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multiple regression (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 08:42:40 -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/t1195141023b8e06nn5g4zxywl.htm/, Retrieved Thu, 15 Nov 2007 16:37:18 +0100

User-defined keywords:

W9Q3G7

Dataseries X:

» Textbox « » Textfile « » CSV «

140 1 132 0 117 0 114 1 113 1 110 1 107 0 103 0 98 0 98 1 137 1 148 0 147 0 139 1 130 0 128 1 127 1 123 1 118 0 114 1 108 0 111 1 151 1 159 1 158 0 148 0 138 0 137 1 136 1 133 1 126 1 120 0 114 0 116 1 153 1 162 1 161 1 149 1 139 0 135 1 130 1 127 1 122 0 117 0 112 0 113 1 149 1 157 1 157 0 147 0 137 0 132 1 125 1 123 0 117 0 114 0 111 1 112 0 144 1 150 1 149 0 134 0 123 0 116 0 117 1 111 0 105 0 102 0 95 0 93 0 124 1 130 1 124 0

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 Y[t] = + 146.931317512971 + 5.83579994896655X[t] + 0.101213765254304M1[t] -6.77126291530474M2[t] -15.6404133100038M3[t] -24.1513303118304M4[t] -27.4383806810127M5[t] -28.9741977423784M6[t] -31.3707148122497M7[t] -35.5184651899375M8[t] -40.832882234292M9[t] -42.8985325864632M10[t] -8.99154961380658M11[t] -0.0189162889788047t + 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) 146.931317512971 5.488206 26.7722 0 0 X 5.83579994896655 3.148062 1.8538 0.068773 0.034386 M1 0.101213765254304 5.528352 0.0183 0.985455 0.492727 M2 -6.77126291530474 5.709779 -1.1859 0.240413 0.120207 M3 -15.6404133100038 6.097814 -2.5649 0.012883 0.006442 M4 -24.1513303118304 5.435809 -4.443 4e-05 2e-05 M5 -27.4383806810127 5.446938 -5.0374 5e-06 2e-06 M6 -28.9741977423784 5.461967 -5.3047 2e-06 1e-06 M7 -31.3707148122497 5.843621 -5.3684 1e-06 1e-06 M8 -35.5184651899375 5.835969 -6.0861 0 0 M9 -40.832882234292 5.82882 -7.0053 0 0 M10 -42.8985325864632 5.44746 -7.875 0 0 M11 -8.99154961380658 5.442336 -1.6521 0.103817 0.051908 t -0.0189162889788047 0.054725 -0.3457 0.730827 0.365414 Multiple Linear Regression - Regression Statistics Multiple R 0.875657079533982 R-squared 0.766775320937982 Adjusted R-squared 0.715386832331097 F-TEST (value) 14.9211494971900 F-TEST (DF numerator) 13 F-TEST (DF denominator) 59 p-value 4.08562073062058e-14 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 9.38451061286577 Sum Squared Residuals 5196.07332713642 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 140 152.849414938213 -12.8494149382133 2 132 140.122222019709 -8.12222201970856 3 117 131.234155336031 -14.2341553360308 4 114 128.540121994192 -14.5401219941919 5 113 125.234155336031 -12.2341553360308 6 110 123.679421985686 -13.6794219856863 7 107 115.428188677870 -8.42818867786978 8 103 111.261522011203 -8.26152201120301 9 98 105.928188677870 -7.92818867786968 10 98 109.679421985686 -11.6794219856864 11 137 143.567488669364 -6.56748866936416 12 148 146.704322045225 1.29567795477467 13 147 146.786619521501 0.213380478499176 14 139 145.731026500930 -6.73102650092954 15 130 131.007159868285 -1.00715986828514 16 128 128.313126526446 -0.313126526446249 17 127 125.007159868285 1.99284013171485 18 123 123.452426517941 -0.45242651794067 19 118 115.201193210124 2.79880678987595 20 114 116.870326492424 -2.87032649242395 21 108 105.701193210124 2.29880678987594 22 111 109.452426517941 1.54757348205935 23 151 143.340493201618 7.65950679838152 24 159 152.313126526446 6.68687347355375 25 158 146.559624053755 11.4403759462448 26 148 139.668231084217 8.3317689157827 27 138 130.780164400539 7.21983559946051 28 137 128.086131058701 8.9138689412994 29 136 124.780164400539 11.2198355994605 30 133 123.225431050195 9.774568949805 31 126 120.809997691345 5.19000230865507 32 120 110.807531075712 9.19246892428826 33 114 105.474197742378 8.5258022576216 34 116 109.225431050195 6.774568949805 35 153 143.113497733873 9.88650226612718 36 162 152.086131058701 9.91386894129941 37 161 152.168428534976 8.83157146502393 38 149 145.277035565438 3.72296443456178 39 139 130.553168932794 8.44683106720616 40 135 127.859135590955 7.14086440904506 41 130 124.553168932794 5.44683106720616 42 127 122.998435582449 4.00156441755064 43 122 114.747202274633 7.25279772536727 44 117 110.580535607966 6.41946439203391 45 112 105.247202274633 6.75279772536725 46 113 108.998435582449 4.00156441755065 47 149 142.886502266127 6.11349773387283 48 157 151.859135590955 5.14086440904506 49 157 146.105633118264 10.8943668817361 50 147 139.214240148726 7.785759851274 51 137 130.326173465048 6.67382653495182 52 132 127.632140123209 4.36785987679072 53 125 124.326173465048 0.67382653495182 54 123 116.935640165737 6.06435983426286 55 117 114.520206806887 2.47979319311292 56 114 110.353540140220 3.64645985977957 57 111 110.856006755854 0.143993244146354 58 112 102.935640165737 9.06435983426287 59 144 142.659506798381 1.34049320161849 60 150 151.632140123209 -1.63214012320928 61 149 145.878637650518 3.1213623494818 62 134 138.987244680980 -4.98724468098035 63 123 130.099177997303 -7.09917799730252 64 116 121.569344706497 -5.56934470649707 65 117 124.099177997303 -7.09917799730252 66 111 116.708644697991 -5.70864469799149 67 105 114.293211339141 -9.29321133914142 68 102 110.126544672475 -8.12654467247477 69 95 104.793211339141 -9.79321133914144 70 93 102.708644697991 -9.70864469799148 71 124 142.432511330636 -18.4325113306359 72 130 151.405144655464 -21.4051446554636 73 124 145.651642182773 -21.6516421827725

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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