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Workshop: Seatbelt Law _ Eigen geg.

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 12:59:59 -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/t11957611148goilzeotwgzkb4.htm/, Retrieved Thu, 22 Nov 2007 20:52:03 +0100

User-defined keywords:

Tinne Van der Eycken Workshop 2

Dataseries X:

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0,9811 0 1,0014 0 1,0183 0 1,0622 0 1,0773 0 1,0807 0 1,0848 0 1,1582 0 1,1663 0 1,1372 0 1,1139 0 1,1222 0 1,1692 0 1,1702 0 1,2286 0 1,2613 0 1,2646 0 1,2262 0 1,1985 0 1,2007 0 1,2138 0 1,2266 0 1,2176 0 1,2218 0 1,249 0 1,2991 0 1,3408 0 1,3119 0 1,3014 0 1,3201 0 1,2938 0 1,2694 0 1,2165 0 1,2037 0 1,2292 0 1,2256 0 1,2015 0 1,1786 0 1,1856 0 1,2103 0 1,1938 0 1,202 0 1,2271 0 1,277 0 1,265 0 1,2684 0 1,2811 0 1,2727 0 1,2611 0 1,2881 1 1,3213 1 1,2999 1 1,3074 1 1,3242 1 1,3516 1 1,3511 1 1,3419 1 1,3716 1 1,3622 1 1,3896 1 1,4227 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] = + 1.09422611464968 + 0.0160037420382166X[t] -0.0110586062455766M1[t] -0.0175241286270345M2[t] + 0.0097782842356689M3[t] + 0.0158406970983724M4[t] + 0.0114831099610758M5[t] + 0.00908552282377927M6[t] + 0.00546793568648273M7[t] + 0.0214503485491862M8[t] + 0.00673276141188964M9[t] + 0.00339517427459313M10[t] -0.00144241286270338M11[t] + 0.00413758713729653t + 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) 1.09422611464968 0.033092 33.0663 0 0 X 0.0160037420382166 0.027252 0.5873 0.559846 0.279923 M1 -0.0110586062455766 0.036713 -0.3012 0.76458 0.38229 M2 -0.0175241286270345 0.038758 -0.4521 0.653246 0.326623 M3 0.0097782842356689 0.038662 0.2529 0.801436 0.400718 M4 0.0158406970983724 0.038576 0.4106 0.683209 0.341605 M5 0.0114831099610758 0.038501 0.2983 0.766821 0.383411 M6 0.00908552282377927 0.038435 0.2364 0.814159 0.407079 M7 0.00546793568648273 0.038379 0.1425 0.887316 0.443658 M8 0.0214503485491862 0.038333 0.5596 0.578427 0.289213 M9 0.00673276141188964 0.038298 0.1758 0.861206 0.430603 M10 0.00339517427459313 0.038272 0.0887 0.929688 0.464844 M11 -0.00144241286270338 0.038257 -0.0377 0.970084 0.485042 t 0.00413758713729653 0.000624 6.6282 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.82710738364271 R-squared 0.684106624076287 Adjusted R-squared 0.59673186052292 F-TEST (value) 7.82956767211671 F-TEST (DF numerator) 13 F-TEST (DF denominator) 47 p-value 5.83070041138001e-08 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.0604815385261967 Sum Squared Residuals 0.171926775617303 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 0.9811 1.0873050955414 -0.106205095541401 2 1.0014 1.08497716029724 -0.0835771602972398 3 1.0183 1.11641716029724 -0.0981171602972399 4 1.0622 1.12661716029724 -0.0644171602972399 5 1.0773 1.12639716029724 -0.0490971602972399 6 1.0807 1.12813716029724 -0.0474371602972399 7 1.0848 1.12865716029724 -0.0438571602972399 8 1.1582 1.14877716029724 0.00942283970276 9 1.1663 1.13819716029724 0.02810283970276 10 1.1372 1.13899716029724 -0.00179716029723992 11 1.1139 1.13829716029724 -0.024397160297240 12 1.1222 1.14387716029724 -0.0216771602972397 13 1.1692 1.13695614118896 0.0322438588110402 14 1.1702 1.13462820594480 0.0355717940552015 15 1.2286 1.16606820594480 0.0625317940552016 16 1.2613 1.17626820594480 0.0850317940552018 17 1.2646 1.17604820594480 0.0885517940552017 18 1.2262 1.17778820594480 0.0484117940552016 19 1.1985 1.17830820594480 0.0201917940552016 20 1.2007 1.19842820594480 0.00227179405520178 21 1.2138 1.18784820594480 0.0259517940552017 22 1.2266 1.18864820594480 0.0379517940552017 23 1.2176 1.18794820594480 0.0296517940552017 24 1.2218 1.19352820594480 0.0282717940552018 25 1.249 1.18660718683652 0.062392813163482 26 1.2991 1.18427925159236 0.114820748407643 27 1.3408 1.21571925159236 0.125080748407643 28 1.3119 1.22591925159236 0.0859807484076433 29 1.3014 1.22569925159236 0.0757007484076432 30 1.3201 1.22743925159236 0.0926607484076433 31 1.2938 1.22795925159236 0.0658407484076433 32 1.2694 1.24807925159236 0.0213207484076434 33 1.2165 1.23749925159236 -0.0209992515923567 34 1.2037 1.23829925159236 -0.0345992515923567 35 1.2292 1.23759925159236 -0.00839925159235656 36 1.2256 1.24317925159236 -0.0175792515923565 37 1.2015 1.23625823248408 -0.0347582324840765 38 1.1786 1.23393029723992 -0.055330297239915 39 1.1856 1.26537029723992 -0.0797702972399151 40 1.2103 1.27557029723991 -0.0652702972399152 41 1.1938 1.27535029723992 -0.081550297239915 42 1.202 1.27709029723992 -0.0750902972399151 43 1.2271 1.27761029723992 -0.050510297239915 44 1.277 1.29773029723991 -0.0207302972399152 45 1.265 1.28715029723991 -0.0221502972399151 46 1.2684 1.28795029723992 -0.019550297239915 47 1.2811 1.28725029723992 -0.0061502972399152 48 1.2727 1.29283029723992 -0.020130297239915 49 1.2611 1.28590927813164 -0.0248092781316348 50 1.2881 1.29958508492569 -0.0114850849256900 51 1.3213 1.33102508492569 -0.00972508492569011 52 1.2999 1.34122508492569 -0.04132508492569 53 1.3074 1.34100508492569 -0.0336050849256901 54 1.3242 1.34274508492569 -0.0185450849256899 55 1.3516 1.34326508492569 0.00833491507430993 56 1.3511 1.36338508492569 -0.0122850849256900 57 1.3419 1.35280508492569 -0.0109050849256899 58 1.3716 1.35360508492569 0.0179949150743100 59 1.3622 1.35290508492569 0.00929491507431009 60 1.3896 1.35848508492569 0.03111491507431 61 1.4227 1.35156406581741 0.0711359341825902

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')

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