Q3

*The author of this computation has been verified*

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

Title produced by software: Multiple Regression

Date of computation: Sun, 23 Nov 2008 15:11:33 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Nov/23/t1227478350mn4lo7hbs08xtdi.htm/, Retrieved Sun, 23 Nov 2008 22:12:38 +0000

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2008/Nov/23/t1227478350mn4lo7hbs08xtdi.htm/}, year = {2008}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

102.3 0 105.8 0 106.7 0 109.6 0 111.9 0 113.3 0 114.6 0 115.7 0 117.3 0 119.8 0 120.6 0 121.4 0 123.5 0 125.2 0 126 0 126.8 0 128.1 0 128.2 0 129.3 0 130.6 0 131.4 0 131.1 0 131.2 0 131.2 0 131.5 0 133.5 0 133.7 0 133.5 0 134 0 135.9 0 135.9 0 137.2 0 138.4 0 140.9 0 143 0 144.1 0 146.8 0 149.1 0 149.6 0 151.2 0 153.3 0 156.9 0 157.2 0 158.5 0 160 0 162.5 0 162.9 0 164.7 0 165 0 167.2 0 168.6 0 169.5 0 169.8 0 171.9 0 172 0 173.7 0 173.9 0 175.9 0 175.6 0 176.1 0 176.3 0 179.4 0 179.7 0 179.9 0 180.4 0 182.5 0 183.6 0 183.9 0 184.5 0 187.6 0 188 0 188.5 0 188.6 0 191.9 0 193.5 0 194.9 0 194.9 0 196.2 0 196.2 0 198 0 198.6 0 201.3 0 203.5 0 204.1 0 204.8 1 206.5 1 207.8 1 208.6 1 209.7 1 210 1 211.7 1 212.4 1 213.7 1 214.8 1 216.4 1 217.5 1 218.6 1 220.4 1 221.8 1 222.5 1 223.4 1 225.5 1 226.5 1 227.8 1 228.5 1 229.1 1 229.9 1

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 computational 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 Y[t] = + 155.132142857143 + 62.6026397515528X[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) 155.132142857143 2.815438 55.1005 0 0 X 62.6026397515528 6.072589 10.3091 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.709239800503977 R-squared 0.503021094618921 Adjusted R-squared 0.49828796218672 F-TEST (value) 106.276573035805 F-TEST (DF numerator) 1 F-TEST (DF denominator) 105 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 25.8039117352387 Sum Squared Residuals 69913.3953881989 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 102.3 155.132142857144 -52.8321428571437 2 105.8 155.132142857143 -49.332142857143 3 106.7 155.132142857143 -48.4321428571428 4 109.6 155.132142857143 -45.5321428571429 5 111.9 155.132142857143 -43.2321428571428 6 113.3 155.132142857143 -41.8321428571429 7 114.6 155.132142857143 -40.5321428571429 8 115.7 155.132142857143 -39.4321428571428 9 117.3 155.132142857143 -37.8321428571429 10 119.8 155.132142857143 -35.3321428571428 11 120.6 155.132142857143 -34.5321428571429 12 121.4 155.132142857143 -33.7321428571428 13 123.5 155.132142857143 -31.6321428571428 14 125.2 155.132142857143 -29.9321428571428 15 126 155.132142857143 -29.1321428571428 16 126.8 155.132142857143 -28.3321428571429 17 128.1 155.132142857143 -27.0321428571429 18 128.2 155.132142857143 -26.9321428571429 19 129.3 155.132142857143 -25.8321428571428 20 130.6 155.132142857143 -24.5321428571429 21 131.4 155.132142857143 -23.7321428571428 22 131.1 155.132142857143 -24.0321428571429 23 131.2 155.132142857143 -23.9321428571429 24 131.2 155.132142857143 -23.9321428571429 25 131.5 155.132142857143 -23.6321428571428 26 133.5 155.132142857143 -21.6321428571429 27 133.7 155.132142857143 -21.4321428571429 28 133.5 155.132142857143 -21.6321428571429 29 134 155.132142857143 -21.1321428571429 30 135.9 155.132142857143 -19.2321428571428 31 135.9 155.132142857143 -19.2321428571428 32 137.2 155.132142857143 -17.9321428571429 33 138.4 155.132142857143 -16.7321428571428 34 140.9 155.132142857143 -14.2321428571428 35 143 155.132142857143 -12.1321428571428 36 144.1 155.132142857143 -11.0321428571429 37 146.8 155.132142857143 -8.33214285714284 38 149.1 155.132142857143 -6.03214285714286 39 149.6 155.132142857143 -5.53214285714286 40 151.2 155.132142857143 -3.93214285714286 41 153.3 155.132142857143 -1.83214285714284 42 156.9 155.132142857143 1.76785714285716 43 157.2 155.132142857143 2.06785714285714 44 158.5 155.132142857143 3.36785714285715 45 160 155.132142857143 4.86785714285715 46 162.5 155.132142857143 7.36785714285715 47 162.9 155.132142857143 7.76785714285716 48 164.7 155.132142857143 9.56785714285714 49 165 155.132142857143 9.86785714285715 50 167.2 155.132142857143 12.0678571428571 51 168.6 155.132142857143 13.4678571428571 52 169.5 155.132142857143 14.3678571428572 53 169.8 155.132142857143 14.6678571428572 54 171.9 155.132142857143 16.7678571428572 55 172 155.132142857143 16.8678571428572 56 173.7 155.132142857143 18.5678571428571 57 173.9 155.132142857143 18.7678571428572 58 175.9 155.132142857143 20.7678571428572 59 175.6 155.132142857143 20.4678571428571 60 176.1 155.132142857143 20.9678571428571 61 176.3 155.132142857143 21.1678571428572 62 179.4 155.132142857143 24.2678571428572 63 179.7 155.132142857143 24.5678571428571 64 179.9 155.132142857143 24.7678571428572 65 180.4 155.132142857143 25.2678571428572 66 182.5 155.132142857143 27.3678571428571 67 183.6 155.132142857143 28.4678571428571 68 183.9 155.132142857143 28.7678571428572 69 184.5 155.132142857143 29.3678571428571 70 187.6 155.132142857143 32.4678571428571 71 188 155.132142857143 32.8678571428571 72 188.5 155.132142857143 33.3678571428571 73 188.6 155.132142857143 33.4678571428571 74 191.9 155.132142857143 36.7678571428572 75 193.5 155.132142857143 38.3678571428571 76 194.9 155.132142857143 39.7678571428572 77 194.9 155.132142857143 39.7678571428572 78 196.2 155.132142857143 41.0678571428571 79 196.2 155.132142857143 41.0678571428571 80 198 155.132142857143 42.8678571428571 81 198.6 155.132142857143 43.4678571428571 82 201.3 155.132142857143 46.1678571428572 83 203.5 155.132142857143 48.3678571428571 84 204.1 155.132142857143 48.9678571428571 85 204.8 217.734782608696 -12.9347826086956 86 206.5 217.734782608696 -11.2347826086957 87 207.8 217.734782608696 -9.93478260869565 88 208.6 217.734782608696 -9.13478260869566 89 209.7 217.734782608696 -8.03478260869567 90 210 217.734782608696 -7.73478260869566 91 211.7 217.734782608696 -6.03478260869567 92 212.4 217.734782608696 -5.33478260869565 93 213.7 217.734782608696 -4.03478260869567 94 214.8 217.734782608696 -2.93478260869565 95 216.4 217.734782608696 -1.33478260869565 96 217.5 217.734782608696 -0.234782608695657 97 218.6 217.734782608696 0.865217391304337 98 220.4 217.734782608696 2.66521739130435 99 221.8 217.734782608696 4.06521739130435 100 222.5 217.734782608696 4.76521739130434 101 223.4 217.734782608696 5.66521739130435 102 225.5 217.734782608696 7.76521739130434 103 226.5 217.734782608696 8.76521739130434 104 227.8 217.734782608696 10.0652173913044 105 228.5 217.734782608696 10.7652173913043 106 229.1 217.734782608696 11.3652173913043 107 229.9 217.734782608696 12.1652173913043

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

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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