Niet fixed en niet linear

*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 11:26:22 -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/t1227551226fjqinimcd35nljb.htm/, Retrieved Mon, 24 Nov 2008 18:27:06 +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/t1227551226fjqinimcd35nljb.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:

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97.3 0 101 0 113.2 0 101 0 105.7 0 113.9 0 86.4 0 96.5 0 103.3 0 114.9 0 105.8 0 94.2 0 98.4 0 99.4 0 108.8 0 112.6 0 104.4 0 112.2 0 81.1 0 97.1 0 112.6 0 113.8 0 107.8 0 103.2 0 103.3 0 101.2 0 107.7 0 110.4 0 101.9 0 115.9 0 89.9 0 88.6 0 117.2 0 123.9 0 100 0 103.6 0 94.1 0 98.7 0 119.5 0 112.7 0 104.4 0 124.7 0 89.1 0 97 0 121.6 0 118.8 0 114 0 111.5 0 97.2 0 102.5 0 113.4 0 109.8 0 104.9 0 126.1 0 80 0 96.8 0 117.2 1 112.3 1 117.3 1 111.1 1 102.2 1 104.3 1 122.9 1 107.6 1 121.3 1 131.5 1 89 1 104.4 1 128.9 1 135.9 1 133.3 1 121.3 1 120.5 1 120.4 1 137.9 1 126.1 1 133.2 1 146.6 1 103.4 1 117.2 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 4 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation y[t] = + 105.089285714286 + 14.3190476190476x[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) 105.089285714286 1.537767 68.3389 0 0 x 14.3190476190476 2.807566 5.1002 2e-06 1e-06 Multiple Linear Regression - Regression Statistics Multiple R 0.500084181866704 R-squared 0.250084188953291 Adjusted R-squared 0.240469883683461 F-TEST (value) 26.0116755121218 F-TEST (DF numerator) 1 F-TEST (DF denominator) 78 p-value 2.32240418229779e-06 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 11.5075961003925 Sum Squared Residuals 10329.1319047619 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 97.3 105.089285714286 -7.78928571428579 2 101 105.089285714286 -4.08928571428572 3 113.2 105.089285714286 8.11071428571429 4 101 105.089285714286 -4.08928571428571 5 105.7 105.089285714286 0.61071428571429 6 113.9 105.089285714286 8.8107142857143 7 86.4 105.089285714286 -18.6892857142857 8 96.5 105.089285714286 -8.58928571428571 9 103.3 105.089285714286 -1.78928571428572 10 114.9 105.089285714286 9.8107142857143 11 105.8 105.089285714286 0.710714285714284 12 94.2 105.089285714286 -10.8892857142857 13 98.4 105.089285714286 -6.68928571428571 14 99.4 105.089285714286 -5.68928571428571 15 108.8 105.089285714286 3.71071428571428 16 112.6 105.089285714286 7.51071428571428 17 104.4 105.089285714286 -0.689285714285708 18 112.2 105.089285714286 7.11071428571429 19 81.1 105.089285714286 -23.9892857142857 20 97.1 105.089285714286 -7.98928571428572 21 112.6 105.089285714286 7.51071428571428 22 113.8 105.089285714286 8.71071428571428 23 107.8 105.089285714286 2.71071428571428 24 103.2 105.089285714286 -1.88928571428571 25 103.3 105.089285714286 -1.78928571428572 26 101.2 105.089285714286 -3.88928571428571 27 107.7 105.089285714286 2.61071428571429 28 110.4 105.089285714286 5.31071428571429 29 101.9 105.089285714286 -3.18928571428571 30 115.9 105.089285714286 10.8107142857143 31 89.9 105.089285714286 -15.1892857142857 32 88.6 105.089285714286 -16.4892857142857 33 117.2 105.089285714286 12.1107142857143 34 123.9 105.089285714286 18.8107142857143 35 100 105.089285714286 -5.08928571428571 36 103.6 105.089285714286 -1.48928571428572 37 94.1 105.089285714286 -10.9892857142857 38 98.7 105.089285714286 -6.38928571428571 39 119.5 105.089285714286 14.4107142857143 40 112.7 105.089285714286 7.61071428571429 41 104.4 105.089285714286 -0.689285714285708 42 124.7 105.089285714286 19.6107142857143 43 89.1 105.089285714286 -15.9892857142857 44 97 105.089285714286 -8.08928571428571 45 121.6 105.089285714286 16.5107142857143 46 118.8 105.089285714286 13.7107142857143 47 114 105.089285714286 8.91071428571429 48 111.5 105.089285714286 6.41071428571429 49 97.2 105.089285714286 -7.88928571428571 50 102.5 105.089285714286 -2.58928571428571 51 113.4 105.089285714286 8.3107142857143 52 109.8 105.089285714286 4.71071428571428 53 104.9 105.089285714286 -0.189285714285708 54 126.1 105.089285714286 21.0107142857143 55 80 105.089285714286 -25.0892857142857 56 96.8 105.089285714286 -8.28928571428571 57 117.2 119.408333333333 -2.20833333333333 58 112.3 119.408333333333 -7.10833333333334 59 117.3 119.408333333333 -2.10833333333334 60 111.1 119.408333333333 -8.30833333333334 61 102.2 119.408333333333 -17.2083333333333 62 104.3 119.408333333333 -15.1083333333333 63 122.9 119.408333333333 3.49166666666667 64 107.6 119.408333333333 -11.8083333333333 65 121.3 119.408333333333 1.89166666666666 66 131.5 119.408333333333 12.0916666666667 67 89 119.408333333333 -30.4083333333333 68 104.4 119.408333333333 -15.0083333333333 69 128.9 119.408333333333 9.49166666666667 70 135.9 119.408333333333 16.4916666666667 71 133.3 119.408333333333 13.8916666666667 72 121.3 119.408333333333 1.89166666666666 73 120.5 119.408333333333 1.09166666666667 74 120.4 119.408333333333 0.991666666666673 75 137.9 119.408333333333 18.4916666666667 76 126.1 119.408333333333 6.69166666666666 77 133.2 119.408333333333 13.7916666666667 78 146.6 119.408333333333 27.1916666666667 79 103.4 119.408333333333 -16.0083333333333 80 117.2 119.408333333333 -2.20833333333333

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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Software written by Ed van Stee & Patrick Wessa

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