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multiple regression aardolie-seizoenaliteit en trend

R Software Module: rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Thu, 29 Nov 2007 02:58:17 -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/29/t1196329717z0i06biirca5313.htm/, Retrieved Thu, 29 Nov 2007 10:48:47 +0100

User-defined keywords:

Dataseries X:

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90.8 0 96.4 0 90 0 92.1 0 97.2 0 95.1 0 88.5 0 91 0 90.5 0 75 0 66.3 0 66 0 68.4 0 70.6 0 83.9 0 90.1 0 90.6 0 87.1 0 90.8 0 94.1 0 99.8 0 96.8 0 87 0 96.3 0 107.1 0 115.2 0 106.1 1 89.5 1 91.3 1 97.6 1 100.7 1 104.6 1 94.7 1 101.8 1 102.5 1 105.3 1 110.3 1 109.8 1 117.3 1 118.8 1 131.3 1 125.9 1 133.1 1 147 1 145.8 1 164.4 1 149.8 1 137.7 1 151.7 1 156.8 1 180 1 180.4 1 170.4 1 191.6 1 199.5 1 218.2 1 217.5 1 205 1 194 1 199.3 1 219.3 1 211.1 1 215.2 1 240.2 1 242.2 1 240.7 1 255.4 1 253 1 218.2 1 203.7 1 205.6 1 215.6 1

Text written by user:

paper

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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Aardolie[t] = + 26.6413265306123 -44.3911564625851Irakoorlog[t] + 17.0772014361301M1[t] + 15.8021352985639M2[t] + 25.3089285714286M3[t] + 25.0838624338624M4[t] + 23.7421296296296M5[t] + 22.9170634920635M6[t] + 24.5919973544973M7[t] + 27.9169312169312M8[t] + 17.6918650793651M9[t] + 11.0667989417990M10[t] + 0.825066137566143M11[t] + 3.32506613756614t + 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) 26.6413265306123 9.260839 2.8768 0.005613 0.002807 Irakoorlog -44.3911564625851 8.731203 -5.0842 4e-06 2e-06 M1 17.0772014361301 11.232989 1.5203 0.133876 0.066938 M2 15.8021352985639 11.216482 1.4088 0.164224 0.082112 M3 25.3089285714286 11.307104 2.2383 0.029054 0.014527 M4 25.0838624338624 11.276108 2.2245 0.03002 0.01501 M5 23.7421296296296 11.248688 2.1107 0.039124 0.019562 M6 22.9170634920635 11.22487 2.0416 0.045745 0.022873 M7 24.5919973544973 11.204676 2.1948 0.032195 0.016098 M8 27.9169312169312 11.188127 2.4952 0.015455 0.007728 M9 17.6918650793651 11.175238 1.5831 0.11883 0.059415 M10 11.0667989417990 11.166023 0.9911 0.325747 0.162873 M11 0.825066137566143 11.16049 0.0739 0.941323 0.470661 t 3.32506613756614 0.202918 16.3863 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.949111791224152 R-squared 0.900813192240718 Adjusted R-squared 0.878581666363637 F-TEST (value) 40.5196295216699 F-TEST (DF numerator) 13 F-TEST (DF denominator) 58 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 19.3273410810022 Sum Squared Residuals 21665.6745691610 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 90.8 47.0435941043083 43.7564058956917 2 96.4 49.0935941043081 47.3064058956919 3 90 61.9254535147394 28.0745464852606 4 92.1 65.0254535147392 27.0745464852608 5 97.2 67.0087868480726 30.1912131519274 6 95.1 69.5087868480725 25.5912131519275 7 88.5 74.5087868480726 13.9912131519274 8 91 81.1587868480726 9.84121315192742 9 90.5 74.2587868480725 16.2412131519275 10 75 70.9587868480725 4.04121315192745 11 66.3 64.042120181406 2.25787981859408 12 66 66.5421201814059 -0.542120181405874 13 68.4 86.944387755102 -18.5443877551021 14 70.6 88.9943877551019 -18.3943877551019 15 83.9 101.826247165533 -17.9262471655328 16 90.1 104.926247165533 -14.8262471655329 17 90.6 106.909580498866 -16.3095804988662 18 87.1 109.409580498866 -22.3095804988662 19 90.8 114.409580498866 -23.6095804988662 20 94.1 121.059580498866 -26.9595804988662 21 99.8 114.159580498866 -14.3595804988662 22 96.8 110.859580498866 -14.0595804988662 23 87 103.942913832200 -16.9429138321995 24 96.3 106.442913832200 -10.1429138321995 25 107.1 126.845181405896 -19.7451814058957 26 115.2 128.895181405896 -13.6951814058957 27 106.1 97.3358843537415 8.76411564625847 28 89.5 100.435884353742 -10.9358843537415 29 91.3 102.419217687075 -11.1192176870749 30 97.6 104.919217687075 -7.3192176870749 31 100.7 109.919217687075 -9.21921768707487 32 104.6 116.569217687075 -11.9692176870749 33 94.7 109.669217687075 -14.9692176870749 34 101.8 106.369217687075 -4.56921768707488 35 102.5 99.4525510204082 3.04744897959180 36 105.3 101.952551020408 3.34744897959183 37 110.3 122.354818594104 -12.0548185941044 38 109.8 124.404818594104 -14.6048185941044 39 117.3 137.236678004535 -19.9366780045351 40 118.8 140.336678004535 -21.5366780045352 41 131.3 142.320011337868 -11.0200113378685 42 125.9 144.820011337868 -18.9200113378685 43 133.1 149.820011337868 -16.7200113378685 44 147 156.470011337868 -9.47001133786849 45 145.8 149.570011337868 -3.77001133786848 46 164.4 146.270011337868 18.1299886621315 47 149.8 139.353344671202 10.4466553287982 48 137.7 141.853344671202 -4.15334467120182 49 151.7 162.255612244898 -10.5556122448980 50 156.8 164.305612244898 -7.50561224489802 51 180 177.137471655329 2.86252834467124 52 180.4 180.237471655329 0.162528344671212 53 170.4 182.220804988662 -11.8208049886621 54 191.6 184.720804988662 6.87919501133787 55 199.5 189.720804988662 9.77919501133788 56 218.2 196.370804988662 21.8291950113379 57 217.5 189.470804988662 28.0291950113379 58 205 186.170804988662 18.8291950113379 59 194 179.254138321995 14.7458616780046 60 199.3 181.754138321995 17.5458616780046 61 219.3 202.156405895692 17.1435941043084 62 211.1 204.206405895692 6.89359410430833 63 215.2 217.038265306122 -1.83826530612242 64 240.2 220.138265306122 20.0617346938776 65 242.2 222.121598639456 20.0784013605442 66 240.7 224.621598639456 16.0784013605442 67 255.4 229.621598639456 25.7784013605442 68 253 236.271598639456 16.7284013605443 69 218.2 229.371598639456 -11.1715986394558 70 203.7 226.071598639456 -22.3715986394558 71 205.6 219.154931972789 -13.5549319727891 72 215.6 221.654931972789 -6.05493197278908

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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