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paper berekening met lineaire trend

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

Title produced by software: Multiple Regression

Date of computation: Wed, 21 Nov 2007 03:59:13 -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/21/t1195642310dzpyulpp9ncx8tk.htm/, Retrieved Wed, 21 Nov 2007 11:52:20 +0100

User-defined keywords:

Dataseries X:

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98,6 0 98 0 106,8 0 96,6 0 100,1 0 107,7 0 91,5 0 97,8 0 107,4 0 117,5 0 105,6 0 97,4 0 99,5 0 98 0 104,3 0 100,6 0 101,1 0 103,9 0 96,9 0 95,5 0 108,4 0 117 0 103,8 0 100,8 0 110,6 0 104 0 112,6 0 107,3 0 98,9 0 109,8 0 104,9 0 102,2 0 123,9 0 124,9 0 112,7 0 121,9 0 100,6 0 104,3 1 120,4 1 107,5 1 102,9 1 125,6 1 107,5 1 108,8 1 128,4 1 121,1 1 119,5 1 128,7 1 108,7 1 105,5 1 119,8 1 111,3 1 110,6 1 120,1 1 97,5 1 107,7 1 127,3 1 117,2 1 119,8 1 116,2 1 111 1 112,4 1 130,6 1 109,1 1 118,8 1 123,9 1 101,6 1 112,8 1 128 1 129,6 1 125,8 1 119,5 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 x[t] = + 102.945194940055 + 1.94092325120366y[t] -6.26354982850302M1[t] -7.96245791245792M2[t] + 3.84545454545455M3[t] -6.746632996633M4[t] -6.98872053872053M5[t] + 2.53585858585859M6[t] -12.8895622895623M7[t] -8.98164983164983M8[t] + 7.20959595959596M9[t] + 7.61750841750841M10[t] + 0.69208754208754M11[t] + 0.242087542087541t + 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) 102.945194940055 2.510907 40.9992 0 0 y 1.94092325120366 2.39492 0.8104 0.421004 0.210502 M1 -6.26354982850302 2.856369 -2.1928 0.032344 0.016172 M2 -7.96245791245792 2.893955 -2.7514 0.007905 0.003952 M3 3.84545454545455 2.88283 1.3339 0.187446 0.093723 M4 -6.746632996633 2.87284 -2.3484 0.022284 0.011142 M5 -6.98872053872053 2.863996 -2.4402 0.017756 0.008878 M6 2.53585858585859 2.856309 0.8878 0.37831 0.189155 M7 -12.8895622895623 2.849788 -4.523 3.1e-05 1.5e-05 M8 -8.98164983164983 2.844442 -3.1576 0.002525 0.001262 M9 7.20959595959596 2.840277 2.5383 0.013845 0.006923 M10 7.61750841750841 2.837298 2.6848 0.009447 0.004723 M11 0.69208754208754 2.835509 0.2441 0.808031 0.404016 t 0.242087542087541 0.058159 4.1625 0.000106 5.3e-05 Multiple Linear Regression - Regression Statistics Multiple R 0.899092095846177 R-squared 0.808366596813071 Adjusted R-squared 0.765414282305656 F-TEST (value) 18.8200940061919 F-TEST (DF numerator) 13 F-TEST (DF denominator) 58 p-value 3.33066907387547e-16 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4.91021278410465 Sum Squared Residuals 1398.39099594072 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 98.6 96.9237326536388 1.67626734636123 2 98 95.466912111772 2.53308788822806 3 106.8 107.516912111772 -0.716912111771939 4 96.6 97.166912111772 -0.56691211177194 5 100.1 97.166912111772 2.93308788822804 6 107.7 106.933578778439 0.766421221561388 7 91.5 91.7502454451053 -0.250245445105314 8 97.8 95.9002454451053 1.89975455489471 9 107.4 112.333578778439 -4.93357877843861 10 117.5 112.983578778439 4.51642122156138 11 105.6 106.300245445105 -0.700245445105284 12 97.4 105.850245445105 -8.45024544510527 13 99.5 99.8287831586898 -0.328783158689799 14 98 98.3719626168224 -0.371962616822434 15 104.3 110.421962616822 -6.12196261682244 16 100.6 100.071962616822 0.528037383177562 17 101.1 100.071962616822 1.02803738317756 18 103.9 109.838629283489 -5.93862928348909 19 96.9 94.6552959501558 2.24470404984424 20 95.5 98.8052959501558 -3.30529595015577 21 108.4 115.238629283489 -6.8386292834891 22 117 115.888629283489 1.11137071651090 23 103.8 109.205295950156 -5.40529595015577 24 100.8 108.755295950156 -7.95529595015577 25 110.6 102.733833663740 7.8661663362597 26 104 101.277013121873 2.72298687812708 27 112.6 113.327013121873 -0.727013121872929 28 107.3 102.977013121873 4.32298687812707 29 98.9 102.977013121873 -4.07701312187292 30 109.8 112.743679788540 -2.94367978853959 31 104.9 97.5603464552063 7.33965354479375 32 102.2 101.710346455206 0.489653544793747 33 123.9 118.143679788540 5.75632021146041 34 124.9 118.793679788540 6.10632021146041 35 112.7 112.110346455206 0.589653544793748 36 121.9 111.660346455206 10.2396535447937 37 100.6 105.638884168791 -5.03888416879078 38 104.3 106.122986878127 -1.82298687812708 39 120.4 118.172986878127 2.22701312187293 40 107.5 107.822986878127 -0.322986878127074 41 102.9 107.822986878127 -4.92298687812707 42 125.6 117.589653544794 8.01034645520626 43 107.5 102.406320211460 5.0936797885396 44 108.8 106.556320211460 2.24367978853959 45 128.4 122.989653544794 5.41034645520626 46 121.1 123.639653544794 -2.53965354479375 47 119.5 116.956320211460 2.54367978853959 48 128.7 116.506320211460 12.1936797885396 49 108.7 110.484857925045 -1.78485792504493 50 105.5 109.028037383178 -3.52803738317757 51 119.8 121.078037383178 -1.27803738317757 52 111.3 110.728037383178 0.571962616822431 53 110.6 110.728037383178 -0.12803738317757 54 120.1 120.494704049844 -0.394704049844239 55 97.5 105.311370716511 -7.8113707165109 56 107.7 109.461370716511 -1.76137071651089 57 127.3 125.894704049844 1.40529595015576 58 117.2 126.544704049844 -9.34470404984422 59 119.8 119.861370716511 -0.0613707165109012 60 116.2 119.411370716511 -3.21137071651090 61 111 113.389908430095 -2.38990843009542 62 112.4 111.933087888228 0.466912111771949 63 130.6 123.983087888228 6.61691211177194 64 109.1 113.633087888228 -4.53308788822806 65 118.8 113.633087888228 5.16691211177195 66 123.9 123.399754554895 0.500245445105281 67 101.6 108.216421221561 -6.61642122156138 68 112.8 112.366421221561 0.433578778438611 69 128 128.799754554895 -0.799754554894722 70 129.6 129.449754554895 0.150245445105276 71 125.8 122.766421221561 3.03357877843861 72 119.5 122.316421221561 -2.81642122156139

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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