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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, 24 Dec 2007 15:51:58 -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/24/t1198535627c51bf79e5isd9zz.htm/, Retrieved Mon, 24 Dec 2007 23:33:50 +0100

User-defined keywords:

s0650062

Dataseries X:

» Textbox « » Textfile « » CSV «

1,3 0 1,2 0 1,6 0 1,7 0 1,5 0 0,9 0 1,5 0 1,4 0 1,6 0 1,7 0 1,4 0 1,8 0 1,7 0 1,4 0 1,2 0 1,0 0 1,7 0 2,4 0 2,0 0 2,1 0 2,0 0 1,8 0 2,7 0 2,3 0 1,9 0 2,0 0 2,3 0 2,8 0 2,4 0 2,3 0 2,7 0 2,7 0 2,9 0 3,0 1 2,2 0 2,3 0 2,8 0 2,8 0 2,8 0 2,2 0 2,6 0 2,8 0 2,5 0 2,4 0 2,3 0 1,9 0 1,7 0 2,0 0 2,1 0 1,7 0 1,8 0 1,8 0 1,8 0 1,3 0 1,3 0 1,3 0 1,2 0 1,4 0 2,2 1 2,9 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 5 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Multiple Linear Regression - Estimated Regression Equation y[t] = + 1.87529411764706 + 0.622058823529412x[t] -0.0960539215686276M1[t] -0.24328431372549M2[t] -0.130514705882353M3[t] -0.177745098039215M4[t] -0.0849754901960783M5[t] -0.152205882352941M6[t] -0.0994362745098037M7[t] -0.126666666666666M8[t] -0.113897058823529M9[t] -0.285539215686274M10[t] -0.212769607843137M11[t] + 0.00723039215686275t + 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) 1.87529411764706 0.303896 6.1708 0 0 x 0.622058823529412 0.381864 1.629 0.110142 0.055071 M1 -0.0960539215686276 0.372439 -0.2579 0.797631 0.398815 M2 -0.24328431372549 0.372086 -0.6538 0.516471 0.258235 M3 -0.130514705882353 0.371786 -0.351 0.727155 0.363578 M4 -0.177745098039215 0.371541 -0.4784 0.634632 0.317316 M5 -0.0849754901960783 0.37135 -0.2288 0.820017 0.410008 M6 -0.152205882352941 0.371214 -0.41 0.683693 0.341847 M7 -0.0994362745098037 0.371132 -0.2679 0.789953 0.394977 M8 -0.126666666666666 0.371105 -0.3413 0.734415 0.367207 M9 -0.113897058823529 0.371132 -0.3069 0.760311 0.380156 M10 -0.285539215686274 0.363718 -0.7851 0.436445 0.218223 M11 -0.212769607843137 0.363635 -0.5851 0.561327 0.280664 t 0.00723039215686275 0.0045 1.6066 0.114976 0.057488 Multiple Linear Regression - Regression Statistics Multiple R 0.397852670050638 R-squared 0.158286747066422 Adjusted R-squared -0.0795887374582847 F-TEST (value) 0.66541849565831 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 0.785096539726594 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.574912981294892 Sum Squared Residuals 15.2041470588235 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 1.3 1.78647058823530 -0.486470588235295 2 1.2 1.64647058823529 -0.446470588235294 3 1.6 1.76647058823529 -0.166470588235294 4 1.7 1.72647058823529 -0.0264705882352942 5 1.5 1.82647058823529 -0.326470588235294 6 0.9 1.76647058823529 -0.866470588235294 7 1.5 1.82647058823529 -0.326470588235294 8 1.4 1.80647058823529 -0.406470588235294 9 1.6 1.82647058823529 -0.226470588235294 10 1.7 1.66205882352941 0.0379411764705885 11 1.4 1.74205882352941 -0.342058823529412 12 1.8 1.96205882352941 -0.162058823529412 13 1.7 1.87323529411765 -0.173235294117647 14 1.4 1.73323529411765 -0.333235294117647 15 1.2 1.85323529411765 -0.653235294117647 16 1 1.81323529411765 -0.813235294117647 17 1.7 1.91323529411765 -0.213235294117647 18 2.4 1.85323529411765 0.546764705882353 19 2 1.91323529411765 0.0867647058823529 20 2.1 1.89323529411765 0.206764705882353 21 2 1.91323529411765 0.086764705882353 22 1.8 1.74882352941176 0.0511764705882355 23 2.7 1.82882352941176 0.871176470588235 24 2.3 2.04882352941176 0.251176470588235 25 1.9 1.96 -0.0599999999999997 26 2 1.82 0.18 27 2.3 1.94 0.36 28 2.8 1.9 0.9 29 2.4 2 0.4 30 2.3 1.94 0.36 31 2.7 2 0.7 32 2.7 1.98 0.72 33 2.9 2 0.9 34 3 2.45764705882353 0.542352941176471 35 2.2 1.91558823529412 0.284411764705882 36 2.3 2.13558823529412 0.164411764705882 37 2.8 2.04676470588235 0.753235294117647 38 2.8 1.90676470588235 0.893235294117647 39 2.8 2.02676470588235 0.773235294117647 40 2.2 1.98676470588235 0.213235294117647 41 2.6 2.08676470588235 0.513235294117647 42 2.8 2.02676470588235 0.773235294117647 43 2.5 2.08676470588235 0.413235294117647 44 2.4 2.06676470588235 0.333235294117647 45 2.3 2.08676470588235 0.213235294117647 46 1.9 1.92235294117647 -0.0223529411764706 47 1.7 2.00235294117647 -0.302352941176471 48 2 2.22235294117647 -0.222352941176471 49 2.1 2.13352941176471 -0.0335294117647055 50 1.7 1.99352941176471 -0.293529411764706 51 1.8 2.11352941176471 -0.313529411764706 52 1.8 2.07352941176471 -0.273529411764706 53 1.8 2.17352941176471 -0.373529411764706 54 1.3 2.11352941176471 -0.813529411764706 55 1.3 2.17352941176471 -0.873529411764706 56 1.3 2.15352941176471 -0.853529411764706 57 1.2 2.17352941176471 -0.973529411764706 58 1.4 2.00911764705882 -0.609117647058824 59 2.2 2.71117647058824 -0.511176470588235 60 2.9 2.93117647058824 -0.0311764705882354

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = 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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