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: Mon, 24 Nov 2008 15:37:41 -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/24/t12275664505l16d2pknz6hk6i.htm/, Retrieved Mon, 24 Nov 2008 22:40:59 +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/24/t12275664505l16d2pknz6hk6i.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 «

94,5 0 114,2 0 104,9 0 106,2 0 99,9 0 97,6 0 103,6 0 192,4 0 113,4 0 106,5 0 104,1 0 98,8 0 92,2 0 120,8 0 97,1 0 89,7 0 105 0 86,2 0 95,1 0 155 0 116,5 0 92,6 0 96 0 82,9 0 81,7 0 106,5 0 96,2 0 84,9 0 93 0 80,9 0 73,9 0 157,4 0 98,2 0 88,3 0 92,6 0 78,4 0 79,2 0 105,5 0 80,6 0 80,9 0 84,6 0 71,2 0 71,4 0 148 0 83,7 0 83,3 0 92,3 0 74,8 0 82,1 0 100 0 71,7 0 79,1 0 86,8 0 64,2 0 75,4 0 139,3 1 77,3 1 112,4 1 98,6 1 77,3 1 73,5 1 100,1 1 76,5 1 77,7 1 80,4 1 72,2 1 65,4 1 181,2 1 96,3 1 106,4 1 90,9 1 75,3 1 71,2 1 96,1 1 80,6 1 77,7 1 83 1 67,5 1 88,5 1 167,6 1 96,4 1 91 1 90,3 1 92,3 1 84,5 1 100,9 1 90 1 84,2 1 97,4 1 78,2 1 90 1 182,4 1 100,2 1 95,1 1 105 1 86,9 1 80,7 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] = + 96.5818181818182 -1.85562770562771x[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) 96.5818181818182 3.344802 28.8752 0 0 x -1.85562770562771 5.083134 -0.3651 0.715881 0.357941 Multiple Linear Regression - Regression Statistics Multiple R 0.0374276924948006 R-squared 0.00140083216548536 Adjusted R-squared -0.00911073802224638 F-TEST (value) 0.133265738654373 F-TEST (DF numerator) 1 F-TEST (DF denominator) 95 p-value 0.715881210233916 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 24.8057130534709 Sum Squared Residuals 58455.723008658 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 94.5 96.581818181818 -2.08181818181796 2 114.2 96.5818181818182 17.6181818181818 3 104.9 96.5818181818182 8.31818181818182 4 106.2 96.5818181818182 9.61818181818182 5 99.9 96.5818181818182 3.31818181818182 6 97.6 96.5818181818182 1.01818181818181 7 103.6 96.5818181818182 7.01818181818181 8 192.4 96.5818181818182 95.8181818181818 9 113.4 96.5818181818182 16.8181818181818 10 106.5 96.5818181818182 9.91818181818181 11 104.1 96.5818181818182 7.51818181818181 12 98.8 96.5818181818182 2.21818181818181 13 92.2 96.5818181818182 -4.38181818181818 14 120.8 96.5818181818182 24.2181818181818 15 97.1 96.5818181818182 0.518181818181808 16 89.7 96.5818181818182 -6.88181818181818 17 105 96.5818181818182 8.41818181818181 18 86.2 96.5818181818182 -10.3818181818182 19 95.1 96.5818181818182 -1.48181818181819 20 155 96.5818181818182 58.4181818181818 21 116.5 96.5818181818182 19.9181818181818 22 92.6 96.5818181818182 -3.98181818181819 23 96 96.5818181818182 -0.581818181818186 24 82.9 96.5818181818182 -13.6818181818182 25 81.7 96.5818181818182 -14.8818181818182 26 106.5 96.5818181818182 9.91818181818181 27 96.2 96.5818181818182 -0.381818181818183 28 84.9 96.5818181818182 -11.6818181818182 29 93 96.5818181818182 -3.58181818181819 30 80.9 96.5818181818182 -15.6818181818182 31 73.9 96.5818181818182 -22.6818181818182 32 157.4 96.5818181818182 60.8181818181818 33 98.2 96.5818181818182 1.61818181818182 34 88.3 96.5818181818182 -8.28181818181819 35 92.6 96.5818181818182 -3.98181818181819 36 78.4 96.5818181818182 -18.1818181818182 37 79.2 96.5818181818182 -17.3818181818182 38 105.5 96.5818181818182 8.91818181818181 39 80.6 96.5818181818182 -15.9818181818182 40 80.9 96.5818181818182 -15.6818181818182 41 84.6 96.5818181818182 -11.9818181818182 42 71.2 96.5818181818182 -25.3818181818182 43 71.4 96.5818181818182 -25.1818181818182 44 148 96.5818181818182 51.4181818181818 45 83.7 96.5818181818182 -12.8818181818182 46 83.3 96.5818181818182 -13.2818181818182 47 92.3 96.5818181818182 -4.28181818181819 48 74.8 96.5818181818182 -21.7818181818182 49 82.1 96.5818181818182 -14.4818181818182 50 100 96.5818181818182 3.41818181818181 51 71.7 96.5818181818182 -24.8818181818182 52 79.1 96.5818181818182 -17.4818181818182 53 86.8 96.5818181818182 -9.78181818181819 54 64.2 96.5818181818182 -32.3818181818182 55 75.4 96.5818181818182 -21.1818181818182 56 139.3 94.7261904761905 44.5738095238095 57 77.3 94.7261904761905 -17.4261904761905 58 112.4 94.7261904761905 17.6738095238095 59 98.6 94.7261904761905 3.87380952380952 60 77.3 94.7261904761905 -17.4261904761905 61 73.5 94.7261904761905 -21.2261904761905 62 100.1 94.7261904761905 5.37380952380952 63 76.5 94.7261904761905 -18.2261904761905 64 77.7 94.7261904761905 -17.0261904761905 65 80.4 94.7261904761905 -14.3261904761905 66 72.2 94.7261904761905 -22.5261904761905 67 65.4 94.7261904761905 -29.3261904761905 68 181.2 94.7261904761905 86.4738095238095 69 96.3 94.7261904761905 1.57380952380952 70 106.4 94.7261904761905 11.6738095238095 71 90.9 94.7261904761905 -3.82619047619047 72 75.3 94.7261904761905 -19.4261904761905 73 71.2 94.7261904761905 -23.5261904761905 74 96.1 94.7261904761905 1.37380952380952 75 80.6 94.7261904761905 -14.1261904761905 76 77.7 94.7261904761905 -17.0261904761905 77 83 94.7261904761905 -11.7261904761905 78 67.5 94.7261904761905 -27.2261904761905 79 88.5 94.7261904761905 -6.22619047619048 80 167.6 94.7261904761905 72.8738095238095 81 96.4 94.7261904761905 1.67380952380953 82 91 94.7261904761905 -3.72619047619048 83 90.3 94.7261904761905 -4.42619047619048 84 92.3 94.7261904761905 -2.42619047619048 85 84.5 94.7261904761905 -10.2261904761905 86 100.9 94.7261904761905 6.17380952380953 87 90 94.7261904761905 -4.72619047619048 88 84.2 94.7261904761905 -10.5261904761905 89 97.4 94.7261904761905 2.67380952380953 90 78.2 94.7261904761905 -16.5261904761905 91 90 94.7261904761905 -4.72619047619048 92 182.4 94.7261904761905 87.6738095238095 93 100.2 94.7261904761905 5.47380952380952 94 95.1 94.7261904761905 0.373809523809516 95 105 94.7261904761905 10.2738095238095 96 86.9 94.7261904761905 -7.82619047619047 97 80.7 94.7261904761905 -14.0261904761905

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')

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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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