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Vraag 3 deel 2

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

Title produced by software: Multiple Regression

Date of computation: Mon, 19 Nov 2007 10:28:51 -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/19/t1195493237kix9xxbmjdl18oj.htm/, Retrieved Mon, 19 Nov 2007 18:27:27 +0100

User-defined keywords:

Dataseries X:

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103,6500 0 103,8700 0 103,9400 0 105,3200 0 105,5400 0 106,0800 0 106,2100 0 105,5300 0 105,5600 0 105,1400 0 105,9700 0 105,4500 0 106,2200 0 106,3100 0 107,3800 0 109,3100 0 110,8200 0 111,2200 0 110,6600 0 110,7600 0 110,6900 0 111,0800 0 110,9700 0 110,2400 0 112,5100 1 111,5200 1 112,1300 1 112,2300 1 112,9200 1 111,8900 1 111,9900 1 111,5100 1 112,3300 1 112,0400 1 112,0900 1 111,4100 1 112,6100 1 113,1400 1 113,6500 1 114,2600 1 114,4000 1 114,9300 1 114,8600 1 114,9500 1 116,1700 1 114,6000 1 114,6200 1 113,8200 1 115,0200 1 115,1800 1 115,5900 1 116,6000 1 117,0700 1 116,9600 1 116,6600 1 116,0700 1 116,0400 1 115,8100 1 116,2200 1 115,8500 1 116,4300 1 117,3900 1 119,1700 1 119,2400 1 120,0300 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] = + 106.982150442478 + 7.28641592920353x[t] -0.766427728613481M1[t] -0.604761061946898M2[t] + 0.136905604719768M3[t] + 0.986905604719766M4[t] + 1.62357227138644M5[t] + 0.862000000000004M6[t] + 0.722000000000002M7[t] + 0.410000000000006M8[t] + 0.804000000000006M9[t] + 0.380000000000005M10[t] + 0.620000000000005M11[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) 106.982150442478 1.214622 88.0785 0 0 x 7.28641592920353 0.66132 11.018 0 0 M1 -0.766427728613481 1.555 -0.4929 0.624173 0.312086 M2 -0.604761061946898 1.555 -0.3889 0.698928 0.349464 M3 0.136905604719768 1.555 0.088 0.930181 0.465091 M4 0.986905604719766 1.555 0.6347 0.528429 0.264214 M5 1.62357227138644 1.555 1.0441 0.30127 0.150635 M6 0.862000000000004 1.623492 0.531 0.597711 0.298856 M7 0.722000000000002 1.623492 0.4447 0.658367 0.329184 M8 0.410000000000006 1.623492 0.2525 0.801618 0.400809 M9 0.804000000000006 1.623492 0.4952 0.622525 0.311262 M10 0.380000000000005 1.623492 0.2341 0.815855 0.407927 M11 0.620000000000005 1.623492 0.3819 0.704097 0.352049 Multiple Linear Regression - Regression Statistics Multiple R 0.841108208711619 R-squared 0.707463018762068 Adjusted R-squared 0.639954484630237 F-TEST (value) 10.4796086577815 F-TEST (DF numerator) 12 F-TEST (DF denominator) 52 p-value 4.29917657029932e-10 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.56696606984224 Sum Squared Residuals 342.644369793508 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 103.65 106.215722713864 -2.56572271386392 2 103.87 106.377389380531 -2.507389380531 3 103.94 107.119056047198 -3.17905604719766 4 105.32 107.969056047198 -2.64905604719766 5 105.54 108.605722713864 -3.06572271386431 6 106.08 107.844150442478 -1.76415044247789 7 106.21 107.704150442478 -1.49415044247789 8 105.53 107.392150442478 -1.86215044247789 9 105.56 107.786150442478 -2.22615044247789 10 105.14 107.362150442478 -2.22215044247789 11 105.97 107.602150442478 -1.63215044247789 12 105.45 106.982150442478 -1.53215044247788 13 106.22 106.215722713864 0.00427728613559486 14 106.31 106.377389380531 -0.0673893805309826 15 107.38 107.119056047198 0.260943952802342 16 109.31 107.969056047198 1.34094395280235 17 110.82 108.605722713864 2.21427728613567 18 111.22 107.844150442478 3.37584955752211 19 110.66 107.704150442478 2.95584955752211 20 110.76 107.392150442478 3.36784955752211 21 110.69 107.786150442478 2.90384955752211 22 111.08 107.362150442478 3.71784955752211 23 110.97 107.602150442478 3.36784955752211 24 110.24 106.982150442478 3.25784955752211 25 112.51 113.502138643068 -0.992138643067918 26 111.52 113.663805309734 -2.14380530973451 27 112.13 114.405471976401 -2.27547197640118 28 112.23 115.255471976401 -3.02547197640117 29 112.92 115.892138643068 -2.97213864306784 30 111.89 115.130566371681 -3.24056637168141 31 111.99 114.990566371681 -3.00056637168141 32 111.51 114.678566371681 -3.16856637168140 33 112.33 115.072566371681 -2.74256637168141 34 112.04 114.648566371681 -2.60856637168140 35 112.09 114.888566371681 -2.79856637168141 36 111.41 114.268566371681 -2.85856637168141 37 112.61 113.502138643068 -0.892138643067924 38 113.14 113.663805309734 -0.523805309734504 39 113.65 114.405471976401 -0.755471976401167 40 114.26 115.255471976401 -0.995471976401165 41 114.4 115.892138643068 -1.49213864306784 42 114.93 115.130566371681 -0.200566371681401 43 114.86 114.990566371681 -0.130566371681406 44 114.95 114.678566371681 0.271433628318593 45 116.17 115.072566371681 1.09743362831859 46 114.6 114.648566371681 -0.0485663716814141 47 114.62 114.888566371681 -0.268566371681404 48 113.82 114.268566371681 -0.44856637168141 49 115.02 113.502138643068 1.51786135693207 50 115.18 113.663805309734 1.51619469026550 51 115.59 114.405471976401 1.18452802359883 52 116.6 115.255471976401 1.34452802359882 53 117.07 115.892138643068 1.17786135693215 54 116.96 115.130566371681 1.82943362831859 55 116.66 114.990566371681 1.66943362831859 56 116.07 114.678566371681 1.39143362831858 57 116.04 115.072566371681 0.967433628318597 58 115.81 114.648566371681 1.16143362831859 59 116.22 114.888566371681 1.33143362831859 60 115.85 114.268566371681 1.58143362831859 61 116.43 113.502138643068 2.92786135693208 62 117.39 113.663805309734 3.72619469026550 63 119.17 114.405471976401 4.76452802359883 64 119.24 115.255471976401 3.98452802359882 65 120.03 115.892138643068 4.13786135693216

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')

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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