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WS8 Q3

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

Title produced by software: Multiple Regression

Date of computation: Sun, 18 Nov 2007 09:30:40 -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/18/t1195403193708pa8m2i5ct9t0.htm/, Retrieved Sun, 18 Nov 2007 17:26:42 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

1178 0 2141 0 2238 0 2685 0 4341 0 5376 0 4478 0 6404 0 4617 0 3024 0 1897 0 2075 0 1351 0 2211 0 2453 0 3042 0 4765 0 4992 1 4601 1 6266 1 4812 1 3159 1 1916 1 2237 1 1595 1 2453 1 2226 1 3597 1 4706 1 4974 1 5756 1 5493 1 5004 1 3225 1 2006 1 2291 1 1588 1 2105 1 2191 1 3591 1 4668 1 4885 1 5822 1 5599 1 5340 1 3082 1 2010 1 2301 1 1514 1 1979 1 2480 1 3499 1 4676 1 5585 1 5610 1 5796 1 6199 1 3030 1 1930 1 2552 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 Huwelijken[t] = + 3192.70588235294 + 512.898768809848Dummy[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) 3192.70588235294 374.518419 8.5248 0 0 Dummy 512.898768809848 442.399451 1.1594 0.251062 0.125531 Multiple Linear Regression - Regression Statistics Multiple R 0.150497149520644 R-squared 0.022649392013839 Adjusted R-squared 0.00579851946235355 F-TEST (value) 1.34410796501112 F-TEST (DF numerator) 1 F-TEST (DF denominator) 58 p-value 0.251061566982259 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1544.1790018652 Sum Squared Residuals 138300349.808482 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 1178 3192.70588235295 -2014.70588235295 2 2141 3192.70588235294 -1051.70588235294 3 2238 3192.70588235294 -954.705882352941 4 2685 3192.70588235294 -507.705882352941 5 4341 3192.70588235294 1148.29411764706 6 5376 3192.70588235294 2183.29411764706 7 4478 3192.70588235294 1285.29411764706 8 6404 3192.70588235294 3211.29411764706 9 4617 3192.70588235294 1424.29411764706 10 3024 3192.70588235294 -168.705882352941 11 1897 3192.70588235294 -1295.70588235294 12 2075 3192.70588235294 -1117.70588235294 13 1351 3192.70588235294 -1841.70588235294 14 2211 3192.70588235294 -981.705882352941 15 2453 3192.70588235294 -739.705882352941 16 3042 3192.70588235294 -150.705882352941 17 4765 3192.70588235294 1572.29411764706 18 4992 3705.60465116279 1286.39534883721 19 4601 3705.60465116279 895.39534883721 20 6266 3705.60465116279 2560.39534883721 21 4812 3705.60465116279 1106.39534883721 22 3159 3705.60465116279 -546.604651162790 23 1916 3705.60465116279 -1789.60465116279 24 2237 3705.60465116279 -1468.60465116279 25 1595 3705.60465116279 -2110.60465116279 26 2453 3705.60465116279 -1252.60465116279 27 2226 3705.60465116279 -1479.60465116279 28 3597 3705.60465116279 -108.604651162791 29 4706 3705.60465116279 1000.39534883721 30 4974 3705.60465116279 1268.39534883721 31 5756 3705.60465116279 2050.39534883721 32 5493 3705.60465116279 1787.39534883721 33 5004 3705.60465116279 1298.39534883721 34 3225 3705.60465116279 -480.604651162791 35 2006 3705.60465116279 -1699.60465116279 36 2291 3705.60465116279 -1414.60465116279 37 1588 3705.60465116279 -2117.60465116279 38 2105 3705.60465116279 -1600.60465116279 39 2191 3705.60465116279 -1514.60465116279 40 3591 3705.60465116279 -114.604651162791 41 4668 3705.60465116279 962.39534883721 42 4885 3705.60465116279 1179.39534883721 43 5822 3705.60465116279 2116.39534883721 44 5599 3705.60465116279 1893.39534883721 45 5340 3705.60465116279 1634.39534883721 46 3082 3705.60465116279 -623.60465116279 47 2010 3705.60465116279 -1695.60465116279 48 2301 3705.60465116279 -1404.60465116279 49 1514 3705.60465116279 -2191.60465116279 50 1979 3705.60465116279 -1726.60465116279 51 2480 3705.60465116279 -1225.60465116279 52 3499 3705.60465116279 -206.604651162791 53 4676 3705.60465116279 970.39534883721 54 5585 3705.60465116279 1879.39534883721 55 5610 3705.60465116279 1904.39534883721 56 5796 3705.60465116279 2090.39534883721 57 6199 3705.60465116279 2493.39534883721 58 3030 3705.60465116279 -675.60465116279 59 1930 3705.60465116279 -1775.60465116279 60 2552 3705.60465116279 -1153.60465116279

Charts produced by software:

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Parameters:

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')

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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