 0.0741059602649007 31 8.1 8.0058940397351 0.0941059602649003 32 8.1 7.9258940397351 0.174105960264901 33 8 7.9058940397351 0.0941059602649005 34 8.6 8.4658940397351 0.134105960264901 35 8.7 8.6058940397351 0.0941059602649003 36 8.7 8.5258940397351 0.174105960264901 37 8.6 8.33865342163356 0.261346578366445 38 8.4 8.23415011037528 0.165849889624724 39 8.4 8.23415011037528 0.165849889624724 40 8.7 8.66004415011037 0.0399558498896246 41 8.7 8.62004415011037 0.0799558498896248 42 8.5 8.46004415011038 0.039955849889625 43 8.3 8.04004415011038 0.259955849889626 44 8.3 7.96004415011037 0.339955849889626 45 8.3 7.94004415011038 0.359955849889626 46 8.1 8.50004415011037 -0.400044150110375 47 8.2 8.64004415011038 -0.440044150110375 48 8.1 8.56004415011037 -0.460044150110375 49 8.1 8.37280353200883 -0.272803532008831 50 7.9 8.26830022075055 -0.368300220750552 51 7.7 8.26830022075055 -0.568300220750552 52 8.1 7.96472406181015 0.135275938189845 53 8 7.92472406181015 0.0752759381898459 54 7.7 7.76472406181015 -0.0647240618101543 55 7.8 7.34472406181015 0.455275938189845 56 7.6 7.26472406181015 0.335275938189845 57 7.4 7.24472406181015 0.155275938189846 58 7.7 7.80472406181015 -0.104724061810154 59 7.8 7.94472406181015 -0.144724061810154 60 7.5 7.86472406181015 -0.364724061810154 61 7.2 7.67748344370861 -0.47748344370861

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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