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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: Thu, 22 Nov 2007 11:18:04 -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/22/t119575524062f2hrnni44sryb.htm/, Retrieved Thu, 22 Nov 2007 19:14:10 +0100

User-defined keywords:

met seizoenaliteit en trend

Dataseries X:

» Textbox « » Textfile « » CSV «

1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,57 0 1,58 0 1,58 0 1,58 0 1,58 0 1,59 1 1,6 1 1,6 1 1,61 1 1,61 1 1,61 1 1,62 1 1,63 1 1,63 1 1,64 1 1,64 1 1,64 1 1,64 1 1,64 1 1,65 1 1,65 1 1,65 1 1,65 1 1,65 1 1,66 1 1,66 1 1,67 1 1,68 1 1,68 1 1,68 1 1,68 1 1,69 1 1,7 1 1,7 1 1,71 1 1,72 1 1,73 1 1,74 1 1,74 1 1,75 1 1,75 1 1,75 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] = + 1.42648039914469 + 0.0519672131147541x[t] + 0.00868828700403912M1[t] + 0.0251233071988595M2[t] + 0.0248916607270135M3[t] + 0.0246600142551675M4[t] + 0.0244283677833214M5[t] + 0.020863387978142M6[t] + 0.0103038726538370M7[t] + 0.00425991922071748M8[t] + 0.0046949394155381M9[t] + 0.00512995961035872M10[t] + 0.00156497980517935M11[t] + 0.00356497980517938t + 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) 1.42648039914469 0.01072 133.063 0 0 x 0.0519672131147541 0.010386 5.0038 7e-06 3e-06 M1 0.00868828700403912 0.0127 0.6841 0.496877 0.248438 M2 0.0251233071988595 0.012694 1.9792 0.052997 0.026499 M3 0.0248916607270135 0.012693 1.9611 0.055135 0.027567 M4 0.0246600142551675 0.012698 1.9421 0.057452 0.028726 M5 0.0244283677833214 0.012708 1.9222 0.059959 0.029979 M6 0.020863387978142 0.012724 1.6396 0.107003 0.053502 M7 0.0103038726538370 0.012691 0.8119 0.420479 0.21024 M8 0.00425991922071748 0.013289 0.3206 0.749797 0.374899 M9 0.0046949394155381 0.01327 0.3538 0.72489 0.362445 M10 0.00512995961035872 0.013257 0.387 0.700324 0.350162 M11 0.00156497980517935 0.013249 0.1181 0.906415 0.453208 t 0.00356497980517938 0.000266 13.3864 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.980262983409438 R-squared 0.960915516642772 Adjusted R-squared 0.951328756574018 F-TEST (value) 100.233604445225 F-TEST (DF numerator) 13 F-TEST (DF denominator) 53 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.0209435227528610 Sum Squared Residuals 0.0232474507008792 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 1.48 1.43873366595391 0.0412663340460929 2 1.48 1.45873366595391 0.0212663340460915 3 1.48 1.46206699928724 0.0179330007127584 4 1.48 1.46540033262057 0.014599667379425 5 1.48 1.46873366595391 0.0112663340460916 6 1.48 1.46873366595391 0.0112663340460916 7 1.48 1.46173913043478 0.0182608695652173 8 1.48 1.45926015680684 0.0207398431931575 9 1.48 1.46326015680684 0.0167398431931575 10 1.48 1.46726015680684 0.0127398431931575 11 1.48 1.46726015680684 0.0127398431931575 12 1.48 1.46926015680684 0.0107398431931574 13 1.48 1.48151342361606 -0.00151342361606112 14 1.48 1.50151342361606 -0.0215134236160609 15 1.48 1.50484675694939 -0.0248467569493942 16 1.48 1.50818009028273 -0.0281800902827275 17 1.48 1.51151342361606 -0.0315134236160609 18 1.48 1.51151342361606 -0.0315134236160609 19 1.48 1.50451888809694 -0.0245188880969352 20 1.48 1.50203991446900 -0.0220399144689950 21 1.48 1.50603991446900 -0.0260399144689950 22 1.48 1.51003991446900 -0.0300399144689950 23 1.48 1.51003991446900 -0.0300399144689950 24 1.48 1.51203991446900 -0.0320399144689951 25 1.48 1.52429318127821 -0.0442931812782136 26 1.57 1.54429318127821 0.0257068187217868 27 1.58 1.54762651461155 0.0323734853884534 28 1.58 1.55095984794488 0.0290401520551200 29 1.58 1.55429318127821 0.0257068187217867 30 1.58 1.55429318127821 0.0257068187217867 31 1.59 1.59926585887384 -0.00926585887384171 32 1.6 1.5967868852459 0.00321311475409846 33 1.6 1.6007868852459 -0.000786885245901553 34 1.61 1.6047868852459 0.00521311475409846 35 1.61 1.6047868852459 0.00521311475409846 36 1.61 1.6067868852459 0.00321311475409844 37 1.62 1.61904015205512 0.000959847944879887 38 1.63 1.63904015205512 -0.00904015205511999 39 1.63 1.64237348538845 -0.0123734853884534 40 1.64 1.64570681872179 -0.00570681872178671 41 1.64 1.64904015205512 -0.00904015205512005 42 1.64 1.64904015205512 -0.00904015205512003 43 1.64 1.64204561653599 -0.00204561653599436 44 1.64 1.63956664290805 0.000433357091945775 45 1.65 1.64356664290805 0.00643335709194579 46 1.65 1.64756664290805 0.00243335709194579 47 1.65 1.64756664290805 0.00243335709194579 48 1.65 1.64956664290805 0.000433357091945767 49 1.65 1.66181990971727 -0.0118199097172728 50 1.66 1.68181990971727 -0.0218199097172724 51 1.66 1.68515324305061 -0.0251532430506059 52 1.67 1.68848657638394 -0.0184865763839392 53 1.68 1.69181990971727 -0.0118199097172725 54 1.68 1.69181990971727 -0.0118199097172725 55 1.68 1.68482537419815 -0.00482537419814682 56 1.68 1.68234640057021 -0.00234640057020668 57 1.69 1.68634640057021 0.00365359942979333 58 1.7 1.69034640057021 0.00965359942979333 59 1.7 1.69034640057021 0.00965359942979332 60 1.71 1.69234640057021 0.0176535994297933 61 1.72 1.70459966737943 0.0154003326205748 62 1.73 1.72459966737942 0.00540033262057511 63 1.74 1.72793300071276 0.0120669992872417 64 1.74 1.73126633404609 0.00873366595390838 65 1.75 1.73459966737942 0.0154003326205751 66 1.75 1.73459966737942 0.0154003326205751 67 1.75 1.7276051318603 0.0223948681397007

Charts produced by software:

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Parameters:

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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