Multiple linear regression bakmeel

*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: Thu, 16 Dec 2010 12:22:52 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/16/t1292502071t1844v4i568py2g.htm/, Retrieved Thu, 16 Dec 2010 13:21:22 +0100

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/2010/Dec/16/t1292502071t1844v4i568py2g.htm/}, year = {2010}, } @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 = {2010}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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0.81 0 0.81 0 0.81 0 0.79 0 0.78 0 0.78 0 0.77 0 0.78 0 0.77 0 0.78 0 0.79 0 0.79 0 0.79 0 0.79 0 0.79 0 0.8 0 0.8 0 0.8 1 0.8 1 0.81 1 0.8 1 0.82 1 0.85 1 0.85 1 0.86 1 0.85 1 0.83 1 0.81 1 0.82 1 0.82 1 0.78 1 0.78 1 0.73 1 0.68 1 0.65 1 0.62 1 0.6 1 0.6 1 0.59 1 0.6 1 0.6 1 0.6 1 0.59 1 0.58 1 0.56 1 0.55 1 0.54 1 0.55 1 0.55 1 0.54 1 0.54 1 0.54 1 0.53 1 0.53 1 0.53 1 0.53 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 9 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Bakmeel[t] = + 0.79 -0.117948717948718Dummy[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) 0.79 0.025485 30.9984 0 0 Dummy -0.117948717948718 0.030539 -3.8623 0.000303 0.000151 Multiple Linear Regression - Regression Statistics Multiple R 0.465243113003899 R-squared 0.216451154197559 Adjusted R-squared 0.201940990386403 F-TEST (value) 14.9172095514965 F-TEST (DF numerator) 1 F-TEST (DF denominator) 54 p-value 0.000302820508684798 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.105078092426881 Sum Squared Residuals 0.596235897435897 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 0.81 0.789999999999997 0.0200000000000032 2 0.81 0.79 0.0200000000000002 3 0.81 0.79 0.0199999999999998 4 0.79 0.79 -1.92987986702420e-16 5 0.78 0.79 -0.0100000000000002 6 0.78 0.79 -0.0100000000000002 7 0.77 0.79 -0.0200000000000002 8 0.78 0.79 -0.0100000000000002 9 0.77 0.79 -0.0200000000000002 10 0.78 0.79 -0.0100000000000002 11 0.79 0.79 -1.92987986702420e-16 12 0.79 0.79 -1.92987986702420e-16 13 0.79 0.79 -1.92987986702420e-16 14 0.79 0.79 -1.92987986702420e-16 15 0.79 0.79 -1.92987986702420e-16 16 0.8 0.79 0.00999999999999982 17 0.8 0.79 0.00999999999999982 18 0.8 0.672051282051282 0.127948717948718 19 0.8 0.672051282051282 0.127948717948718 20 0.81 0.672051282051282 0.137948717948718 21 0.8 0.672051282051282 0.127948717948718 22 0.82 0.672051282051282 0.147948717948718 23 0.85 0.672051282051282 0.177948717948718 24 0.85 0.672051282051282 0.177948717948718 25 0.86 0.672051282051282 0.187948717948718 26 0.85 0.672051282051282 0.177948717948718 27 0.83 0.672051282051282 0.157948717948718 28 0.81 0.672051282051282 0.137948717948718 29 0.82 0.672051282051282 0.147948717948718 30 0.82 0.672051282051282 0.147948717948718 31 0.78 0.672051282051282 0.107948717948718 32 0.78 0.672051282051282 0.107948717948718 33 0.73 0.672051282051282 0.057948717948718 34 0.68 0.672051282051282 0.007948717948718 35 0.65 0.672051282051282 -0.022051282051282 36 0.62 0.672051282051282 -0.052051282051282 37 0.6 0.672051282051282 -0.072051282051282 38 0.6 0.672051282051282 -0.072051282051282 39 0.59 0.672051282051282 -0.082051282051282 40 0.6 0.672051282051282 -0.072051282051282 41 0.6 0.672051282051282 -0.072051282051282 42 0.6 0.672051282051282 -0.072051282051282 43 0.59 0.672051282051282 -0.082051282051282 44 0.58 0.672051282051282 -0.092051282051282 45 0.56 0.672051282051282 -0.112051282051282 46 0.55 0.672051282051282 -0.122051282051282 47 0.54 0.672051282051282 -0.132051282051282 48 0.55 0.672051282051282 -0.122051282051282 49 0.55 0.672051282051282 -0.122051282051282 50 0.54 0.672051282051282 -0.132051282051282 51 0.54 0.672051282051282 -0.132051282051282 52 0.54 0.672051282051282 -0.132051282051282 53 0.53 0.672051282051282 -0.142051282051282 54 0.53 0.672051282051282 -0.142051282051282 55 0.53 0.672051282051282 -0.142051282051282 56 0.53 0.672051282051282 -0.142051282051282 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.00447443566161274 0.00894887132322547 0.995525564338387 6 0.00105426173467979 0.00210852346935958 0.99894573826532 7 0.000383883155670059 0.000767766311340117 0.99961611684433 8 6.9264576888387e-05 0.000138529153776774 0.999930735423112 9 1.84000619519919e-05 3.68001239039839e-05 0.999981599938048 10 2.90708507595718e-06 5.81417015191435e-06 0.999997092914924 11 3.89324200533243e-07 7.78648401066485e-07 0.9999996106758 12 4.90443940600859e-08 9.80887881201719e-08 0.999999950955606 13 5.8356376105415e-09 1.1671275221083e-08 0.999999994164362 14 6.5812652985639e-10 1.31625305971278e-09 0.999999999341873 15 7.0563313117603e-11 1.41126626235206e-10 0.999999999929437 16 1.00880529033183e-11 2.01761058066366e-11 0.999999999989912 17 1.36502465444163e-12 2.73004930888327e-12 0.999999999998635 18 1.66079394666091e-13 3.32158789332181e-13 0.999999999999834 19 2.03226391866192e-14 4.06452783732384e-14 0.99999999999998 20 3.31055582998039e-15 6.62111165996079e-15 0.999999999999997 21 4.40786177709557e-16 8.81572355419114e-16 1 22 1.59105115829066e-16 3.18210231658131e-16 1 23 3.30391269058085e-15 6.60782538116169e-15 0.999999999999997 24 1.25348590772437e-14 2.50697181544874e-14 0.999999999999987 25 9.4000316054504e-14 1.88000632109008e-13 0.999999999999906 26 1.93322149493597e-13 3.86644298987194e-13 0.999999999999807 27 1.89676349400537e-13 3.79352698801073e-13 0.99999999999981 28 3.15300315193383e-13 6.30600630386765e-13 0.999999999999685 29 9.28810079180568e-13 1.85762015836114e-12 0.999999999999071 30 9.47836438616303e-12 1.89567287723261e-11 0.999999999990522 31 1.34097873739727e-09 2.68195747479454e-09 0.999999998659021 32 7.55063942517344e-07 1.51012788503469e-06 0.999999244936058 33 0.00344906727085516 0.00689813454171032 0.996550932729145 34 0.354195194876153 0.708390389752306 0.645804805123847 35 0.910193164219652 0.179613671560696 0.0898068357803481 36 0.991879120166003 0.0162417596679936 0.00812087983399681 37 0.998632954083706 0.0027340918325887 0.00136704591629435 38 0.999631929471067 0.00073614105786587 0.000368070528932935 39 0.999827660362415 0.000344679275169829 0.000172339637584915 40 0.999931340201606 0.000137319596787945 6.86597983939726e-05 41 0.999977138617614 4.57227647730971e-05 2.28613823865485e-05 42 0.999996107305467 7.78538906536215e-06 3.89269453268107e-06 43 0.999999491106645 1.01778670965964e-06 5.08893354829818e-07 44 0.999999966909665 6.61806702058055e-08 3.30903351029027e-08 45 0.999999975827422 4.83451567389779e-08 2.41725783694889e-08 46 0.999999923353619 1.53292763022764e-07 7.66463815113821e-08 47 0.999999378096975 1.24380604977586e-06 6.21903024887929e-07 48 0.999998096987506 3.80602498870734e-06 1.90301249435367e-06 49 0.999997322483486 5.3550330285618e-06 2.6775165142809e-06 50 0.999974883857939 5.02322841224189e-05 2.51161420612095e-05 51 0.999803495143708 0.000393009712584695 0.000196504856292348 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 44 0.936170212765957 NOK 5% type I error level 45 0.957446808510638 NOK 10% type I error level 45 0.957446808510638 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No 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) library(lmtest) n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test 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)) if (n > n25) { kp3 <- k + 3 nmkm3 <- n - k - 3 gqarr <- array(NA, dim=c(nmkm3-kp3+1,3)) numgqtests <- 0 numsignificant1 <- 0 numsignificant5 <- 0 numsignificant10 <- 0 for (mypoint in kp3:nmkm3) { j <- 0 numgqtests <- numgqtests + 1 for (myalt in c('greater', 'two.sided', 'less')) { j <- j + 1 gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value } if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1 if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1 if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1 } gqarr } bitmap(file='test0.png') plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index') points(x[,1]-mysum$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') qqline(mysum$resid) grid() dev.off() (myerror <- as.ts(mysum$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() if (n > n25) { bitmap(file='test9.png') plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint') grid() 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') if (n > n25) { a<-table.start() a<-table.row.start(a) a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'p-values',header=TRUE) a<-table.element(a,'Alternative Hypothesis',3,header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'breakpoint index',header=TRUE) a<-table.element(a,'greater',header=TRUE) a<-table.element(a,'2-sided',header=TRUE) a<-table.element(a,'less',header=TRUE) a<-table.row.end(a) for (mypoint in kp3:nmkm3) { a<-table.row.start(a) a<-table.element(a,mypoint,header=TRUE) a<-table.element(a,gqarr[mypoint-kp3+1,1]) a<-table.element(a,gqarr[mypoint-kp3+1,2]) a<-table.element(a,gqarr[mypoint-kp3+1,3]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable5.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Description',header=TRUE) a<-table.element(a,'# significant tests',header=TRUE) a<-table.element(a,'% significant tests',header=TRUE) a<-table.element(a,'OK/NOK',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'1% type I error level',header=TRUE) a<-table.element(a,numsignificant1) a<-table.element(a,numsignificant1/numgqtests) if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'5% type I error level',header=TRUE) a<-table.element(a,numsignificant5) a<-table.element(a,numsignificant5/numgqtests) if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'10% type I error level',header=TRUE) a<-table.element(a,numsignificant10) a<-table.element(a,numsignificant10/numgqtests) if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable6.tab') }

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