Q3

*The author of this computation has been verified*

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

Title produced by software: Multiple Regression

Date of computation: Mon, 24 Nov 2008 04:08:30 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Nov/24/t12275249608lw2lsvzdrm1ir6.htm/, Retrieved Mon, 24 Nov 2008 11:09:20 +0000

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2008/Nov/24/t12275249608lw2lsvzdrm1ir6.htm/}, year = {2008}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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8638,7 0 11063,7 0 11855,7 0 10684,5 0 11337,4 0 10478 0 11123,9 0 12909,3 0 11339,9 0 10462,2 0 12733,5 0 10519,2 0 10414,9 0 12476,8 0 12384,6 0 12266,7 0 12919,9 0 11497,3 0 12142 0 13919,4 0 12656,8 0 12034,1 0 13199,7 0 10881,3 0 11301,2 0 13643,9 0 12517 0 13981,1 0 14275,7 0 13435 0 13565,7 0 16216,3 0 12970 0 14079,9 0 14235 0 12213,4 0 12581 0 14130,4 0 14210,8 0 14378,5 0 13142,8 0 13714,7 1 13621,9 1 15379,8 1 13306,3 1 14391,2 1 14909,9 1 14025,4 1 12951,2 1 14344,3 1 16213,3 1 15544,5 1 14750,6 1 17292,7 1 17568,5 1 17930,8 1 18644,7 1 16694,8 1 17242,8 1 16979,9 1

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 computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 5 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Multiple Linear Regression - Estimated Regression Equation y[t] = + 9196.87601518027 -137.010626185959x[t] -618.301831119547M1[t] + 1231.06905123340M2[t] + 1430.47993358634M3[t] + 1260.21081593928M4[t] + 1069.38169829222M5[t] + 989.994705882353M6[t] + 1205.80558823529M7[t] + 2767.47647058823M8[t] + 1174.84735294118M9[t] + 818.698235294118M10[t] + 1645.38911764706M11[t] + 105.049117647059t + 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) 9196.87601518027 487.865742 18.8512 0 0 x -137.010626185959 420.147406 -0.3261 0.745827 0.372913 M1 -618.301831119547 561.92625 -1.1003 0.276915 0.138458 M2 1231.06905123340 560.910921 2.1948 0.033266 0.016633 M3 1430.47993358634 560.119947 2.5539 0.014031 0.007015 M4 1260.21081593928 559.554282 2.2522 0.029128 0.014564 M5 1069.38169829222 559.214608 1.9123 0.062078 0.031039 M6 989.994705882353 560.94006 1.7649 0.084222 0.042111 M7 1205.80558823529 559.696664 2.1544 0.036481 0.018241 M8 2767.47647058823 558.677283 4.9536 1e-05 5e-06 M9 1174.84735294118 557.883143 2.1059 0.0407 0.02035 M10 818.698235294118 557.315207 1.469 0.148638 0.074319 M11 1645.38911764706 556.974168 2.9542 0.004928 0.002464 t 105.049117647059 11.254875 9.3337 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.930644670268518 R-squared 0.866099502299199 Adjusted R-squared 0.828258057296799 F-TEST (value) 22.8875906362524 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 8.88178419700125e-16 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 880.47366671941 Sum Squared Residuals 35660758.3781708 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 8638.7 8683.6233017078 -44.9233017077905 2 11063.7 10638.0433017078 425.656698292222 3 11855.7 10942.5033017078 913.196698292222 4 10684.5 10877.2833017078 -192.783301707781 5 11337.4 10791.5033017078 545.896698292221 6 10478 10817.1654269450 -339.165426944971 7 11123.9 11138.0254269450 -14.1254269449718 8 12909.3 12804.7454269450 104.554573055028 9 11339.9 11317.1654269450 22.7345730550294 10 10462.2 11066.0654269450 -603.86542694497 11 12733.5 11997.8054269450 735.694573055029 12 10519.2 10457.4654269450 61.7345730550297 13 10414.9 9944.21271347248 470.687286527517 14 12476.8 11898.6327134725 578.167286527514 15 12384.6 12203.0927134725 181.507286527515 16 12266.7 12137.8727134725 128.827286527515 17 12919.9 12052.0927134725 867.807286527514 18 11497.3 12077.7548387097 -580.454838709678 19 12142 12398.6148387097 -256.614838709677 20 13919.4 14065.3348387097 -145.934838709677 21 12656.8 12577.7548387097 79.0451612903225 22 12034.1 12326.6548387097 -292.554838709677 23 13199.7 13258.3948387097 -58.6948387096761 24 10881.3 11718.0548387097 -836.754838709678 25 11301.2 11204.8021252372 96.3978747628114 26 13643.9 13159.2221252372 484.677874762808 27 12517 13463.6821252372 -946.682125237192 28 13981.1 13398.4621252372 582.637874762808 29 14275.7 13312.6821252372 963.017874762809 30 13435 13338.3442504744 96.6557495256166 31 13565.7 13659.2042504744 -93.5042504743822 32 16216.3 15325.9242504744 890.375749525617 33 12970 13838.3442504744 -868.344250474384 34 14079.9 13587.2442504744 492.655749525616 35 14235 14518.9842504744 -283.984250474384 36 12213.4 12978.6442504744 -765.244250474385 37 12581 12465.3915370019 115.608462998104 38 14130.4 14419.8115370019 -289.411537001898 39 14210.8 14724.2715370019 -513.471537001899 40 14378.5 14659.0515370019 -280.551537001897 41 13142.8 14573.2715370019 -1430.4715370019 42 13714.7 14461.9230360531 -747.22303605313 43 13621.9 14782.7830360531 -1160.88303605313 44 15379.8 16449.5030360531 -1069.70303605313 45 13306.3 14961.9230360531 -1655.62303605313 46 14391.2 14710.8230360531 -319.62303605313 47 14909.9 15642.5630360531 -732.663036053131 48 14025.4 14102.2230360531 -76.8230360531314 49 12951.2 13588.9703225806 -637.770322580642 50 14344.3 15543.3903225806 -1199.09032258065 51 16213.3 15847.8503225806 365.449677419354 52 15544.5 15782.6303225806 -238.130322580645 53 14750.6 15696.8503225806 -946.250322580644 54 17292.7 15722.5124478178 1570.18755218216 55 17568.5 16043.3724478178 1525.12755218216 56 17930.8 17710.0924478178 220.707552182163 57 18644.7 16222.5124478178 2422.18755218216 58 16694.8 15971.4124478178 723.387552182162 59 17242.8 16903.1524478178 339.647552182162 60 16979.9 15362.8124478178 1617.08755218216

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

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')

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Software written by Ed van Stee & Patrick Wessa

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