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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: Sun, 16 Dec 2007 07:49:42 -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/Dec/16/t1197815624ixfnukib342912c.htm/, Retrieved Sun, 16 Dec 2007 15:33:44 +0100

User-defined keywords:

Dataseries X:

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36429 0.77632 32720 0.80364 34490 0.83065 34749 0.76103 30945 0.72187 34302 0.72929 30400 0.73339 25543 0.75884 32188 0.75423 34395 0.77581 27148 0.77753 26634 0.77016 34257 0.76800 34794 0.76352 38927 0.80984 38512 0.83697 33325 0.86371 40658 0.85027 32719 0.86945 29323 0.92155 34384 0.93647 35153 0.98323 30937 0.95760 28079 0.93332 39703 0.90135 35245 0.92446 41324 0.98061 40802 1.01953 37732 1.00784 41527 1.07107 33441 1.09458 32885 1.10923 36804 1.12907 35593 1.12374 34355 1.07400 27045 1.04497 45587 1.06290 40370 1.06646 48209 1.08848 40275 1.11763 36760 1.10842 42588 1.10560 35365 1.11306 33014 1.11039 36944 1.05590 35649 1.03703 34814 1.04327 26041 1.03839 45636 0.99784 40040 1.01526 47725 1.05461 40263 1.08300 43339 1.08503 47283 1.09953 40492 1.11442 35768 1.10371 28539 1.13018 42971 1.15868 36144 1.24067 26950 1.21680

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 6 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Multiple Linear Regression - Estimated Regression Equation inschrijv[t] = + 17180.6891294509 + 5306.33688043914`prijs `[t] + 15262.7389981197M1[t] + 11379.2497343920M2[t] + 16554.0482174195M3[t] + 13158.1129788859M4[t] + 10567.4613968375M5[t] + 15221.8920490527M6[t] + 8236.45738442385M7[t] + 4852.14965159447M8[t] + 7191.23051383726M9[t] + 9970.6814133921M10[t] + 5758.74949680261M11[t] + 123.858638246139t + 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) 17180.6891294509 4298.911069 3.9965 0.00023 0.000115 `prijs ` 5306.33688043914 5563.896509 0.9537 0.345216 0.172608 M1 15262.7389981197 1635.508747 9.3321 0 0 M2 11379.2497343920 1631.377142 6.9752 0 0 M3 16554.0482174195 1631.155965 10.1487 0 0 M4 13158.1129788859 1630.49705 8.07 0 0 M5 10567.4613968375 1624.765101 6.504 0 0 M6 15221.8920490527 1624.667666 9.3692 0 0 M7 8236.45738442385 1625.596611 5.0667 7e-06 4e-06 M8 4852.14965159447 1628.59789 2.9793 0.004601 0.0023 M9 7191.23051383726 1624.306444 4.4273 5.8e-05 2.9e-05 M10 9970.6814133921 1627.279315 6.1272 0 0 M11 5758.74949680261 1624.574359 3.5448 0.000915 0.000458 t 123.858638246139 45.582787 2.7172 0.009248 0.004624 Multiple Linear Regression - Regression Statistics Multiple R 0.914847528080632 R-squared 0.836945999635243 Adjusted R-squared 0.79086552127129 F-TEST (value) 18.1627020671286 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 6.60582699651968e-14 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2558.83620018381 Sum Squared Residuals 301191564.171071 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 36429 36686.7022128393 -257.702212839261 2 32720 33072.0407109313 -352.040710931266 3 34490 38514.0219913456 -4024.02199134557 4 34749 34872.5182174419 -123.518217441926 5 30945 32197.9291214017 -1252.92912140173 6 34302 37015.5914315159 -2713.59143151590 7 30400 30175.771386343 224.228613657024 8 25543 27050.3685653669 -1507.36856536691 9 32188 29488.845852837 2699.15414716298 10 34395 32506.6661405179 1888.33385948212 11 27148 28427.7197616089 -1279.71976160887 12 26634 22753.7212002436 3880.27879975643 13 34257 38128.8571489476 -3871.85714894763 14 34794 34345.4541342417 448.545865758285 15 38927 39889.9007798173 -962.900779817293 16 38512 36761.7850990962 1750.21490090385 17 33325 34436.8836034769 -1111.88360347688 18 40658 39143.8557262651 1514.14427373491 19 32719 32384.0552412492 334.944758750804 20 29323 29400.0662981368 -77.0662981368352 21 34384 31942.1763448819 2441.82365511808 22 35153 35093.6101952122 59.3898047877682 23 30937 30869.5355026232 67.4644973767837 24 28079 25105.8067846097 2973.19321539031 25 39703 40322.7608309079 -619.760830907862 26 35245 36685.7596507333 -1440.75965073326 27 41324 42282.3675878436 -958.367587843556 28 40802 39216.8136189428 1585.18638105721 29 37732 36687.9895970082 1044.01040299176 30 41527 41801.7985684197 -274.798568419717 31 33441 35064.9745220961 -1623.97452209613 32 32885 31882.2632628113 1002.73673718868 33 36804 34450.4804870082 2353.51951299183 34 35593 37325.5072492364 -1732.50724923641 35 34355 32973.49677446 1381.50322553999 36 27045 27184.5629562644 -139.562956264389 37 45587 42666.3032128965 2920.69678710353 38 40370 38925.5631467093 1444.43685329071 39 48209 44341.0658060902 3867.93419390981 40 40275 41223.6689258675 -948.668925867537 41 36760 38708.0046193965 -1948.00461939648 42 42588 43471.3300398549 -883.330039854948 43 35365 36649.3392866003 -1284.33928660031 44 33014 33374.7222725463 -360.722272546299 45 36944 35548.5194764201 1395.48052357989 46 35649 38351.6984372872 -2702.6984372872 47 34814 34296.7367010778 517.263298922221 48 26041 28635.9509185448 -2594.95091854477 49 45636 43807.3765944088 1828.62340559123 50 40040 40140.1823573845 -100.182357384472 51 47725 45647.6438349034 2077.35616509661 52 40263 42526.2141386516 -2263.2141386516 53 43339 40070.1930587167 3268.80694128332 54 47283 44925.4242339444 2357.57576605564 55 40492 38142.8595637114 2349.14043628862 56 35768 34825.5796011386 942.420398861362 57 28539 37428.9778388528 -8889.9778388528 58 42971 40483.5179777463 2487.48202225371 59 36144 36830.5112602301 -686.511260230134 60 26950 31068.9581403376 -4118.95814033758

Charts produced by software:

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Parameters (Session):

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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