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

Title produced by software: Multiple Regression

Date of computation: Wed, 12 Dec 2007 03:42:31 -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/Dec/12/t1197455390dfi5pm7b81je9qb.htm/, Retrieved Wed, 12 Dec 2007 11:30:00 +0100

User-defined keywords:

fredje

Dataseries X:

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12398.4 0 13882.3 0 15861.5 0 13286.1 0 15634.9 0 14211 0 13646.8 0 12224.6 0 15916.4 0 16535.9 0 15796 0 14418.6 0 15044.5 0 14944.2 0 16754.8 0 14254 0 15454.9 0 15644.8 0 14568.3 0 12520.2 0 14803 0 15873.2 0 14755.3 0 12875.1 0 14291.1 1 14205.3 1 15859.4 1 15258.9 1 15498.6 1 14106.5 1 15023.6 1 12083 1 15761.3 1 16943 1 15070.3 1 13659.6 1 14768.9 1 14725.1 1 15998.1 1 15370.6 1 14956.9 1 15469.7 1 15101.8 1 11703.7 1 16283.6 1 16726.5 1 14968.9 1 14861 1 14583.3 1 15305.8 1 17903.9 1 16379.4 1 15420.3 1 17870.5 1 15912.8 1 13866.5 1 17823.2 1 17872 1 17420.4 1 16704.4 1 15991.2 1 16583.6 1 19123.5 1 17838.7 1 17209.4 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 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation y[t] = + 13897.1161061947 + 1011.03982300885x[t] -58.2426548672657M1[t] + 369.90734513274M2[t] + 2345.72401179940M3[t] + 826.80734513274M4[t] + 1124.69067846607M5[t] + 956.759999999998M6[t] + 346.919999999997M7[t] -2024.14000000000M8[t] + 1613.76000000000M9[t] + 2286.38000000000M10[t] + 1098.44000000000M11[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) 13897.1161061947 489.390569 28.3968 0 0 x 1011.03982300885 266.456284 3.7944 0.000388 0.000194 M1 -58.2426548672657 626.534367 -0.093 0.926293 0.463146 M2 369.90734513274 626.534367 0.5904 0.557478 0.278739 M3 2345.72401179940 626.534367 3.744 0.000454 0.000227 M4 826.80734513274 626.534367 1.3197 0.192732 0.096366 M5 1124.69067846607 626.534367 1.7951 0.078451 0.039225 M6 956.759999999998 654.130731 1.4626 0.149583 0.074792 M7 346.919999999997 654.130731 0.5304 0.598125 0.299063 M8 -2024.14000000000 654.130731 -3.0944 0.003172 0.001586 M9 1613.76000000000 654.130731 2.467 0.016955 0.008477 M10 2286.38000000000 654.130731 3.4953 0.000977 0.000489 M11 1098.44000000000 654.130731 1.6792 0.099106 0.049553 Multiple Linear Regression - Regression Statistics Multiple R 0.795013353019579 R-squared 0.632046231479433 Adjusted R-squared 0.547133823359302 F-TEST (value) 7.44350849860763 F-TEST (DF numerator) 12 F-TEST (DF denominator) 52 p-value 9.83498817941353e-08 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1034.27149828694 Sum Squared Residuals 55625311.672773 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 12398.4 13838.8734513275 -1440.47345132747 2 13882.3 14267.0234513274 -384.723451327436 3 15861.5 16242.8401179941 -381.340117994102 4 13286.1 14723.9234513274 -1437.82345132743 5 15634.9 15021.8067846608 613.093215339238 6 14211 14853.8761061947 -642.876106194688 7 13646.8 14244.0361061947 -597.236106194688 8 12224.6 11872.9761061947 351.623893805311 9 15916.4 15510.8761061947 405.523893805312 10 16535.9 16183.4961061947 352.403893805314 11 15796 14995.5561061947 800.44389380531 12 14418.6 13897.1161061947 521.483893805311 13 15044.5 13838.8734513274 1205.62654867258 14 14944.2 14267.0234513274 677.176548672571 15 16754.8 16242.8401179941 511.959882005902 16 14254 14723.9234513274 -469.923451327431 17 15454.9 15021.8067846608 433.093215339234 18 15644.8 14853.8761061947 790.92389380531 19 14568.3 14244.0361061947 324.263893805310 20 12520.2 11872.9761061947 647.223893805313 21 14803 15510.8761061947 -707.876106194689 22 15873.2 16183.4961061947 -310.296106194689 23 14755.3 14995.5561061947 -240.256106194690 24 12875.1 13897.1161061947 -1022.01610619469 25 14291.1 14849.9132743363 -558.813274336275 26 14205.3 15278.0632743363 -1072.76327433628 27 15859.4 17253.8799410029 -1394.47994100295 28 15258.9 15734.9632743363 -476.063274336284 29 15498.6 16032.8466076696 -534.246607669618 30 14106.5 15864.9159292035 -1758.41592920354 31 15023.6 15255.0759292035 -231.475929203541 32 12083 12884.0159292035 -801.015929203541 33 15761.3 16521.9159292035 -760.615929203542 34 16943 17194.5359292035 -251.535929203542 35 15070.3 16006.5959292035 -936.295929203542 36 13659.6 14908.1559292035 -1248.55592920354 37 14768.9 14849.9132743363 -81.013274336276 38 14725.1 15278.0632743363 -552.963274336282 39 15998.1 17253.8799410029 -1255.77994100295 40 15370.6 15734.9632743363 -364.363274336283 41 14956.9 16032.8466076696 -1075.94660766962 42 15469.7 15864.9159292035 -395.215929203541 43 15101.8 15255.0759292035 -153.275929203542 44 11703.7 12884.0159292035 -1180.31592920354 45 16283.6 16521.9159292035 -238.315929203540 46 16726.5 17194.5359292035 -468.035929203542 47 14968.9 16006.5959292035 -1037.69592920354 48 14861 14908.1559292035 -47.1559292035431 49 14583.3 14849.9132743363 -266.613274336276 50 15305.8 15278.0632743363 27.7367256637172 51 17903.9 17253.8799410029 650.020058997052 52 16379.4 15734.9632743363 644.436725663716 53 15420.3 16032.8466076696 -612.546607669619 54 17870.5 15864.9159292035 2005.58407079646 55 15912.8 15255.0759292035 657.724070796458 56 13866.5 12884.0159292035 982.48407079646 57 17823.2 16521.9159292035 1301.28407079646 58 17872 17194.5359292035 677.464070796458 59 17420.4 16006.5959292035 1413.80407079646 60 16704.4 14908.1559292035 1796.24407079646 61 15991.2 14849.9132743363 1141.28672566372 62 16583.6 15278.0632743363 1305.53672566372 63 19123.5 17253.8799410029 1869.62005899705 64 17838.7 15734.9632743363 2103.73672566372 65 17209.4 16032.8466076696 1176.55339233038

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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Software written by Ed van Stee & Patrick Wessa

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