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multiple regression: 3 Irak seiz+LT

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

Title produced by software: Multiple Regression

Date of computation: Sat, 17 Nov 2007 08:11:31 -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/17/t1195311975pxvi7fz7e8vpm9n.htm/, Retrieved Sat, 17 Nov 2007 16:06:25 +0100

User-defined keywords:

s0650921

Dataseries X:

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99.9 0 98.2 0 104.5 0 100.8 0 101.5 0 103.9 0 99.6 0 98.4 0 112.7 0 118.4 0 108.1 0 105.4 0 114.6 0 106.9 0 115.9 1 109.8 1 101.8 1 114.2 2 110.8 2 108.4 2 127.5 2 128.6 2 116.6 2 127.4 2 105 2 108.3 2 125 2 111.6 2 106.5 2 130.3 2 115 2 116.1 2 134 2 126.5 2 125.8 2 136.4 2 114.9 2 110.9 2 125.5 2 116.8 2 116.8 2 125.5 2 104.2 2 115.1 2 132.8 2 123.3 2 124.8 2 122 2 117.4 2 117.9 2 137.4 2 114.6 2 124.7 2 129.6 2 109.4 2 120.9 2 134.9 2 136.3 2 133.2 2 127.2 2

Text written by user:

met maandseizonaliteit en LT-trend

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] = + 109.038912048805 + 3.48261311642096x[t] -9.1558998474836M1[t] -11.3278139298424M2[t] + 0.94374936451449M3[t] -10.2481647178444M4[t] -10.9600788002033M5[t] -1.46851550584647M6[t] -14.6204295882054M7[t] -10.8923436705643M8[t] + 5.45574224707676M9[t] + 3.44382816471783M10[t] -1.72808591764109M11[t] + 0.251914082358923t + 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) 109.038912048805 2.708965 40.2511 0 0 x 3.48261311642096 1.268821 2.7448 0.008608 0.004304 M1 -9.1558998474836 3.277355 -2.7937 0.007571 0.003786 M2 -11.3278139298424 3.272439 -3.4616 0.001171 0.000585 M3 0.94374936451449 3.273008 0.2883 0.774379 0.38719 M4 -10.2481647178444 3.266694 -3.1372 0.002973 0.001487 M5 -10.9600788002033 3.261557 -3.3604 0.001573 0.000787 M6 -1.46851550584647 3.270343 -0.449 0.655511 0.327756 M7 -14.6204295882054 3.263818 -4.4795 4.9e-05 2.5e-05 M8 -10.8923436705643 3.25847 -3.3428 0.001655 0.000828 M9 5.45574224707676 3.254305 1.6765 0.100431 0.050215 M10 3.44382816471783 3.251326 1.0592 0.295036 0.147518 M11 -1.72808591764109 3.249537 -0.5318 0.597427 0.298714 t 0.251914082358923 0.062255 4.0465 0.000197 9.8e-05 Multiple Linear Regression - Regression Statistics Multiple R 0.9113358675062 R-squared 0.830533063403278 Adjusted R-squared 0.78264023349551 F-TEST (value) 17.3414906783061 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 1.54098955817972e-13 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 5.13702681040599 Sum Squared Residuals 1213.89604473818 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 99.9 100.134926283681 -0.234926283681134 2 98.2 98.2149262836808 -0.0149262836807459 3 104.5 110.738403660397 -6.23840366039651 4 100.8 99.7984036603965 1.0015963396035 5 101.5 99.3384036603965 2.16159633960349 6 103.9 109.081881037112 -5.18188103711232 7 99.6 96.1818810371124 3.41811896288764 8 98.4 100.161881037112 -1.76188103711232 9 112.7 116.761881037112 -4.06188103711233 10 118.4 115.001881037112 3.39811896288767 11 108.1 110.081881037112 -1.98188103711233 12 105.4 112.061881037112 -6.66188103711233 13 114.6 103.157895271988 11.4421047280123 14 106.9 101.237895271988 5.66210472801223 15 115.9 117.243985765125 -1.34398576512455 16 109.8 106.303985765125 3.49601423487545 17 101.8 105.843985765125 -4.04398576512455 18 114.2 119.070076258261 -4.87007625826131 19 110.8 106.170076258261 4.62992374173869 20 108.4 110.150076258261 -1.75007625826131 21 127.5 126.750076258261 0.749923741738689 22 128.6 124.990076258261 3.60992374173869 23 116.6 120.070076258261 -3.47007625826130 24 127.4 122.050076258261 5.34992374173869 25 105 113.146090493137 -8.14609049313666 26 108.3 111.226090493137 -2.92609049313676 27 125 123.749567869853 1.25043213014742 28 111.6 112.809567869853 -1.20956786985258 29 106.5 112.349567869853 -5.84956786985257 30 130.3 122.093045246568 8.20695475343162 31 115 109.193045246568 5.80695475343163 32 116.1 113.173045246568 2.92695475343161 33 134 129.773045246568 4.22695475343162 34 126.5 128.013045246568 -1.51304524656838 35 125.8 123.093045246568 2.70695475343162 36 136.4 125.073045246568 11.3269547534316 37 114.9 116.169059481444 -1.26905948144372 38 110.9 114.249059481444 -3.34905948144382 39 125.5 126.772536858160 -1.27253685815965 40 116.8 115.832536858160 0.967463141840352 41 116.8 115.372536858160 1.42746314184035 42 125.5 125.116014234875 0.383985765124540 43 104.2 112.216014234875 -8.01601423487544 44 115.1 116.196014234875 -1.09601423487546 45 132.8 132.796014234875 0.00398576512455416 46 123.3 131.036014234875 -7.73601423487546 47 124.8 126.116014234875 -1.31601423487545 48 122 128.096014234875 -6.09601423487546 49 117.4 119.192028469751 -1.79202846975079 50 117.9 117.272028469751 0.627971530249106 51 137.4 129.795505846467 7.60449415353328 52 114.6 118.855505846467 -4.25550584646672 53 124.7 118.395505846467 6.30449415353329 54 129.6 128.138983223183 1.46101677681746 55 109.4 115.238983223183 -5.83898322318251 56 120.9 119.218983223183 1.68101677681748 57 134.9 135.818983223183 -0.918983223182524 58 136.3 134.058983223183 2.24101677681748 59 133.2 129.138983223183 4.06101677681747 60 127.2 131.118983223183 -3.91898322318253

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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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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