s

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

Title produced by software: Multiple Regression

Date of computation: Sun, 06 Jan 2008 10:15:46 -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/Jan/06/t1199639724qregpshh5mwzc00.htm/, Retrieved Sun, 06 Jan 2008 18:15:34 +0100

User-defined keywords:

diesel verklaren door inflatie

Dataseries X:

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0.73 1.79 0.74 1.95 0.75 2.26 0.74 2.04 0.76 2.16 0.76 2.75 0.78 2.79 0.79 2.88 0.89 3.36 0.88 2.97 0.88 3.1 0.84 2.49 0.76 2.2 0.77 2.25 0.76 2.09 0.77 2.79 0.78 3.14 0.79 2.93 0.78 2.65 0.76 2.67 0.78 2.26 0.76 2.35 0.74 2.13 0.73 2.18 0.72 2.9 0.71 2.63 0.73 2.67 0.75 1.81 0.75 1.33 0.72 0.88 0.72 1.28 0.72 1.26 0.74 1.26 0.78 1.29 0.74 1.1 0.74 1.37 0.75 1.21 0.78 1.74 0.81 1.76 0.75 1.48 0.7 1.04 0.71 1.62 0.71 1.49 0.73 1.79 0.74 1.8 0.74 1.58 0.75 1.86 0.74 1.74 0.74 1.59 0.73 1.26 0.76 1.13 0.8 1.92 0.83 2.61 0.81 2.26 0.83 2.41 0.88 2.26 0.89 2.03 0.93 2.86 0.91 2.55 0.9 2.27 0.86 2.26 0.88 2.57 0.93 3.07 0.98 2.76 0.97 2.51 1.03 2.87 1.06 3.14 1.06 3.11 1.08 3.16 1.09 2.47 1.04 2.57 1 2.89

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 5 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation dsl[t] = + 0.596610740118349 + 0.098248900453546`inf `[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) 0.596610740118349 0.035055 17.0192 0 0 `inf ` 0.098248900453546 0.015385 6.3859 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.60672287067846 R-squared 0.368112641804311 Adjusted R-squared 0.359085679544373 F-TEST (value) 40.7792379323432 F-TEST (DF numerator) 1 F-TEST (DF denominator) 70 p-value 1.61221743733009e-08 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.0825879693636396 Sum Squared Residuals 0.477454087852663 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 0.73 0.772476271930194 -0.0424762719301944 2 0.74 0.788196096002764 -0.0481960960027644 3 0.75 0.818653255143363 -0.0686532551433633 4 0.74 0.797038497043583 -0.0570384970435832 5 0.76 0.808828365098009 -0.0488283650980087 6 0.76 0.8667952163656 -0.106795216365601 7 0.78 0.870725172383743 -0.0907251723837427 8 0.79 0.879567573424562 -0.0895675734245618 9 0.89 0.926727045642264 -0.0367270456422639 10 0.88 0.888409974465381 -0.00840997446538102 11 0.88 0.901182331524342 -0.0211823315243420 12 0.84 0.84125050224768 -0.00125050224767895 13 0.76 0.81275832111615 -0.0527583211161506 14 0.77 0.817670766138828 -0.0476707661388278 15 0.76 0.80195094206626 -0.0419509420662605 16 0.77 0.870725172383743 -0.100725172383743 17 0.78 0.905112287542484 -0.125112287542484 18 0.79 0.884480018447239 -0.094480018447239 19 0.78 0.856970326320246 -0.0769703263202462 20 0.76 0.858935304329317 -0.0989353043293172 21 0.78 0.818653255143363 -0.0386532551433633 22 0.76 0.827495656184182 -0.0674956561841824 23 0.74 0.805880898084402 -0.0658808980844023 24 0.73 0.81079334310708 -0.0807933431070797 25 0.72 0.881532551433633 -0.161532551433633 26 0.71 0.855005348311175 -0.145005348311175 27 0.73 0.858935304329317 -0.128935304329317 28 0.75 0.774441249939268 -0.0244412499392676 29 0.75 0.727281777721566 0.0227182222784345 30 0.72 0.68306977251747 0.0369302274825302 31 0.72 0.722369332698888 -0.00236933269888824 32 0.72 0.720404354689817 -0.000404354689817324 33 0.74 0.720404354689817 0.0195956453101827 34 0.78 0.723351821703424 0.0566481782965764 35 0.74 0.70468453061725 0.0353154693827501 36 0.74 0.731211733739707 0.00878826626029263 37 0.75 0.71549190966714 0.03450809033286 38 0.78 0.76756382690752 0.0124361730924806 39 0.81 0.76952880491659 0.0404711950834098 40 0.75 0.742019112789597 0.00798088721040259 41 0.7 0.698789596590037 0.0012104034099628 42 0.71 0.755773958853094 -0.0457739588530939 43 0.71 0.743001601794133 -0.0330016017941329 44 0.73 0.772476271930197 -0.0424762719301967 45 0.74 0.773458760934732 -0.0334587609347321 46 0.74 0.751844002834952 -0.0118440028349520 47 0.75 0.779353694961945 -0.0293536949619449 48 0.74 0.76756382690752 -0.0275638269075194 49 0.74 0.752826491839487 -0.0128264918394875 50 0.73 0.720404354689817 0.00959564531018268 51 0.76 0.707631997630856 0.0523680023691437 52 0.8 0.785248628989158 0.0147513710108424 53 0.83 0.853040370302104 -0.0230403703021044 54 0.81 0.818653255143363 -0.00865325514336324 55 0.83 0.833390590211395 -0.00339059021139527 56 0.88 0.818653255143363 0.0613467448566367 57 0.89 0.796056008039048 0.0939439919609523 58 0.93 0.87760259541549 0.0523974045845091 59 0.91 0.847145436274892 0.0628545637251084 60 0.9 0.819635744147899 0.0803642558521012 61 0.86 0.818653255143363 0.0413467448566367 62 0.88 0.849110414283963 0.0308895857160374 63 0.93 0.898234864510736 0.0317651354892645 64 0.98 0.867777705370136 0.112222294629864 65 0.97 0.84321548025675 0.126784519743250 66 1.03 0.878585084420026 0.151414915579974 67 1.06 0.905112287542484 0.154887712457516 68 1.06 0.902164820528877 0.157835179471123 69 1.08 0.907077265551555 0.172922734448445 70 1.09 0.839285524238608 0.250714475761392 71 1.04 0.849110414283963 0.190889585716037 72 1 0.880550062429097 0.119449937570903

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No 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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