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Works 6 T1

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 03:27:18 -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/t1195467640a97uui1v73ib42z.htm/, Retrieved Mon, 19 Nov 2007 11:21:32 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

110.40 0 96.40 0 101.90 0 106.20 0 81.00 0 94.70 0 101.00 0 109.40 1 102.30 1 90.70 1 96.20 1 96.10 1 106.00 1 103.10 1 102.00 1 104.70 1 86.00 1 92.10 1 106.90 1 112.60 1 101.70 1 92.00 1 97.40 1 97.00 1 105.40 1 102.70 1 98.10 1 104.50 1 87.40 1 89.90 1 109.80 1 111.70 1 98.60 1 96.90 1 95.10 1 97.00 1 112.70 1 102.90 1 97.40 1 111.40 1 87.40 1 96.80 1 114.10 1 110.30 1 103.90 1 101.60 1 94.60 1 95.90 1 104.70 1 102.80 1 98.10 1 113.90 1 80.90 1 95.70 1 113.20 1 105.90 1 108.80 1 102.30 1 99.00 1 100.70 1 115.50 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 y[t] = + 98.8 + 2.38148148148147`x `[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) 98.8 3.066235 32.2219 0 0 `x ` 2.38148148148147 3.258918 0.7308 0.467819 0.233909 Multiple Linear Regression - Regression Statistics Multiple R 0.0947089920200564 R-squared 0.00896979316945512 Adjusted R-squared -0.0078273289802151 F-TEST (value) 0.534007735940124 F-TEST (DF numerator) 1 F-TEST (DF denominator) 59 p-value 0.467818896835352 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 8.1124945289804 Sum Squared Residuals 3882.94148148148 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 110.4 98.8 11.6000000000001 2 96.4 98.8 -2.40000000000000 3 101.9 98.8 3.1 4 106.2 98.8 7.4 5 81 98.8 -17.8 6 94.7 98.8 -4.10000000000001 7 101 98.8 2.19999999999999 8 109.4 101.181481481481 8.21851851851852 9 102.3 101.181481481481 1.11851851851851 10 90.7 101.181481481481 -10.4814814814815 11 96.2 101.181481481481 -4.98148148148148 12 96.1 101.181481481481 -5.08148148148149 13 106 101.181481481481 4.81851851851852 14 103.1 101.181481481481 1.91851851851851 15 102 101.181481481481 0.818518518518517 16 104.7 101.181481481481 3.51851851851852 17 86 101.181481481481 -15.1814814814815 18 92.1 101.181481481481 -9.0814814814815 19 106.9 101.181481481481 5.71851851851852 20 112.6 101.181481481481 11.4185185185185 21 101.7 101.181481481481 0.518518518518519 22 92 101.181481481481 -9.18148148148148 23 97.4 101.181481481481 -3.78148148148148 24 97 101.181481481481 -4.18148148148148 25 105.4 101.181481481481 4.21851851851852 26 102.7 101.181481481481 1.51851851851852 27 98.1 101.181481481481 -3.08148148148149 28 104.5 101.181481481481 3.31851851851852 29 87.4 101.181481481481 -13.7814814814815 30 89.9 101.181481481481 -11.2814814814815 31 109.8 101.181481481481 8.61851851851852 32 111.7 101.181481481481 10.5185185185185 33 98.6 101.181481481481 -2.58148148148149 34 96.9 101.181481481481 -4.28148148148148 35 95.1 101.181481481481 -6.08148148148149 36 97 101.181481481481 -4.18148148148148 37 112.7 101.181481481481 11.5185185185185 38 102.9 101.181481481481 1.71851851851852 39 97.4 101.181481481481 -3.78148148148148 40 111.4 101.181481481481 10.2185185185185 41 87.4 101.181481481481 -13.7814814814815 42 96.8 101.181481481481 -4.38148148148149 43 114.1 101.181481481481 12.9185185185185 44 110.3 101.181481481481 9.11851851851852 45 103.9 101.181481481481 2.71851851851852 46 101.6 101.181481481481 0.418518518518511 47 94.6 101.181481481481 -6.58148148148149 48 95.9 101.181481481481 -5.28148148148148 49 104.7 101.181481481481 3.51851851851852 50 102.8 101.181481481481 1.61851851851851 51 98.1 101.181481481481 -3.08148148148149 52 113.9 101.181481481481 12.7185185185185 53 80.9 101.181481481481 -20.2814814814815 54 95.7 101.181481481481 -5.48148148148148 55 113.2 101.181481481481 12.0185185185185 56 105.9 101.181481481481 4.71851851851852 57 108.8 101.181481481481 7.61851851851851 58 102.3 101.181481481481 1.11851851851851 59 99 101.181481481481 -2.18148148148148 60 100.7 101.181481481481 -0.48148148148148 61 115.5 101.181481481481 14.3185185185185

Charts produced by software:

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Parameters:

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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