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multiple regression (monthly dummy)

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 08:39:50 -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/t1195140894h1dlcc5cs0gmujn.htm/, Retrieved Thu, 15 Nov 2007 16:35:06 +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] = + 145.890405293631 + 6.13151364764265X[t] + 0.357733664185238M1[t] -6.43424317617864M2[t] -15.2237386269644M3[t] -24M4[t] -27.3552522746071M5[t] -28.8114143920596M6[t] -31.0789909015716M7[t] -35.2456575682382M8[t] -40.5789909015715M9[t] -42.8114143920596M10[t] -9.02191894127379M11[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) 145.890405293631 4.554462 32.0324 0 0 X 6.13151364764265 3.007277 2.0389 0.045874 0.022937 M1 0.357733664185238 5.43797 0.0658 0.947768 0.473884 M2 -6.43424317617864 5.584484 -1.1522 0.253824 0.126912 M3 -15.2237386269644 5.933455 -2.5657 0.012812 0.006406 M4 -24 5.378246 -4.4624 3.6e-05 1.8e-05 M5 -27.3552522746071 5.40155 -5.0643 4e-06 2e-06 M6 -28.8114143920596 5.40155 -5.3339 2e-06 1e-06 M7 -31.0789909015716 5.73977 -5.4147 1e-06 1e-06 M8 -35.2456575682382 5.73977 -6.1406 0 0 M9 -40.5789909015715 5.73977 -7.0698 0 0 M10 -42.8114143920596 5.40155 -7.9258 0 0 M11 -9.02191894127379 5.40155 -1.6702 0.10008 0.05004 Multiple Linear Regression - Regression Statistics Multiple R 0.875387351584385 R-squared 0.766303015313923 Adjusted R-squared 0.719563618376708 F-TEST (value) 16.3952268434976 F-TEST (DF numerator) 12 F-TEST (DF denominator) 60 p-value 1.03250741290140e-14 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 9.31539581111443 Sum Squared Residuals 5206.5959470637 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 140 152.379652605459 -12.3796526054593 2 132 139.456162117452 -7.45616211745239 3 117 130.666666666667 -13.6666666666667 4 114 128.021918941274 -14.0219189412737 5 113 124.666666666667 -11.6666666666667 6 110 123.210504549214 -13.2105045492142 7 107 114.811414392060 -7.81141439205963 8 103 110.644747725393 -7.64474772539285 9 98 105.311414392060 -7.31141439205952 10 98 109.210504549214 -11.2105045492143 11 137 143 -6.00000000000002 12 148 145.890405293631 2.10959470636889 13 147 146.248138957816 0.751861042183654 14 139 145.587675765095 -6.58767576509511 15 130 130.666666666667 -0.666666666666664 16 128 128.021918941274 -0.0219189412737837 17 127 124.666666666667 2.33333333333333 18 123 123.210504549214 -0.210504549214221 19 118 114.811414392060 3.18858560794045 20 114 116.776261373036 -2.77626137303555 21 108 105.311414392060 2.68858560794044 22 111 109.210504549214 1.78949545078580 23 151 143 8 24 159 152.021918941274 6.97808105872622 25 158 146.248138957816 11.7518610421837 26 148 139.456162117452 8.54383788254755 27 138 130.666666666667 7.33333333333334 28 137 128.021918941274 8.97808105872621 29 136 124.666666666667 11.3333333333333 30 133 123.210504549214 9.78949545078578 31 126 120.942928039702 5.05707196029781 32 120 110.644747725393 9.3552522746071 33 114 105.311414392060 8.68858560794044 34 116 109.210504549214 6.78949545078579 35 153 143 10 36 162 152.021918941274 9.97808105872622 37 161 152.379652605459 8.620347394541 38 149 145.587675765095 3.41232423490489 39 139 130.666666666667 8.33333333333334 40 135 128.021918941274 6.97808105872621 41 130 124.666666666667 5.33333333333333 42 127 123.210504549214 3.78949545078578 43 122 114.811414392060 7.18858560794046 44 117 110.644747725393 6.3552522746071 45 112 105.311414392060 6.68858560794044 46 113 109.210504549214 3.78949545078579 47 149 143 6 48 157 152.021918941274 4.97808105872621 49 157 146.248138957816 10.7518610421837 50 147 139.456162117452 7.54383788254755 51 137 130.666666666667 6.33333333333333 52 132 128.021918941274 3.97808105872621 53 125 124.666666666667 0.333333333333333 54 123 117.078990901572 5.92100909842843 55 117 114.811414392060 2.18858560794045 56 114 110.644747725393 3.3552522746071 57 111 111.442928039702 -0.442928039702218 58 112 103.078990901572 8.92100909842845 59 144 143 1.00000000000000 60 150 152.021918941274 -2.02191894127378 61 149 146.248138957816 2.75186104218366 62 134 139.456162117452 -5.45616211745245 63 123 130.666666666667 -7.66666666666666 64 116 121.890405293631 -5.89040529363112 65 117 124.666666666667 -7.66666666666667 66 111 117.078990901572 -6.07899090157157 67 105 114.811414392060 -9.81141439205955 68 102 110.644747725393 -8.6447477253929 69 95 105.311414392060 -10.3114143920596 70 93 103.078990901572 -10.0789909015715 71 124 143 -19 72 130 152.021918941274 -22.0219189412738 73 124 146.248138957816 -22.2481389578163

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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