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

Title produced by software: Multiple Regression

Date of computation: Sat, 15 Dec 2007 07:06:22 -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/Dec/15/t1197727940nskcetud9rswcba.htm/, Retrieved Sat, 15 Dec 2007 15:12:30 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

99,5 0 101,6 0 103,9 0 106,6 0 108,3 0 102 0 93,8 0 91,6 0 97,7 0 94,8 0 98 0 103,8 0 97,8 0 91,2 0 89,3 0 87,5 0 90,4 0 94,2 0 102,2 0 101,3 0 96 0 90,8 0 93,2 0 90,9 0 91,1 0 90,2 0 94,3 0 96 0 99 0 103,3 0 113,1 0 112,8 0 112,1 0 107,4 0 111 0 110,5 0 110,8 0 112,4 0 111,5 0 116,2 0 122,5 0 121,3 0 113,9 0 110,7 0 120,8 0 141,1 1 147,4 1 148 1 158,1 1 165 1 187 1 190,3 1 182,4 1 168,8 1 151,2 1 120,1 0 112,5 0 106,2 0 107,1 0 108,5 0 106,5 0 108,3 0 125,6 0 124 0 127,2 0 136,9 0 135,8 0 124,3 0 115,4 0 113,6 0 114,4 0 118,4 0 117 0 116,5 0 115,4 0 113,6 0 117,4 0 116,9 0 116,4 0 111,1 0 110,2 0 118,9 0 131,8 0 130,6 0 138,3 0 148,4 0 148,7 0 144,3 0 152,5 0 162,9 0 167,2 0 166,5 0 185,6 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 Oliezaden[t] = + 113.762650602410 + 50.1673493975905Fluctuatie[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) 113.762650602410 2.121521 53.6232 0 0 Fluctuatie 50.1673493975905 6.469768 7.7541 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.630757374750707 R-squared 0.397854865802404 Adjusted R-squared 0.391237886305727 F-TEST (value) 60.1263561421356 F-TEST (DF numerator) 1 F-TEST (DF denominator) 91 p-value 1.23299148668821e-11 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 19.3279718772729 Sum Squared Residuals 33994.9152168675 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 99.5 113.762650602409 -14.2626506024095 2 101.6 113.762650602410 -12.1626506024101 3 103.9 113.762650602410 -9.86265060240963 4 106.6 113.762650602410 -7.16265060240964 5 108.3 113.762650602410 -5.46265060240964 6 102 113.762650602410 -11.7626506024096 7 93.8 113.762650602410 -19.9626506024096 8 91.6 113.762650602410 -22.1626506024096 9 97.7 113.762650602410 -16.0626506024096 10 94.8 113.762650602410 -18.9626506024096 11 98 113.762650602410 -15.7626506024096 12 103.8 113.762650602410 -9.96265060240964 13 97.8 113.762650602410 -15.9626506024096 14 91.2 113.762650602410 -22.5626506024096 15 89.3 113.762650602410 -24.4626506024096 16 87.5 113.762650602410 -26.2626506024096 17 90.4 113.762650602410 -23.3626506024096 18 94.2 113.762650602410 -19.5626506024096 19 102.2 113.762650602410 -11.5626506024096 20 101.3 113.762650602410 -12.4626506024096 21 96 113.762650602410 -17.7626506024096 22 90.8 113.762650602410 -22.9626506024096 23 93.2 113.762650602410 -20.5626506024096 24 90.9 113.762650602410 -22.8626506024096 25 91.1 113.762650602410 -22.6626506024096 26 90.2 113.762650602410 -23.5626506024096 27 94.3 113.762650602410 -19.4626506024096 28 96 113.762650602410 -17.7626506024096 29 99 113.762650602410 -14.7626506024096 30 103.3 113.762650602410 -10.4626506024096 31 113.1 113.762650602410 -0.66265060240964 32 112.8 113.762650602410 -0.962650602409638 33 112.1 113.762650602410 -1.66265060240964 34 107.4 113.762650602410 -6.36265060240963 35 111 113.762650602410 -2.76265060240963 36 110.5 113.762650602410 -3.26265060240963 37 110.8 113.762650602410 -2.96265060240964 38 112.4 113.762650602410 -1.36265060240963 39 111.5 113.762650602410 -2.26265060240963 40 116.2 113.762650602410 2.43734939759037 41 122.5 113.762650602410 8.73734939759037 42 121.3 113.762650602410 7.53734939759036 43 113.9 113.762650602410 0.137349397590371 44 110.7 113.762650602410 -3.06265060240963 45 120.8 113.762650602410 7.03734939759036 46 141.1 163.93 -22.83 47 147.4 163.93 -16.53 48 148 163.93 -15.93 49 158.1 163.93 -5.83 50 165 163.93 1.07000000000001 51 187 163.93 23.07 52 190.3 163.93 26.37 53 182.4 163.93 18.47 54 168.8 163.93 4.87000000000002 55 151.2 163.93 -12.73 56 120.1 113.762650602410 6.33734939759036 57 112.5 113.762650602410 -1.26265060240963 58 106.2 113.762650602410 -7.56265060240963 59 107.1 113.762650602410 -6.66265060240964 60 108.5 113.762650602410 -5.26265060240963 61 106.5 113.762650602410 -7.26265060240963 62 108.3 113.762650602410 -5.46265060240964 63 125.6 113.762650602410 11.8373493975904 64 124 113.762650602410 10.2373493975904 65 127.2 113.762650602410 13.4373493975904 66 136.9 113.762650602410 23.1373493975904 67 135.8 113.762650602410 22.0373493975904 68 124.3 113.762650602410 10.5373493975904 69 115.4 113.762650602410 1.63734939759037 70 113.6 113.762650602410 -0.162650602409641 71 114.4 113.762650602410 0.63734939759037 72 118.4 113.762650602410 4.63734939759037 73 117 113.762650602410 3.23734939759037 74 116.5 113.762650602410 2.73734939759037 75 115.4 113.762650602410 1.63734939759037 76 113.6 113.762650602410 -0.162650602409641 77 117.4 113.762650602410 3.63734939759037 78 116.9 113.762650602410 3.13734939759037 79 116.4 113.762650602410 2.63734939759037 80 111.1 113.762650602410 -2.66265060240964 81 110.2 113.762650602410 -3.56265060240963 82 118.9 113.762650602410 5.13734939759037 83 131.8 113.762650602410 18.0373493975904 84 130.6 113.762650602410 16.8373493975904 85 138.3 113.762650602410 24.5373493975904 86 148.4 113.762650602410 34.6373493975904 87 148.7 113.762650602410 34.9373493975904 88 144.3 113.762650602410 30.5373493975904 89 152.5 113.762650602410 38.7373493975904 90 162.9 113.762650602410 49.1373493975904 91 167.2 113.762650602410 53.4373493975904 92 166.5 113.762650602410 52.7373493975904 93 185.6 113.762650602410 71.8373493975904

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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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