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WS9Q3

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 13:11:24 -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/t1195416306f606spvuf044329.htm/, Retrieved Sun, 18 Nov 2007 21:05:06 +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 1 2453 1 3042 1 4765 1 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 6 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Multiple Linear Regression - Estimated Regression Equation Huwelijken[t] = + 2028.02504347826 + 51.1426086956523`x `[t] -767.85843478261M1[t] -51.6608695652176M2[t] + 81.965217391304M3[t] + 1040.99130434783M4[t] + 2383.21739130435M5[t] + 2908.24347826087M6[t] + 2993.06956521739M7[t] + 3645.09565217391M8[t] + 2921.72173913043M9[t] + 825.147826086957M10[t] -333.226086956522M11[t] + 6.17391304347827t + 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) 2028.02504347826 169.093278 11.9935 0 0 `x ` 51.1426086956523 145.62224 0.3512 0.727041 0.363521 M1 -767.85843478261 203.366082 -3.7757 0.000456 0.000228 M2 -51.6608695652176 204.625781 -0.2525 0.801806 0.400903 M3 81.965217391304 204.055248 0.4017 0.689779 0.344889 M4 1040.99130434783 203.543415 5.1143 6e-06 3e-06 M5 2383.21739130435 203.090727 11.7347 0 0 M6 2908.24347826087 202.69758 14.3477 0 0 M7 2993.06956521739 202.36432 14.7905 0 0 M8 3645.09565217391 202.091244 18.0369 0 0 M9 2921.72173913043 201.878596 14.4727 0 0 M10 825.147826086957 201.726568 4.0904 0.000172 8.6e-05 M11 -333.226086956522 201.635296 -1.6526 0.105219 0.05261 t 6.17391304347827 3.503127 1.7624 0.084645 0.042323 Multiple Linear Regression - Regression Statistics Multiple R 0.983345616767098 R-squared 0.966968602015064 Adjusted R-squared 0.957633641714973 F-TEST (value) 103.585721945243 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 318.765276504085 Sum Squared Residuals 4674119.8692174 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 1178 1266.34052173913 -88.3405217391346 2 2141 1988.712 152.288000000000 3 2238 2128.512 109.487999999999 4 2685 3093.712 -408.712 5 4341 4442.112 -101.111999999999 6 5376 4973.312 402.687999999999 7 4478 5064.312 -586.312000000001 8 6404 5722.512 681.488000000001 9 4617 5005.312 -388.312000000001 10 3024 2914.912 109.088000000001 11 1897 1762.712 134.288000000001 12 2075 2102.112 -27.1119999999993 13 1351 1340.42747826087 10.5725217391319 14 2211 2113.94156521739 97.0584347826086 15 2453 2253.74156521739 199.258434782609 16 3042 3218.94156521739 -176.941565217391 17 4765 4567.34156521739 197.658434782609 18 4992 5098.54156521739 -106.541565217391 19 4601 5189.54156521739 -588.541565217391 20 6266 5847.74156521739 418.258434782608 21 4812 5130.54156521739 -318.541565217391 22 3159 3040.14156521739 118.858434782609 23 1916 1887.94156521739 28.0584347826086 24 2237 2227.34156521739 9.65843478260848 25 1595 1465.65704347826 129.342956521740 26 2453 2188.02852173913 264.971478260870 27 2226 2327.82852173913 -101.828521739130 28 3597 3293.02852173913 303.971478260870 29 4706 4641.42852173913 64.5714782608694 30 4974 5172.62852173913 -198.628521739130 31 5756 5263.62852173913 492.37147826087 32 5493 5921.82852173913 -428.828521739131 33 5004 5204.62852173913 -200.628521739130 34 3225 3114.22852173913 110.771478260869 35 2006 1962.02852173913 43.9714782608692 36 2291 2301.42852173913 -10.4285217391307 37 1588 1539.744 48.2560000000009 38 2105 2262.11547826087 -157.115478260870 39 2191 2401.91547826087 -210.915478260870 40 3591 3367.11547826087 223.884521739130 41 4668 4715.51547826087 -47.5154782608697 42 4885 5246.71547826087 -361.715478260869 43 5822 5337.71547826087 484.284521739131 44 5599 5995.91547826087 -396.91547826087 45 5340 5278.71547826087 61.2845217391304 46 3082 3188.31547826087 -106.315478260870 47 2010 2036.11547826087 -26.1154782608700 48 2301 2375.51547826087 -74.5154782608699 49 1514 1613.83095652174 -99.8309565217383 50 1979 2336.20243478261 -357.202434782609 51 2480 2476.00243478261 3.99756521739145 52 3499 3441.20243478261 57.7975652173911 53 4676 4789.60243478261 -113.602434782609 54 5585 5320.80243478261 264.197565217391 55 5610 5411.80243478261 198.197565217392 56 5796 6070.00243478261 -274.002434782609 57 6199 5352.80243478261 846.197565217392 58 3030 3262.40243478261 -232.402434782609 59 1930 2110.20243478261 -180.202434782609 60 2552 2449.60243478261 102.397565217391

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')

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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