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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: Mon, 19 Nov 2007 03:48:20 -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/19/t11954688860i2v7m1sbqqfjmm.htm/, Retrieved Mon, 19 Nov 2007 11:41:36 +0100

User-defined keywords:

Dataseries X:

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106.8 0 113.7 0 102.5 0 96.6 0 92.1 0 95.6 0 102.3 0 98.6 0 98.2 0 104.5 0 84 0 73.8 0 103.9 0 106 0 97.2 0 102.6 0 89 0 93.8 0 116.7 0 106.8 0 98.5 0 118.7 0 90 0 91.9 0 113.3 0 113.1 1 104.1 1 108.7 1 96.7 1 101 1 116.9 1 105.8 1 99 1 129.4 1 83 1 88.9 1 115.9 1 104.2 1 113.4 1 112.2 1 100.8 1 107.3 1 126.6 1 102.9 1 117.9 1 128.8 1 87.5 1 93.8 1 122.7 1 126.2 1 124.6 1 116.7 1 115.2 1 111.1 1 129.9 1 113.3 1 118.5 1 133.5 1 102.1 1 102.4 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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation totmet[t] = + 83.3308333333333 + 11.3819444444444ramp[t] + 24.6363888888889M1[t] + 22.48M2[t] + 18.2M3[t] + 17.2M4[t] + 8.6M5[t] + 11.6000000000000M6[t] + 28.32M7[t] + 15.32M8[t] + 16.26M9[t] + 32.82M10[t] -0.839999999999998M11[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) 83.3308333333333 3.298708 25.2617 0 0 ramp 11.3819444444444 1.832616 6.2108 0 0 M1 24.6363888888889 4.413523 5.582 1e-06 1e-06 M2 22.48 4.398278 5.1111 6e-06 3e-06 M3 18.2 4.398278 4.138 0.000144 7.2e-05 M4 17.2 4.398278 3.9106 0.000295 0.000147 M5 8.6 4.398278 1.9553 0.056507 0.028253 M6 11.6000000000000 4.398278 2.6374 0.01129 0.005645 M7 28.32 4.398278 6.4389 0 0 M8 15.32 4.398278 3.4832 0.001083 0.000541 M9 16.26 4.398278 3.6969 0.00057 0.000285 M10 32.82 4.398278 7.462 0 0 M11 -0.839999999999998 4.398278 -0.191 0.849361 0.42468 Multiple Linear Regression - Regression Statistics Multiple R 0.876749763742216 R-squared 0.768690148222031 Adjusted R-squared 0.709632313725528 F-TEST (value) 13.0158878119304 F-TEST (DF numerator) 12 F-TEST (DF denominator) 47 p-value 3.53489459925527e-11 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 6.95428737428651 Sum Squared Residuals 2273.01930555556 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 106.8 107.967222222222 -1.16722222222219 2 113.7 105.810833333333 7.8891666666667 3 102.5 101.530833333333 0.969166666666645 4 96.6 100.530833333333 -3.93083333333331 5 92.1 91.9308333333333 0.169166666666652 6 95.6 94.9308333333333 0.66916666666666 7 102.3 111.650833333333 -9.35083333333335 8 98.6 98.6508333333333 -0.0508333333332928 9 98.2 99.5908333333334 -1.39083333333336 10 104.5 116.150833333333 -11.6508333333333 11 84 82.4908333333333 1.50916666666666 12 73.8 83.3308333333333 -9.53083333333335 13 103.9 107.967222222222 -4.06722222222223 14 106 105.810833333333 0.189166666666657 15 97.2 101.530833333333 -4.33083333333333 16 102.6 100.530833333333 2.06916666666665 17 89 91.9308333333333 -2.93083333333333 18 93.8 94.9308333333333 -1.13083333333334 19 116.7 111.650833333333 5.04916666666666 20 106.8 98.6508333333333 8.14916666666665 21 98.5 99.5908333333333 -1.09083333333333 22 118.7 116.150833333333 2.54916666666665 23 90 82.4908333333333 7.50916666666667 24 91.9 83.3308333333333 8.56916666666667 25 113.3 107.967222222222 5.33277777777776 26 113.1 117.192777777778 -4.09277777777779 27 104.1 112.912777777778 -8.81277777777778 28 108.7 111.912777777778 -3.21277777777778 29 96.7 103.312777777778 -6.61277777777777 30 101 106.312777777778 -5.31277777777777 31 116.9 123.032777777778 -6.13277777777777 32 105.8 110.032777777778 -4.23277777777779 33 99 110.972777777778 -11.9727777777778 34 129.4 127.532777777778 1.86722222222222 35 83 93.8727777777778 -10.8727777777778 36 88.9 94.7127777777778 -5.81277777777777 37 115.9 119.349166666667 -3.44916666666667 38 104.2 117.192777777778 -12.9927777777778 39 113.4 112.912777777778 0.487222222222235 40 112.2 111.912777777778 0.287222222222217 41 100.8 103.312777777778 -2.51277777777777 42 107.3 106.312777777778 0.987222222222224 43 126.6 123.032777777778 3.56722222222222 44 102.9 110.032777777778 -7.13277777777778 45 117.9 110.972777777778 6.92722222222223 46 128.8 127.532777777778 1.26722222222222 47 87.5 93.8727777777778 -6.37277777777778 48 93.8 94.7127777777778 -0.912777777777777 49 122.7 119.349166666667 3.35083333333333 50 126.2 117.192777777778 9.00722222222222 51 124.6 112.912777777778 11.6872222222222 52 116.7 111.912777777778 4.78722222222222 53 115.2 103.312777777778 11.8872222222222 54 111.1 106.312777777778 4.78722222222222 55 129.9 123.032777777778 6.86722222222223 56 113.3 110.032777777778 3.26722222222221 57 118.5 110.972777777778 7.52722222222223 58 133.5 127.532777777778 5.96722222222221 59 102.1 93.8727777777778 8.22722222222222 60 102.4 94.7127777777778 7.68722222222223

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')

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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