9/11 en prijs diesel test 2

*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: Sun, 23 Nov 2008 13:07:48 -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/23/t1227470924pytkmqgx1m8l54p.htm/, Retrieved Sun, 23 Nov 2008 20:08:52 +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/23/t1227470924pytkmqgx1m8l54p.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}, }

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Original text written by user:

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Dataseries X:

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0.84 0 0.76 0 0.77 0 0.76 0 0.77 0 0.78 0 0.79 0 0.78 0 0.76 0 0.78 1 0.76 1 0.74 1 0.73 1 0.72 1 0.71 1 0.73 1 0.75 1 0.75 1 0.72 1 0.72 1 0.72 1 0.74 1 0.78 1 0.74 1 0.74 1 0.75 1 0.78 1 0.81 1 0.75 1 0.7 1 0.71 1 0.71 1 0.73 1 0.74 1 0.74 1 0.75 1 0.74 1 0.74 1 0.73 1 0.76 1 0.8 1 0.83 1 0.81 1 0.83 1 0.88 1 0.89 1 0.93 1 0.91 1 0.9 1 0.86 1 0.88 1 0.93 1 0.98 1 0.97 1 1.03 1 1.06 1 1.06 1 1.09 1 1.04 1 1 1 1.04 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 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation y[t] = + 0.76161379310345 -0.160982758620690x[t] + 0.0084152298850578M1[t] -0.0310385057471264M2[t] -0.0293543103448277M3[t] -0.0116701149425288M4[t] -0.00598591954022995M5[t] -0.0163017241379312M6[t] -0.0166175287356323M7[t] -0.0149333333333335M8[t] -0.0112491379310346M9[t] + 0.0326316091954023M10[t] + 0.0283158045977011M11[t] + 0.00631580459770114t + 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) 0.76161379310345 0.036716 20.7436 0 0 x -0.160982758620690 0.029493 -5.4584 2e-06 1e-06 M1 0.0084152298850578 0.038289 0.2198 0.826992 0.413496 M2 -0.0310385057471264 0.040121 -0.7736 0.443031 0.221515 M3 -0.0293543103448277 0.040092 -0.7322 0.467704 0.233852 M4 -0.0116701149425288 0.040072 -0.2912 0.77216 0.38608 M5 -0.00598591954022995 0.040061 -0.1494 0.88186 0.44093 M6 -0.0163017241379312 0.040058 -0.407 0.685887 0.342943 M7 -0.0166175287356323 0.040063 -0.4148 0.680187 0.340093 M8 -0.0149333333333335 0.040077 -0.3726 0.71111 0.355555 M9 -0.0112491379310346 0.0401 -0.2805 0.780302 0.390151 M10 0.0326316091954023 0.039801 0.8199 0.416425 0.208213 M11 0.0283158045977011 0.039788 0.7117 0.480186 0.240093 t 0.00631580459770114 0.000585 10.789 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.855163567900384 R-squared 0.731304727864114 Adjusted R-squared 0.656984758975465 F-TEST (value) 9.83994932720975 F-TEST (DF numerator) 13 F-TEST (DF denominator) 47 p-value 1.83569648370963e-09 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.0629031210770387 Sum Squared Residuals 0.185969724137932 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 0.84 0.776344827586205 0.0636551724137951 2 0.76 0.743206896551724 0.0167931034482763 3 0.77 0.751206896551724 0.0187931034482756 4 0.76 0.775206896551724 -0.0152068965517243 5 0.77 0.787206896551724 -0.0172068965517245 6 0.78 0.783206896551724 -0.00320689655172441 7 0.79 0.789206896551724 0.000793103448275535 8 0.78 0.797206896551724 -0.0172068965517244 9 0.76 0.807206896551725 -0.0472068965517245 10 0.78 0.696420689655172 0.0835793103448276 11 0.76 0.698420689655172 0.0615793103448276 12 0.74 0.676420689655172 0.0635793103448275 13 0.73 0.691151724137931 0.0388482758620685 14 0.72 0.658013793103448 0.0619862068965519 15 0.71 0.666013793103448 0.0439862068965518 16 0.73 0.690013793103448 0.0399862068965517 17 0.75 0.702013793103448 0.0479862068965518 18 0.75 0.698013793103448 0.0519862068965517 19 0.72 0.704013793103448 0.0159862068965518 20 0.72 0.712013793103448 0.0079862068965517 21 0.72 0.722013793103448 -0.00201379310344828 22 0.74 0.772210344827586 -0.0322103448275863 23 0.78 0.774210344827586 0.00578965517241375 24 0.74 0.752210344827586 -0.0122103448275863 25 0.74 0.766941379310345 -0.0269413793103453 26 0.75 0.733803448275862 0.0161965517241377 27 0.78 0.741803448275862 0.038196551724138 28 0.81 0.765803448275862 0.044196551724138 29 0.75 0.777803448275862 -0.027803448275862 30 0.7 0.773803448275862 -0.073803448275862 31 0.71 0.779803448275862 -0.069803448275862 32 0.71 0.787803448275862 -0.077803448275862 33 0.73 0.797803448275862 -0.067803448275862 34 0.74 0.848 -0.108 35 0.74 0.85 -0.11 36 0.75 0.828 -0.078 37 0.74 0.842731034482759 -0.102731034482759 38 0.74 0.809593103448276 -0.069593103448276 39 0.73 0.817593103448276 -0.0875931034482758 40 0.76 0.841593103448276 -0.0815931034482758 41 0.8 0.853593103448276 -0.0535931034482758 42 0.83 0.849593103448276 -0.0195931034482758 43 0.81 0.855593103448276 -0.0455931034482757 44 0.83 0.863593103448276 -0.0335931034482758 45 0.88 0.873593103448276 0.00640689655172419 46 0.89 0.923789655172414 -0.0337896551724138 47 0.93 0.925789655172414 0.00421034482758626 48 0.91 0.903789655172414 0.00621034482758623 49 0.9 0.918520689655173 -0.0185206896551727 50 0.86 0.88538275862069 -0.0253827586206899 51 0.88 0.89338275862069 -0.0133827586206895 52 0.93 0.91738275862069 0.0126172413793105 53 0.98 0.92938275862069 0.0506172413793105 54 0.97 0.92538275862069 0.0446172413793105 55 1.03 0.93138275862069 0.0986172413793105 56 1.06 0.93938275862069 0.120617241379311 57 1.06 0.94938275862069 0.110617241379311 58 1.09 0.999579310344827 0.0904206896551725 59 1.04 1.00157931034483 0.0384206896551726 60 1 0.979579310344827 0.0204206896551725 61 1.04 0.994310344827587 0.0456896551724135

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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Software written by Ed van Stee & Patrick Wessa

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