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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 05:27:22 -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/t1195129424t68y3ljegaa64rz.htm/, Retrieved Thu, 15 Nov 2007 13:23:55 +0100

User-defined keywords:

Dataseries X:

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140 -1 132 -1 117 -1 114 -1 113 -1 110 -1 107 -1 103 -1 98 -1 98 -1 137 -1 148 -1 147 -1 139 -1 130 -1 128 -1 127 -1 123 -1 118 -1 114 -1 108 -1 111 -1 151 0 159 0 158 0 148 0 138 0 137 0 136 0 133 0 126 0 120 0 114 0 116 0 153 0 162 0 161 0 149 1 139 1 135 1 130 1 127 1 122 1 117 1 112 1 113 1 149 1 157 1 157 1 147 1 137 1 132 1 125 1 123 1 117 1 114 1 111 1 112 1 144 1 150 1 149 1 134 0 123 0 116 0 117 0 111 0 105 0 102 0 95 0 93 0 124 0 130 0 124 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 -25[t] = + 163.547479367605 + 11.0329123993239`invloed>25`[t] -2.87383580259192M1[t] -11.0864903384044M2[t] -21.5772927645752M3[t] -24.9014285240794M4[t] -26.8922309502502M5[t] -30.0497000430877M6[t] -35.0405024692585M7[t] -38.8646382287627M8[t] -43.8554406549335M9[t] -42.6795764144377M10[t] -8.3425309071625M11[t] -0.342530907162507t + 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) 163.547479367605 3.481595 46.9749 0 0 `invloed>25` 11.0329123993239 1.422543 7.7558 0 0 M1 -2.87383580259192 3.784525 -0.7594 0.450658 0.225329 M2 -11.0864903384044 3.943247 -2.8115 0.006683 0.003342 M3 -21.5772927645752 3.938527 -5.4785 1e-06 0 M4 -24.9014285240794 3.934542 -6.3289 0 0 M5 -26.8922309502502 3.931293 -6.8406 0 0 M6 -30.0497000430877 3.928782 -7.6486 0 0 M7 -35.0405024692585 3.927011 -8.9229 0 0 M8 -38.8646382287627 3.92598 -9.8993 0 0 M9 -43.8554406549335 3.92569 -11.1714 0 0 M10 -42.6795764144377 3.926142 -10.8706 0 0 M11 -8.3425309071625 3.92248 -2.1269 0.037624 0.018812 t -0.342530907162507 0.053949 -6.3492 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.936903713692415 R-squared 0.877788568730638 Adjusted R-squared 0.850860626247559 F-TEST (value) 32.5976843304014 F-TEST (DF numerator) 13 F-TEST (DF denominator) 59 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 6.79329216225658 Sum Squared Residuals 2722.78028570483 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 140 149.298200258527 -9.29820025852665 2 132 140.743014815551 -8.74301481555134 3 117 129.909681482218 -12.909681482218 4 114 126.243014815551 -12.2430148155514 5 113 123.909681482218 -10.9096814822180 6 110 120.409681482218 -10.4096814822181 7 107 115.076348148885 -8.07634814888472 8 103 110.909681482218 -7.90968148221798 9 98 105.576348148885 -7.5763481488847 10 98 106.409681482218 -8.40968148221801 11 137 140.404196082331 -3.40419608233070 12 148 148.404196082331 -0.404196082330704 13 147 145.187829372576 1.81217062742375 14 139 136.632643929601 2.36735607039873 15 130 125.799310596268 4.20068940373207 16 128 122.132643929601 5.86735607039874 17 127 119.799310596268 7.20068940373206 18 123 116.299310596268 6.70068940373208 19 118 110.965977262935 7.03402273706541 20 114 106.799310596268 7.20068940373207 21 108 101.465977262935 6.53402273706542 22 111 102.299310596268 8.70068940373207 23 151 147.326737595704 3.67326240429553 24 159 155.326737595704 3.67326240429554 25 158 152.11037088595 5.88962911404997 26 148 143.555185442975 4.44481455702496 27 138 132.721852109642 5.2781478903583 28 137 129.055185442975 7.94481455702497 29 136 126.721852109642 9.27814789035829 30 133 123.221852109642 9.7781478903583 31 126 117.888518776308 8.11148122369164 32 120 113.721852109642 6.27814789035829 33 114 108.388518776308 5.61148122369164 34 116 109.221852109642 6.7781478903583 35 153 143.216366709754 9.7836332902456 36 162 151.216366709754 10.7836332902456 37 161 148 13.0000000000000 38 149 150.477726956349 -1.47772695634882 39 139 139.644393623015 -0.644393623015476 40 135 135.977726956349 -0.97772695634881 41 130 133.644393623016 -3.64439362301549 42 127 130.144393623015 -3.14439362301548 43 122 124.811060289682 -2.81106028968214 44 117 120.644393623015 -3.64439362301549 45 112 115.311060289682 -3.31106028968215 46 113 116.144393623015 -3.14439362301549 47 149 150.138908223128 -1.13890822312817 48 157 158.138908223128 -1.13890822312816 49 157 154.922541513374 2.07745848662627 50 147 146.367356070399 0.632643929601259 51 137 135.534022737065 1.46597726293460 52 132 131.867356070399 0.132643929601268 53 125 129.534022737065 -4.53402273706541 54 123 126.034022737065 -3.0340227370654 55 117 120.700689403732 -3.70068940373206 56 114 116.534022737065 -2.53402273706541 57 111 111.200689403732 -0.200689403732075 58 112 112.034022737065 -0.0340227370654120 59 144 146.028537337178 -2.02853733717810 60 150 154.028537337178 -4.02853733717808 61 149 150.812170627424 -1.81217062742366 62 134 131.224072785125 2.77592721487519 63 123 120.390739451791 2.60926054820853 64 116 116.724072785125 -0.724072785124802 65 117 114.390739451791 2.60926054820853 66 111 110.890739451791 0.109260548208544 67 105 105.557406118458 -0.557406118458123 68 102 101.390739451791 0.609260548208527 69 95 96.0574061184581 -1.05740611845812 70 93 96.8907394517915 -3.89073945179146 71 124 130.885254051904 -6.88525405190416 72 130 138.885254051904 -8.88525405190415 73 124 135.668887342150 -11.6688873421497

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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