Q3 Multiple Regression met dummies en lineaire trend

*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, 01 Dec 2008 12:51:08 -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/Dec/01/t12281611046iv9aax9p550qja.htm/, Retrieved Mon, 01 Dec 2008 19:51:53 +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/Dec/01/t12281611046iv9aax9p550qja.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)

Feedback Forum:

2008-11-27 13:41:43 [a2386b643d711541400692649981f2dc]  [reply]  test Post a new message

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

7.8 0 7.6 0 7.5 0 7.6 0 7.5 0 7.3 0 7.6 0 7.5 0 7.6 0 7.9 0 7.9 0 8.1 0 8.2 0 8.0 0 7.5 0 6.8 0 6.5 0 6.6 0 7.6 0 8.0 0 8.0 0 7.7 0 7.5 0 7.6 0 7.7 0 7.9 0 7.8 0 7.5 0 7.5 0 7.1 0 7.5 0 7.5 0 7.6 0 7.7 0 7.7 0 7.9 1 8.1 1 8.2 1 8.2 1 8.1 1 7.9 1 7.3 1 6.9 1 6.6 1 6.7 1 6.9 1 7.0 1 7.1 1 7.2 1 7.1 1 6.9 1 7.0 1 6.8 1 6.4 1 6.7 1 6.7 1 6.4 1 6.3 1 6.2 1 6.5 1 6.8 1 6.8 1 6.5 1 6.3 1 5.9 1 5.9 1 6.4 1 6.4 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] = + 8.217 + 0.135000000000000x[t] + 0.0876666666666688M1[t] + 0.0781666666666671M2[t] -0.0979999999999992M3[t] -0.2575M4[t] -0.433666666666666M5[t] -0.659833333333333M6[t] -0.286000000000000M7[t] -0.262166666666666M8[t] -0.224499999999999M9[t] -0.160666666666666M10[t] -0.176833333333333M11[t] -0.0238333333333334t + 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) 8.217 0.225413 36.453 0 0 x 0.135000000000000 0.221036 0.6108 0.543921 0.27196 M1 0.0876666666666688 0.268051 0.3271 0.744893 0.372446 M2 0.0781666666666671 0.267924 0.2917 0.771596 0.385798 M3 -0.0979999999999992 0.267916 -0.3658 0.715954 0.357977 M4 -0.2575 0.268026 -0.9607 0.340971 0.170485 M5 -0.433666666666666 0.268254 -1.6166 0.111786 0.055893 M6 -0.659833333333333 0.268599 -2.4566 0.017272 0.008636 M7 -0.286000000000000 0.269062 -1.063 0.292534 0.146267 M8 -0.262166666666666 0.269641 -0.9723 0.335247 0.167623 M9 -0.224499999999999 0.281261 -0.7982 0.428255 0.214128 M10 -0.160666666666666 0.281751 -0.5702 0.570877 0.285439 M11 -0.176833333333333 0.282352 -0.6263 0.533766 0.266883 t -0.0238333333333334 0.005627 -4.2353 8.9e-05 4.5e-05 Multiple Linear Regression - Regression Statistics Multiple R 0.768394761499566 R-squared 0.590430509499974 Adjusted R-squared 0.491830446972191 F-TEST (value) 5.98813524416986 F-TEST (DF numerator) 13 F-TEST (DF denominator) 54 p-value 1.04081999896533e-06 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.442072140920209 Sum Squared Residuals 10.5531000000000 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 7.8 8.28083333333332 -0.480833333333324 2 7.6 8.2475 -0.6475 3 7.5 8.0475 -0.547500000000001 4 7.6 7.86416666666667 -0.264166666666666 5 7.5 7.66416666666667 -0.164166666666668 6 7.3 7.41416666666667 -0.114166666666667 7 7.6 7.76416666666667 -0.164166666666668 8 7.5 7.76416666666667 -0.264166666666667 9 7.6 7.778 -0.178 10 7.9 7.818 0.0819999999999997 11 7.9 7.778 0.122000000000000 12 8.1 7.931 0.169000000000000 13 8.2 7.99483333333334 0.205166666666664 14 8 7.9615 0.0385000000000004 15 7.5 7.7615 -0.2615 16 6.8 7.57816666666667 -0.778166666666667 17 6.5 7.37816666666667 -0.878166666666667 18 6.6 7.12816666666667 -0.528166666666667 19 7.6 7.47816666666667 0.121833333333333 20 8 7.47816666666667 0.521833333333333 21 8 7.492 0.508 22 7.7 7.532 0.168 23 7.5 7.492 0.00799999999999969 24 7.6 7.645 -0.0449999999999998 25 7.7 7.70883333333333 -0.0088333333333347 26 7.9 7.6755 0.2245 27 7.8 7.4755 0.3245 28 7.5 7.29216666666667 0.207833333333334 29 7.5 7.09216666666667 0.407833333333333 30 7.1 6.84216666666667 0.257833333333333 31 7.5 7.19216666666667 0.307833333333334 32 7.5 7.19216666666667 0.307833333333333 33 7.6 7.206 0.394 34 7.7 7.246 0.454 35 7.7 7.206 0.494 36 7.9 7.494 0.406000000000001 37 8.1 7.55783333333333 0.542166666666665 38 8.2 7.5245 0.675499999999999 39 8.2 7.3245 0.8755 40 8.1 7.14116666666667 0.958833333333333 41 7.9 6.94116666666667 0.958833333333334 42 7.3 6.69116666666667 0.608833333333333 43 6.9 7.04116666666667 -0.141166666666666 44 6.6 7.04116666666667 -0.441166666666667 45 6.7 7.055 -0.355 46 6.9 7.095 -0.195000000000000 47 7 7.055 -0.0550000000000002 48 7.1 7.208 -0.108000000000000 49 7.2 7.27183333333333 -0.0718333333333345 50 7.1 7.2385 -0.138500000000000 51 6.9 7.0385 -0.138499999999999 52 7 6.85516666666667 0.144833333333334 53 6.8 6.65516666666667 0.144833333333333 54 6.4 6.40516666666667 -0.00516666666666602 55 6.7 6.75516666666667 -0.0551666666666663 56 6.7 6.75516666666667 -0.0551666666666664 57 6.4 6.769 -0.368999999999999 58 6.3 6.809 -0.509 59 6.2 6.769 -0.569 60 6.5 6.922 -0.421999999999999 61 6.8 6.98583333333333 -0.185833333333335 62 6.8 6.9525 -0.152500000000000 63 6.5 6.7525 -0.252500000000000 64 6.3 6.56916666666667 -0.269166666666666 65 5.9 6.36916666666667 -0.469166666666666 66 5.9 6.11916666666667 -0.219166666666666 67 6.4 6.46916666666667 -0.069166666666666 68 6.4 6.46916666666667 -0.069166666666666

Charts produced by software:

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Parameters (Session):

par1 = 0 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 0 ; 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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Software written by Ed van Stee & Patrick Wessa

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