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Workshop6-q3b

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

Title produced by software: Multiple Regression

Date of computation: Thu, 15 Nov 2007 15:22:14 -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/15/t1195165014nfe598k8ikthcr5.htm/, Retrieved Thu, 15 Nov 2007 23:17:04 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

36409 0 33163 0 34122 0 35225 0 28249 0 30374 0 26311 0 22069 0 23651 0 28628 0 23187 0 14727 0 43080 0 32519 0 39657 0 33614 0 28671 0 34243 0 27336 0 22916 0 24537 0 26128 0 22602 0 15744 0 41086 0 39690 0 43129 0 37863 0 35953 0 29133 0 24693 0 22205 0 21725 0 27192 0 21790 0 13253 0 37702 0 30364 0 32609 0 30212 0 29965 0 28352 0 25814 0 22414 0 20506 0 28806 0 22228 0 13971 0 36845 0 35338 0 35022 0 34777 0 26887 0 23970 0 22780 0 17351 0 21382 0 24561 0 17409 0 11514 0 31514 0 27071 0 29462 0 26105 0 22397 0 23843 0 21705 0 18089 0 20764 0 25316 0 17704 0 15548 0 28029 0 29383 0 36438 0 32034 0 22679 0 24319 0 18004 0 17537 0 20366 0 22782 0 19169 0 13807 0 29743 0 25591 0 29096 1 26482 1 22405 1 27044 1 17970 1 18730 1 19684 1 19785 1 18479 1 10698 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 Inschr_pw[t] = + 14166.525 -4070.19999999997Olieprijzen[t] + 21384.475M1[t] + 17473.3500000000M2[t] + 21284.1250000000M3[t] + 18381.2500M4[t] + 13493M5[t] + 14002M6[t] + 9418.875M7[t] + 6506.12500000001M8[t] + 7919.125M9[t] + 11742M10[t] + 6663.25M11[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) 14166.525 1245.265409 11.3763 0 0 Olieprijzen -4070.19999999997 1182.286517 -3.4427 0.000905 0.000452 M1 21384.475 1754.859319 12.1859 0 0 M2 17473.3500000000 1754.859319 9.9571 0 0 M3 21284.1250000000 1748.62534 12.1719 0 0 M4 18381.2500 1748.62534 10.5118 0 0 M5 13493 1748.62534 7.7163 0 0 M6 14002 1748.62534 8.0074 0 0 M7 9418.875 1748.62534 5.3864 1e-06 0 M8 6506.12500000001 1748.62534 3.7207 0.00036 0.00018 M9 7919.125 1748.62534 4.5288 2e-05 1e-05 M10 11742 1748.62534 6.715 0 0 M11 6663.25 1748.62534 3.8106 0.000265 0.000133 Multiple Linear Regression - Regression Statistics Multiple R 0.894616415750474 R-squared 0.800338531330225 Adjusted R-squared 0.77147181296833 F-TEST (value) 27.7253036280942 F-TEST (DF numerator) 12 F-TEST (DF denominator) 83 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3497.25068097819 Sum Squared Residuals 1015153273.025 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 36409 35551 858.000000000023 2 33163 31639.8750000001 1523.12499999994 3 34122 35450.65 -1328.65000000003 4 35225 32547.7750000001 2677.22499999994 5 28249 27659.5250000000 589.475000000051 6 30374 28168.525 2205.47500000001 7 26311 23585.4 2725.59999999999 8 22069 20672.6500000000 1396.35000000002 9 23651 22085.65 1565.35000000000 10 28628 25908.525 2719.475 11 23187 20829.775 2357.225 12 14727 14166.525 560.474999999998 13 43080 35551 7528.99999999999 14 32519 31639.875 879.125000000004 15 39657 35450.65 4206.35000000000 16 33614 32547.775 1066.22500000001 17 28671 27659.525 1011.47499999999 18 34243 28168.525 6074.475 19 27336 23585.4 3750.6 20 22916 20672.65 2243.35000000000 21 24537 22085.65 2451.35 22 26128 25908.525 219.475000000001 23 22602 20829.775 1772.225 24 15744 14166.525 1577.47500000000 25 41086 35551 5535 26 39690 31639.875 8050.12500000001 27 43129 35450.65 7678.35 28 37863 32547.775 5315.22500000001 29 35953 27659.525 8293.475 30 29133 28168.525 964.474999999999 31 24693 23585.4 1107.6 32 22205 20672.65 1532.35000000000 33 21725 22085.65 -360.649999999999 34 27192 25908.525 1283.475 35 21790 20829.775 960.225 36 13253 14166.525 -913.524999999998 37 37702 35551 2151.00000000000 38 30364 31639.875 -1275.87499999999 39 32609 35450.65 -2841.65 40 30212 32547.775 -2335.77499999999 41 29965 27659.525 2305.47499999999 42 28352 28168.525 183.474999999999 43 25814 23585.4 2228.6 44 22414 20672.65 1741.35000000000 45 20506 22085.65 -1579.65 46 28806 25908.525 2897.475 47 22228 20829.775 1398.225 48 13971 14166.525 -195.524999999998 49 36845 35551 1294.00000000000 50 35338 31639.875 3698.12500000000 51 35022 35450.65 -428.649999999996 52 34777 32547.775 2229.22500000001 53 26887 27659.525 -772.525000000006 54 23970 28168.525 -4198.525 55 22780 23585.4 -805.4 56 17351 20672.65 -3321.65000000000 57 21382 22085.65 -703.65 58 24561 25908.525 -1347.525 59 17409 20829.775 -3420.775 60 11514 14166.525 -2652.52500000000 61 31514 35551 -4037 62 27071 31639.875 -4568.875 63 29462 35450.65 -5988.65 64 26105 32547.775 -6442.77499999999 65 22397 27659.525 -5262.52500000001 66 23843 28168.525 -4325.525 67 21705 23585.4 -1880.4 68 18089 20672.65 -2583.65000000000 69 20764 22085.65 -1321.65 70 25316 25908.525 -592.525 71 17704 20829.775 -3125.775 72 15548 14166.525 1381.47500000000 73 28029 35551 -7522 74 29383 31639.875 -2256.87500000000 75 36438 35450.65 987.350000000004 76 32034 32547.775 -513.774999999992 77 22679 27659.525 -4980.52500000001 78 24319 28168.525 -3849.525 79 18004 23585.4 -5581.4 80 17537 20672.65 -3135.65000000000 81 20366 22085.65 -1719.65 82 22782 25908.525 -3126.525 83 19169 20829.775 -1660.775 84 13807 14166.525 -359.524999999998 85 29743 35551 -5808 86 25591 31639.875 -6048.875 87 29096 31380.45 -2284.45000000000 88 26482 28477.575 -1995.57499999999 89 22405 23589.325 -1184.32500000001 90 27044 24098.325 2945.675 91 17970 19515.2 -1545.20000000000 92 18730 16602.45 2127.54999999999 93 19684 18015.45 1668.55 94 19785 21838.325 -2053.325 95 18479 16759.575 1719.425 96 10698 10096.325 601.675000000003

Charts produced by software:

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Parameters:

par1 = 1 ; par2 = Include Monthly 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')

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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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