Openstaande VDAB-vacatures

*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: Tue, 30 Nov 2010 10:09:41 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Nov/30/t1291111723gjjse2hxdfi6hjx.htm/, Retrieved Tue, 30 Nov 2010 11:08:56 +0100

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/2010/Nov/30/t1291111723gjjse2hxdfi6hjx.htm/}, year = {2010}, } @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 = {2010}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

27951 29781 32914 33488 35652 36488 35387 35676 34844 32447 31068 29010 29812 30951 32974 32936 34012 32946 31948 30599 27691 25073 23406 22248 22896 25317 26558 26471 27543 26198 24725 25005 23462 20780 19815 19761 21454 23899 24939 23580 24562 24696 23785 23812 21917 19713 19282 18788 21453 24482 27474 27264 27349 30632 29429 30084 26290 24379 23335 21346 21106 24514 28353 30805 31348 34556 33855 34787 32529 29998 29257 28155 30466 35704 39327 39351 42234 43630 43722 43121 37985 37135 34646 33026 35087 38846 42013 43908 42868 44423 44167 43636 44382 42142 43452 36912 42413 45344 44873 47510 49554 47369 45998 48140 48441 44928 40454 38661 37246 36843 36424 37594 38144 38737 34560 36080 33508 35462 33374 32110 35533 35532 37903 36763 40399 44164 44496 43110 43880

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 8 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 19301.6755555556 + 2240.75639730639M1[t] + 4454.02875420874M2[t] + 6371.21020202022M3[t] + 6777.39164983165M4[t] + 7917.84582491583M5[t] + 8710.93636363636M6[t] + 7509.39053872055M7[t] + 7557.39016835017M8[t] + 5687.29888888889M9[t] + 3467.63710437711M10[t] + 1939.01855218855M11[t] + 131.818552188552t + 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) 19301.6755555556 2068.547608 9.331 0 0 M1 2240.75639730639 2563.01167 0.8743 0.383779 0.19189 M2 4454.02875420874 2562.672873 1.738 0.084857 0.042429 M3 6371.21020202022 2562.409334 2.4864 0.014327 0.007164 M4 6777.39164983165 2562.221076 2.6451 0.009298 0.004649 M5 7917.84582491583 2562.108114 3.0904 0.002503 0.001252 M6 8710.93636363636 2562.070459 3.4 0.000925 0.000462 M7 7509.39053872055 2562.108114 2.9309 0.004071 0.002036 M8 7557.39016835017 2562.221076 2.9495 0.00385 0.001925 M9 5687.29888888889 2562.409334 2.2195 0.028397 0.014198 M10 3467.63710437711 2622.509873 1.3223 0.188683 0.094342 M11 1939.01855218855 2622.399508 0.7394 0.461154 0.230577 t 131.818552188552 13.890693 9.4897 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.71058290556023 R-squared 0.504928065674419 Adjusted R-squared 0.453713727640738 F-TEST (value) 9.85911533880132 F-TEST (DF numerator) 12 F-TEST (DF denominator) 116 p-value 4.90607554581857e-13 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 5863.78129990337 Sum Squared Residuals 3988536011.43919 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 27951 21674.2505050506 6276.7494949494 2 29781 24019.3414141414 5761.65858585858 3 32914 26068.3414141414 6845.65858585862 4 33488 26606.3414141414 6881.65858585857 5 35652 27878.6141414141 7773.38585858585 6 36488 28803.5232323233 7684.47676767675 7 35387 27733.7959595959 7653.20404040405 8 35676 27913.6141414142 7762.38585858584 9 34844 26175.3414141414 8668.65858585859 10 32447 24087.4981818182 8359.50181818182 11 31068 22690.6981818182 8377.30181818182 12 29010 20883.4981818182 8126.50181818182 13 29812 23256.0731313131 6555.92686868692 14 30951 25601.1640404040 5349.83595959596 15 32974 27650.1640404040 5323.83595959596 16 32936 28188.1640404040 4747.83595959597 17 34012 29460.4367676768 4551.56323232323 18 32946 30385.3458585859 2560.65414141414 19 31948 29315.6185858586 2632.38141414141 20 30599 29495.4367676768 1103.56323232324 21 27691 27757.1640404040 -66.1640404040355 22 25073 25669.3208080808 -596.320808080806 23 23406 24272.5208080808 -866.52080808081 24 22248 22465.3208080808 -217.320808080808 25 22896 24837.8957575757 -1941.89575757575 26 25317 27182.9866666667 -1865.98666666666 27 26558 29231.9866666667 -2673.98666666667 28 26471 29769.9866666667 -3298.98666666666 29 27543 31042.2593939394 -3499.25939393939 30 26198 31967.1684848485 -5769.16848484848 31 24725 30897.4412121212 -6172.44121212121 32 25005 31077.2593939394 -6072.25939393939 33 23462 29338.9866666667 -5876.98666666667 34 20780 27251.1434343434 -6471.14343434344 35 19815 25854.3434343434 -6039.34343434344 36 19761 24047.1434343434 -4286.14343434343 37 21454 26419.7183838384 -4965.71838383838 38 23899 28764.8092929293 -4865.80929292929 39 24939 30813.8092929293 -5874.8092929293 40 23580 31351.8092929293 -7771.80929292929 41 24562 32624.082020202 -8062.08202020202 42 24696 33548.9911111111 -8852.99111111111 43 23785 32479.2638383838 -8694.26383838384 44 23812 32659.082020202 -8847.08202020202 45 21917 30920.8092929293 -9003.80929292929 46 19713 28832.9660606061 -9119.96606060606 47 19282 27436.1660606061 -8154.16606060606 48 18788 25628.9660606061 -6840.96606060606 49 21453 28001.541010101 -6548.541010101 50 24482 30346.6319191919 -5864.63191919192 51 27474 32395.6319191919 -4921.63191919192 52 27264 32933.6319191919 -5669.63191919191 53 27349 34205.9046464646 -6856.90464646465 54 30632 35130.8137373737 -4498.81373737374 55 29429 34061.0864646465 -4632.08646464647 56 30084 34240.9046464646 -4156.90464646464 57 26290 32502.6319191919 -6212.63191919192 58 24379 30414.7886868687 -6035.78868686869 59 23335 29017.9886868687 -5682.98868686869 60 21346 27210.7886868687 -5864.78868686869 61 21106 29583.3636363636 -8477.36363636363 62 24514 31928.4545454545 -7414.45454545454 63 28353 33977.4545454546 -5624.45454545455 64 30805 34515.4545454545 -3710.45454545454 65 31348 35787.7272727273 -4439.72727272727 66 34556 36712.6363636364 -2156.63636363637 67 33855 35642.9090909091 -1787.90909090909 68 34787 35822.7272727273 -1035.72727272727 69 32529 34084.4545454545 -1555.45454545454 70 29998 31996.6113131313 -1998.61131313131 71 29257 30599.8113131313 -1342.81131313131 72 28155 28792.6113131313 -637.611313131313 73 30466 31165.1862626263 -699.186262626257 74 35704 33510.2771717172 2193.72282828283 75 39327 35559.2771717172 3767.72282828282 76 39351 36097.2771717172 3253.72282828283 77 42234 37369.5498989899 4864.4501010101 78 43630 38294.458989899 5335.54101010101 79 43722 37224.7317171717 6497.26828282828 80 43121 37404.5498989899 5716.4501010101 81 37985 35666.2771717172 2318.72282828283 82 37135 33578.4339393939 3556.56606060606 83 34646 32181.6339393939 2464.36606060606 84 33026 30374.4339393939 2651.56606060606 85 35087 32747.0088888889 2339.99111111112 86 38846 35092.0997979798 3753.9002020202 87 42013 37141.0997979798 4871.9002020202 88 43908 37679.0997979798 6228.9002020202 89 42868 38951.3725252525 3916.62747474747 90 44423 39876.2816161616 4546.71838383838 91 44167 38806.5543434343 5360.44565656565 92 43636 38986.3725252525 4649.62747474748 93 44382 37248.0997979798 7133.9002020202 94 42142 35160.2565656566 6981.74343434343 95 43452 33763.4565656566 9688.54343434343 96 36912 31956.2565656566 4955.74343434343 97 42413 34328.8315151515 8084.16848484849 98 45344 36673.9224242424 8670.07757575758 99 44873 38722.9224242424 6150.07757575757 100 47510 39260.9224242424 8249.07757575758 101 49554 40533.1951515152 9020.80484848485 102 47369 41458.1042424242 5910.89575757576 103 45998 40388.376969697 5609.62303030303 104 48140 40568.1951515152 7571.80484848485 105 48441 38829.9224242424 9611.07757575757 106 44928 36742.0791919192 8185.9208080808 107 40454 35345.2791919192 5108.72080808081 108 38661 33538.0791919192 5122.92080808081 109 37246 35910.6541414141 1335.34585858586 110 36843 38255.7450505051 -1412.74505050505 111 36424 40304.7450505051 -3880.74505050506 112 37594 40842.745050505 -3248.74505050505 113 38144 42115.0177777778 -3971.01777777778 114 38737 43039.9268686869 -4302.92686868687 115 34560 41970.1995959596 -7410.1995959596 116 36080 42150.0177777778 -6070.01777777778 117 33508 40411.7450505051 -6903.74505050505 118 35462 38323.9018181818 -2861.90181818182 119 33374 36927.1018181818 -3553.10181818182 120 32110 35119.9018181818 -3009.90181818182 121 35533 37492.4767676768 -1959.47676767676 122 35532 39837.5676767677 -4305.56767676768 123 37903 41886.5676767677 -3983.56767676769 124 36763 42424.5676767677 -5661.56767676768 125 40399 43696.8404040404 -3297.84040404041 126 44164 44621.7494949495 -457.7494949495 127 44496 43552.0222222222 943.97777777777 128 43110 43731.8404040404 -621.840404040406 129 43880 41993.5676767677 1886.43232323232

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/30/t1291111723gjjse2hxdfi6hjx/14jnv1291111772.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291111723gjjse2hxdfi6hjx/14jnv1291111772.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291111723gjjse2hxdfi6hjx/2fbmg1291111772.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291111723gjjse2hxdfi6hjx/2fbmg1291111772.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291111723gjjse2hxdfi6hjx/3fbmg1291111772.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291111723gjjse2hxdfi6hjx/3fbmg1291111772.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291111723gjjse2hxdfi6hjx/4fbmg1291111772.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291111723gjjse2hxdfi6hjx/4fbmg1291111772.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291111723gjjse2hxdfi6hjx/5fbmg1291111772.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291111723gjjse2hxdfi6hjx/5fbmg1291111772.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291111723gjjse2hxdfi6hjx/6qk3j1291111772.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291111723gjjse2hxdfi6hjx/6qk3j1291111772.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291111723gjjse2hxdfi6hjx/7jblm1291111772.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291111723gjjse2hxdfi6hjx/7jblm1291111772.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291111723gjjse2hxdfi6hjx/8jblm1291111772.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291111723gjjse2hxdfi6hjx/8jblm1291111772.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291111723gjjse2hxdfi6hjx/9jblm1291111772.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291111723gjjse2hxdfi6hjx/9jblm1291111772.ps (open in new window)

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')

Copyright

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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FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

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