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-25 tov economische situatie met seisoen en zonder trend

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

Title produced by software: Multiple Regression

Date of computation: Thu, 15 Nov 2007 06:06:06 -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/15/t11951316583fqla84frjxuph3.htm/, Retrieved Thu, 15 Nov 2007 14:01:09 +0100

User-defined keywords:

Dataseries X:

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140 -1 132 -2 117 -2 114 -1 113 1 110 1 107 1 103 1 98 1 98 1 137 0 148 -1 147 -1 139 -1 130 -1 128 -1 127 -2 123 -2 118 -2 114 -1 108 -1 111 -1 151 -1 159 -1 158 -1 148 -1 138 0 137 0 136 1 133 1 126 1 120 1 114 -1 116 1 153 -1 162 1 161 0 149 -1 139 -1 135 -1 130 -1 127 -1 122 1 117 -1 112 -2 113 -2 149 -2 157 -1 157 -2 147 -1 137 -1 132 -1 125 -1 123 -1 117 -1 114 -1 111 -1 112 -1 144 0 150 -1 149 -1 134 1 123 1 116 -1 117 -1 111 0 105 -1 102 1 95 1 93 1 124 0 130 -1 124 -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 <25[t] = + 150.040609137056 -1.43908629441624eco[t] -3.47969543147209M1[t] -9.739847715736M2[t] -20.3333333333333M3[t] -24.2398477157360M4[t] -26.0934856175973M5[t] -29.3536379018613M6[t] -34.4471235194585M7[t] -38.3739424703892M8[t] -44.4268189509306M9[t] -43.1137901861252M10[t] -8M11[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) 150.040609137056 3.962288 37.8672 0 0 eco -1.43908629441624 1.174101 -1.2257 0.225104 0.112552 M1 -3.47969543147209 5.307729 -0.6556 0.514594 0.257297 M2 -9.739847715736 5.496581 -1.772 0.081475 0.040737 M3 -20.3333333333333 5.493097 -3.7016 0.000468 0.000234 M4 -24.2398477157360 5.496581 -4.41 4.4e-05 2.2e-05 M5 -26.0934856175973 5.496581 -4.7472 1.3e-05 7e-06 M6 -29.3536379018613 5.507021 -5.3302 2e-06 1e-06 M7 -34.4471235194585 5.524377 -6.2355 0 0 M8 -38.3739424703892 5.548584 -6.916 0 0 M9 -44.4268189509306 5.496581 -8.0826 0 0 M10 -43.1137901861252 5.524377 -7.8043 0 0 M11 -8 5.493097 -1.4564 0.150503 0.075251 Multiple Linear Regression - Regression Statistics Multiple R 0.869606485316494 R-squared 0.756215439304505 Adjusted R-squared 0.707458527165406 F-TEST (value) 15.509912464249 F-TEST (DF numerator) 12 F-TEST (DF denominator) 60 p-value 3.44169137633799e-14 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 9.51432225516791 Sum Squared Residuals 5431.339678511 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 140 148.000000000000 -8.00000000000028 2 132 143.178934010152 -11.1789340101523 3 117 132.585448392555 -15.5854483925550 4 114 127.239847715736 -13.2398477157361 5 113 122.508037225042 -9.50803722504226 6 110 119.247884940778 -9.24788494077836 7 107 114.154399323181 -7.15439932318104 8 103 110.227580372250 -7.22758037225039 9 98 104.174703891709 -6.17470389170896 10 98 105.487732656514 -7.48773265651439 11 137 142.040609137056 -5.04060913705584 12 148 151.479695431472 -3.47969543147208 13 147 148 -0.99999999999996 14 139 141.739847715736 -2.73984771573605 15 130 131.146362098139 -1.14636209813874 16 128 127.239847715736 0.760152284263968 17 127 126.825296108291 0.174703891708963 18 123 123.565143824027 -0.565143824027069 19 118 118.471658206430 -0.471658206429764 20 114 113.105752961083 0.894247038917088 21 108 107.052876480541 0.947123519458542 22 111 108.365905245347 2.63409475465314 23 151 143.479695431472 7.52030456852792 24 159 151.479695431472 7.52030456852793 25 158 148 10.0000000000000 26 148 141.739847715736 6.26015228426396 27 138 129.707275803722 8.2927241962775 28 137 125.800761421320 11.1992385786802 29 136 122.508037225042 13.4919627749577 30 133 119.247884940778 13.7521150592217 31 126 114.154399323181 11.8456006768189 32 120 110.227580372250 9.77241962774957 33 114 107.052876480541 6.94712351945854 34 116 105.487732656514 10.5122673434856 35 153 143.479695431472 9.52030456852792 36 162 148.601522842640 13.3984771573604 37 161 146.560913705584 14.4390862944163 38 149 141.739847715736 7.26015228426396 39 139 131.146362098139 7.85363790186126 40 135 127.239847715736 7.76015228426397 41 130 125.386209813875 4.61379018612521 42 127 122.126057529611 4.87394247038918 43 122 114.154399323181 7.84560067681895 44 117 113.105752961083 3.89424703891709 45 112 108.491962774958 3.50803722504232 46 113 109.804991539763 3.19500846023689 47 149 144.918781725888 4.08121827411169 48 157 151.479695431472 5.52030456852794 49 157 149.439086294416 7.5609137055838 50 147 141.739847715736 5.26015228426396 51 137 131.146362098139 5.85363790186126 52 132 127.239847715736 4.76015228426397 53 125 125.386209813875 -0.386209813874792 54 123 122.126057529611 0.873942470389178 55 117 117.032571912014 -0.0325719120135387 56 114 113.105752961083 0.894247038917088 57 111 107.052876480541 3.94712351945854 58 112 108.365905245347 3.63409475465314 59 144 142.040609137056 1.95939086294416 60 150 151.479695431472 -1.47969543147207 61 149 148 1.00000000000005 62 134 138.861675126904 -4.86167512690357 63 123 128.268189509306 -5.26818950930626 64 116 127.239847715736 -11.2398477157360 65 117 125.386209813875 -8.3862098138748 66 111 120.686971235195 -9.68697123519459 67 105 117.032571912014 -12.0325719120135 68 102 110.227580372250 -8.22758037225043 69 95 104.174703891709 -9.17470389170897 70 93 105.487732656514 -12.4877326565144 71 124 142.040609137056 -18.0406091370558 72 130 151.479695431472 -21.4796954314721 73 124 148 -24.0000000000000

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')

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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