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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: Tue, 04 Dec 2007 08:19:01 -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/04/t1196780812xbyrtpygm67i6zu.htm/, Retrieved Tue, 04 Dec 2007 16:07:02 +0100

User-defined keywords:

paper, regressie

Dataseries X:

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97,3 0 101 0 113,2 0 101 0 105,7 0 113,9 0 86,4 0 96,5 0 103,3 0 114,9 0 105,8 0 94,2 0 98,4 0 99,4 0 108,8 0 112,6 0 104,4 0 112,2 0 81,1 0 97,1 0 112,6 0 113,8 0 107,8 0 103,2 0 103,3 0 101,2 0 107,7 0 110,4 0 101,9 0 115,9 0 89,9 0 88,6 0 117,2 0 123,9 0 100 0 103,6 0 94,1 0 98,7 0 119,5 0 112,7 0 104,4 0 124,7 0 89,1 0 97 0 121,6 0 118,8 0 114 0 111,5 0 97,2 0 102,5 0 113,4 0 109,8 0 104,9 0 126,1 0 80 0 96,8 0 117,2 1 112,3 1 117,3 1 111,1 1 102,2 1 104,3 1 122,9 1 107,6 1 121,3 1 131,5 1 89 1 104,4 1 128,9 1 135,9 1 133,3 1 121,3 1 120,5 1 120,4 1 137,9 1 126,1 1 133,2 1 146,6 1 103,4 1 117,2 1

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] = + 101.112108908202 + 8.73704508419336`x `[t] + 0.139550063371357t + 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) 101.112108908202 3.003934 33.6599 0 0 `x ` 8.73704508419336 4.576468 1.9091 0.059972 0.029986 t 0.139550063371357 0.090819 1.5366 0.128495 0.064248 Multiple Linear Regression - Regression Statistics Multiple R 0.521914763859964 R-squared 0.272395020735002 Adjusted R-squared 0.253496190104743 F-TEST (value) 14.4133267324413 F-TEST (DF numerator) 2 F-TEST (DF denominator) 77 p-value 4.81928936868492e-06 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 11.4084889276863 Sum Squared Residuals 10021.8287102118 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 97.3 101.251658971574 -3.95165897157371 2 101 101.391209034945 -0.391209034944769 3 113.2 101.530759098316 11.6692409016839 4 101 101.670309161687 -0.670309161687471 5 105.7 101.809859225059 3.89014077494118 6 113.9 101.949409288430 11.9505907115698 7 86.4 102.088959351802 -15.6889593518015 8 96.5 102.228509415173 -5.7285094151729 9 103.3 102.368059478544 0.931940521455743 10 114.9 102.507609541916 12.3923904580844 11 105.8 102.647159605287 3.15284039471303 12 94.2 102.786709668658 -8.58670966865832 13 98.4 102.926259732030 -4.52625973202967 14 99.4 103.065809795401 -3.66580979540103 15 108.8 103.205359858772 5.5946401412276 16 112.6 103.344909922144 9.25509007785624 17 104.4 103.484459985515 0.915540014484898 18 112.2 103.624010048886 8.57598995111354 19 81.1 103.763560112258 -22.6635601122578 20 97.1 103.903110175629 -6.80311017562918 21 112.6 104.042660239001 8.55733976099946 22 113.8 104.182210302372 9.6177896976281 23 107.8 104.321760365743 3.47823963425675 24 103.2 104.461310429115 -1.26131042911460 25 103.3 104.600860492486 -1.30086049248596 26 101.2 104.740410555857 -3.54041055585731 27 107.7 104.879960619229 2.82003938077133 28 110.4 105.0195106826 5.38048931739997 29 101.9 105.159060745971 -3.25906074597138 30 115.9 105.298610809343 10.6013891906573 31 89.9 105.438160872714 -15.5381608727141 32 88.6 105.577710936085 -16.9777109360855 33 117.2 105.717260999457 11.4827390005432 34 123.9 105.856811062828 18.0431889371718 35 100 105.996361126200 -5.99636112619953 36 103.6 106.135911189571 -2.53591118957089 37 94.1 106.275461252942 -12.1754612529422 38 98.7 106.415011316314 -7.7150113163136 39 119.5 106.554561379685 12.9454386203150 40 112.7 106.694111443056 6.00588855694369 41 104.4 106.833661506428 -2.43366150642766 42 124.7 106.973211569799 17.7267884302010 43 89.1 107.112761633170 -18.0127616331704 44 97 107.252311696542 -10.2523116965417 45 121.6 107.391861759913 14.2081382400869 46 118.8 107.531411823284 11.2685881767155 47 114 107.670961886656 6.32903811334419 48 111.5 107.810511950027 3.68948804997284 49 97.2 107.950062013399 -10.7500620133985 50 102.5 108.089612076770 -5.58961207676988 51 113.4 108.229162140141 5.17083785985877 52 109.8 108.368712203513 1.43128779648741 53 104.9 108.508262266884 -3.60826226688394 54 126.1 108.647812330255 17.4521876697447 55 80 108.787362393627 -28.7873623936267 56 96.8 108.926912456998 -12.1269124569980 57 117.2 117.803507604563 -0.603507604562729 58 112.3 117.943057667934 -5.64305766793409 59 117.3 118.082607731305 -0.782607731305448 60 111.1 118.222157794677 -7.12215779467681 61 102.2 118.361707858048 -16.1617078580482 62 104.3 118.501257921420 -14.2012579214195 63 122.9 118.640807984791 4.25919201520913 64 107.6 118.780358048162 -11.1803580481622 65 121.3 118.919908111534 2.38009188846641 66 131.5 119.059458174905 12.4405418250951 67 89 119.199008238276 -30.1990082382763 68 104.4 119.338558301648 -14.9385583016476 69 128.9 119.478108365019 9.421891634981 70 135.9 119.617658428390 16.2823415716096 71 133.3 119.757208491762 13.5427915082383 72 121.3 119.896758555133 1.40324144486692 73 120.5 120.036308618504 0.463691381495562 74 120.4 120.175858681876 0.224141318124211 75 137.9 120.315408745247 17.5845912547529 76 126.1 120.454958808619 5.64504119138149 77 133.2 120.594508871990 12.6054911280101 78 146.6 120.734058935361 25.8659410646388 79 103.4 120.873608998733 -17.4736089987326 80 117.2 121.013159062104 -3.81315906210393

Charts produced by software:

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Parameters:

par1 = 1 ; par2 = Do not include Seasonal 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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