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WS8 Q3 Monthly

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 09:54:03 -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/18/t1195404448ve5czyvaqwa9s7u.htm/, Retrieved Sun, 18 Nov 2007 17:47:38 +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] = + 2132.44137931034 + 198.448275862069Dummy[t] -806.310344827587M1[t] -73.7103448275845M2[t] + 66.0896551724116M3[t] + 1031.28965517242M4[t] + 2379.68965517241M5[t] + 2871.2M6[t] + 2962.20000000000M7[t] + 3620.4M8[t] + 2903.2M9[t] + 812.8M10[t] -339.4M11[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) 2132.44137931034 166.262186 12.8258 0 0 Dummy 198.448275862069 96.637933 2.0535 0.045609 0.022805 M1 -806.310344827587 209.059813 -3.8568 0.000348 0.000174 M2 -73.7103448275845 209.059813 -0.3526 0.725979 0.36299 M3 66.0896551724116 209.059813 0.3161 0.753305 0.376653 M4 1031.28965517242 209.059813 4.933 1.1e-05 5e-06 M5 2379.68965517241 209.059813 11.3828 0 0 M6 2871.2 208.164478 13.7929 0 0 M7 2962.20000000000 208.164478 14.2301 0 0 M8 3620.4 208.164478 17.392 0 0 M9 2903.2 208.164478 13.9467 0 0 M10 812.8 208.164478 3.9046 3e-04 0.00015 M11 -339.4 208.164478 -1.6304 0.109693 0.054846 Multiple Linear Regression - Regression Statistics Multiple R 0.981844481859706 R-squared 0.964018586558354 Adjusted R-squared 0.954831842700913 F-TEST (value) 104.935829442711 F-TEST (DF numerator) 12 F-TEST (DF denominator) 47 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 329.136939390896 Sum Squared Residuals 5091562.86896551 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 1178 1326.13103448276 -148.131034482759 2 2141 2058.73103448276 82.2689655172425 3 2238 2198.53103448276 39.4689655172429 4 2685 3163.73103448276 -478.73103448276 5 4341 4512.13103448275 -171.131034482752 6 5376 5003.64137931035 372.358620689652 7 4478 5094.64137931034 -616.64137931034 8 6404 5752.84137931035 651.158620689654 9 4617 5035.64137931035 -418.641379310348 10 3024 2945.24137931035 78.7586206896522 11 1897 1793.04137931035 103.958620689654 12 2075 2132.44137931034 -57.4413793103445 13 1351 1326.13103448276 24.8689655172416 14 2211 2058.73103448276 152.268965517241 15 2453 2198.53103448276 254.468965517241 16 3042 3163.73103448276 -121.731034482758 17 4765 4512.13103448276 252.86896551724 18 4992 5202.08965517241 -210.089655172413 19 4601 5293.08965517242 -692.089655172415 20 6266 5951.28965517241 314.710344827587 21 4812 5234.08965517241 -422.089655172413 22 3159 3143.68965517241 15.3103448275869 23 1916 1991.48965517241 -75.4896551724136 24 2237 2330.88965517241 -93.8896551724135 25 1595 1524.57931034483 70.4206896551726 26 2453 2257.17931034483 195.820689655172 27 2226 2396.97931034483 -170.979310344828 28 3597 3362.17931034483 234.820689655173 29 4706 4710.57931034483 -4.57931034482927 30 4974 5202.08965517241 -228.089655172413 31 5756 5293.08965517241 462.910344827585 32 5493 5951.28965517241 -458.289655172414 33 5004 5234.08965517241 -230.089655172413 34 3225 3143.68965517241 81.310344827587 35 2006 1991.48965517241 14.5103448275864 36 2291 2330.88965517241 -39.8896551724135 37 1588 1524.57931034483 63.4206896551726 38 2105 2257.17931034483 -152.179310344828 39 2191 2396.97931034483 -205.979310344828 40 3591 3362.17931034483 228.820689655173 41 4668 4710.57931034483 -42.5793103448292 42 4885 5202.08965517241 -317.089655172413 43 5822 5293.08965517242 528.910344827585 44 5599 5951.28965517241 -352.289655172414 45 5340 5234.08965517241 105.910344827587 46 3082 3143.68965517241 -61.6896551724131 47 2010 1991.48965517241 18.5103448275864 48 2301 2330.88965517241 -29.8896551724135 49 1514 1524.57931034483 -10.5793103448274 50 1979 2257.17931034483 -278.179310344828 51 2480 2396.97931034483 83.020689655172 52 3499 3362.17931034483 136.820689655173 53 4676 4710.57931034483 -34.5793103448293 54 5585 5202.08965517241 382.910344827586 55 5610 5293.08965517242 316.910344827585 56 5796 5951.28965517241 -155.289655172414 57 6199 5234.08965517241 964.910344827587 58 3030 3143.68965517241 -113.689655172413 59 1930 1991.48965517241 -61.4896551724136 60 2552 2330.88965517241 221.110344827587

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')

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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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