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Case III Question III+

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 11:28:03 -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/t1195755648x95a9q10o6t81mj.htm/, Retrieved Thu, 22 Nov 2007 19:20:48 +0100

User-defined keywords:

Eigen gegevens Export naar Finland met monthly dummies en linear trend

Dataseries X:

» Textbox « » Textfile « » CSV «

77,80 0 81,30 0 87,70 0 78,40 0 76,20 0 85,30 0 69,30 0 66,80 0 77,10 0 79,40 0 68,60 0 70,60 0 75,60 0 71,50 0 92,20 0 76,40 0 75,00 0 86,40 0 66,90 0 76,00 0 80,40 0 106,20 0 83,90 0 99,50 0 100,10 0 97,00 0 112,70 0 89,10 0 99,10 0 89,20 0 71,70 0 80,00 0 90,50 0 100,80 0 102,70 0 87,70 0 109,10 0 113,50 0 122,50 0 89,30 1 107,80 1 94,00 1 83,00 1 92,40 1 94,10 1 97,80 1 101,70 1 73,40 1 98,90 1 95,90 1 108,00 1 98,50 1 97,60 1 97,30 1 86,50 1 96,80 1 106,70 1 112,60 1 96,10 1 86,80 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 10 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Multiple Linear Regression - Estimated Regression Equation export[t] = + 60.7357575757576 -11.7393939393940Schengen[t] + 14.7732323232323M1[t] + 13.5476767676768M2[t] + 25.5621212121212M3[t] + 8.86444444444445M4[t] + 12.8988888888889M5[t] + 11.4333333333333M6[t] -4.29222222222222M7[t] + 1.86222222222223M8[t] + 8.45666666666667M9[t] + 17.2911111111111M10[t] + 7.76555555555556M11[t] + 0.765555555555556t + 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) 60.7357575757576 4.309608 14.0931 0 0 Schengen -11.7393939393940 3.758156 -3.1237 0.003088 0.001544 M1 14.7732323232323 4.873442 3.0314 0.003989 0.001995 M2 13.5476767676768 4.86347 2.7856 0.007734 0.003867 M3 25.5621212121212 4.855699 5.2644 4e-06 2e-06 M4 8.86444444444445 4.898435 1.8096 0.076887 0.038443 M5 12.8988888888889 4.881888 2.6422 0.01122 0.00561 M6 11.4333333333333 4.867502 2.3489 0.02318 0.01159 M7 -4.29222222222222 4.855295 -0.884 0.381278 0.190639 M8 1.86222222222223 4.845286 0.3843 0.7025 0.35125 M9 8.45666666666667 4.837486 1.7482 0.087109 0.043555 M10 17.2911111111111 4.831907 3.5785 0.000828 0.000414 M11 7.76555555555556 4.828557 1.6083 0.114622 0.057311 t 0.765555555555556 0.10387 7.3703 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.865502410308471 R-squared 0.749094422249773 Adjusted R-squared 0.678186324189926 F-TEST (value) 10.5643000270228 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 7.4904793478936e-10 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 7.6328516455139 Sum Squared Residuals 2679.97951515151 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 77.8 76.2745454545455 1.52545454545444 2 81.3 75.8145454545454 5.48545454545456 3 87.7 88.5945454545455 -0.89454545454545 4 78.4 72.6624242424242 5.73757575757577 5 76.2 77.4624242424242 -1.26242424242423 6 85.3 76.7624242424242 8.53757575757576 7 69.3 61.8024242424242 7.49757575757576 8 66.8 68.7224242424242 -1.92242424242424 9 77.1 76.0824242424242 1.01757575757576 10 79.4 85.6824242424242 -6.28242424242423 11 68.6 76.9224242424242 -8.32242424242425 12 70.6 69.9224242424242 0.67757575757576 13 75.6 85.4612121212121 -9.8612121212121 14 71.5 85.0012121212121 -13.5012121212121 15 92.2 97.7812121212121 -5.58121212121212 16 76.4 81.8490909090909 -5.4490909090909 17 75 86.6490909090909 -11.6490909090909 18 86.4 85.9490909090909 0.450909090909094 19 66.9 70.9890909090909 -4.08909090909091 20 76 77.9090909090909 -1.90909090909091 21 80.4 85.2690909090909 -4.8690909090909 22 106.2 94.869090909091 11.3309090909091 23 83.9 86.1090909090909 -2.20909090909090 24 99.5 79.1090909090909 20.3909090909091 25 100.1 94.6478787878788 5.45212121212124 26 97 94.1878787878788 2.8121212121212 27 112.7 106.967878787879 5.73212121212121 28 89.1 91.0357575757576 -1.93575757575759 29 99.1 95.8357575757576 3.26424242424242 30 89.2 95.1357575757576 -5.93575757575758 31 71.7 80.1757575757576 -8.47575757575758 32 80 87.0957575757576 -7.09575757575758 33 90.5 94.4557575757576 -3.95575757575758 34 100.8 104.055757575758 -3.25575757575758 35 102.7 95.2957575757576 7.40424242424243 36 87.7 88.2957575757576 -0.595757575757575 37 109.1 103.834545454545 5.26545454545456 38 113.5 103.374545454545 10.1254545454545 39 122.5 116.154545454545 6.34545454545454 40 89.3 88.4830303030303 0.816969696969695 41 107.8 93.2830303030303 14.5169696969697 42 94 92.5830303030303 1.4169696969697 43 83 77.6230303030303 5.3769696969697 44 92.4 84.5430303030303 7.8569696969697 45 94.1 91.9030303030303 2.19696969696970 46 97.8 101.503030303030 -3.70303030303030 47 101.7 92.7430303030303 8.9569696969697 48 73.4 85.7430303030303 -12.3430303030303 49 98.9 101.281818181818 -2.38181818181815 50 95.9 100.821818181818 -4.92181818181818 51 108 113.601818181818 -5.60181818181818 52 98.5 97.669696969697 0.830303030303028 53 97.6 102.469696969697 -4.86969696969698 54 97.3 101.769696969697 -4.46969696969698 55 86.5 86.809696969697 -0.309696969696973 56 96.8 93.729696969697 3.07030303030302 57 106.7 101.089696969697 5.61030303030303 58 112.6 110.689696969697 1.91030303030302 59 96.1 101.929696969697 -5.82969696969698 60 86.8 94.929696969697 -8.12969696969698

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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Software written by Ed van Stee & Patrick Wessa

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