multiple regression

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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: Fri, 20 Nov 2009 14:23:16 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Nov/20/t12587523186ddhs9nl9dj0mdu.htm/, Retrieved Fri, 20 Nov 2009 22:25:30 +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/2009/Nov/20/t12587523186ddhs9nl9dj0mdu.htm/}, year = {2009}, } @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 = {2009}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

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User-defined keywords:

Dataseries X:

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107.11 107.56 107.57 107.70 107.81 107.67 108.75 107.67 109.43 107.72 109.62 108.35 109.54 108.25 109.53 108.26 109.84 108.31 109.67 108.33 109.79 108.36 109.56 108.36 110.22 108.97 110.40 109.62 110.69 109.60 110.72 109.64 110.89 109.65 110.58 109.64 110.94 109.93 110.91 109.81 111.22 109.77 111.09 110.10 111.00 110.40 111.06 110.50 111.55 111.89 112.32 112.10 112.64 111.92 112.36 112.15 112.04 112.16 112.37 112.17 112.59 112.32 112.89 112.38 113.22 112.34 112.85 113.14 113.06 113.18 112.99 113.21 113.32 113.76 113.74 113.99 113.91 113.95 114.52 113.93 114.96 114.01 114.91 114.10 115.30 114.11 115.44 114.10 115.52 114.12 116.08 114.68 115.94 114.71 115.56 114.73 115.88 115.81 116.66 116.01 117.41 116.12 117.68 116.49 117.85 116.51 118.21 116.60 118.92 117.01 119.03 117.01 119.17 117.12 118.95 117.22 118.92 118.38 118.90 118.80

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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = -0.0956913721724628 + 1.00521297181906X[t] -0.468065856891305M1[t] -0.233556766831644M2[t] + 0.152610048266569M3[t] + 0.341963639761006M4[t] + 0.535786398719157M5[t] + 0.476941897284473M6[t] + 0.644149525567973M7[t] + 0.7582120812298M8[t] + 0.972107821793418M9[t] + 0.54222072599492M10[t] + 0.242594278787373M11[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) -0.0956913721724628 2.760814 -0.0347 0.972497 0.486249 X 1.00521297181906 0.024293 41.3781 0 0 M1 -0.468065856891305 0.376634 -1.2428 0.220121 0.11006 M2 -0.233556766831644 0.376015 -0.6211 0.537511 0.268756 M3 0.152610048266569 0.376078 0.4058 0.686736 0.343368 M4 0.341963639761006 0.375844 0.9099 0.367541 0.18377 M5 0.535786398719157 0.375783 1.4258 0.160539 0.080269 M6 0.476941897284473 0.375522 1.2701 0.210309 0.105154 M7 0.644149525567973 0.375313 1.7163 0.092693 0.046346 M8 0.7582120812298 0.375328 2.0201 0.04909 0.024545 M9 0.972107821793418 0.375303 2.5902 0.012733 0.006367 M10 0.54222072599492 0.374957 1.4461 0.154789 0.077395 M11 0.242594278787373 0.374825 0.6472 0.520638 0.260319 Multiple Linear Regression - Regression Statistics Multiple R 0.987125789053487 R-squared 0.974417323414469 Adjusted R-squared 0.967885576201141 F-TEST (value) 149.181726051232 F-TEST (DF numerator) 12 F-TEST (DF denominator) 47 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.592634001321065 Sum Squared Residuals 16.5071077975254 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 107.11 107.556950019794 -0.446950019794272 2 107.57 107.932188925909 -0.362188925909045 3 107.81 108.288199351853 -0.47819935185267 4 108.75 108.477552943347 0.272447056652891 5 109.43 108.721636350896 0.708363649103795 6 109.62 109.296076021708 0.323923978292471 7 109.54 109.362762352809 0.177237647190873 8 109.53 109.486877038189 0.0431229618108451 9 109.84 109.751033427344 0.08896657265628 10 109.67 109.341250590982 0.328749409018399 11 109.79 109.071780532929 0.718219467071378 12 109.56 108.829186254141 0.730813745858746 13 110.22 108.974300310060 1.24569968994042 14 110.4 109.862197831802 0.537802168198367 15 110.69 110.228260387463 0.461739612536538 16 110.72 110.457822497831 0.262177502169334 17 110.89 110.661697386507 0.228302613492988 18 110.58 110.592800755354 -0.0128007553541341 19 110.94 111.051520145465 -0.111520145465170 20 110.91 111.044957144509 -0.134957144508706 21 111.22 111.218644366200 0.00135563380044771 22 111.09 111.120477551101 -0.0304775511013389 23 111 111.122414995440 -0.122414995439526 24 111.06 110.980342013834 0.0796579861659482 25 111.55 111.909522187771 -0.359522187771252 26 112.32 112.355126001913 -0.0351260019129142 27 112.64 112.560354482084 0.0796455179163046 28 112.36 112.980907057097 -0.620907057096522 29 112.04 113.184781945773 -1.14478194577285 30 112.37 113.135989574056 -0.765989574056362 31 112.59 113.453979148113 -0.863979148112714 32 112.89 113.628354482084 -0.73835448208369 33 113.22 113.802041703775 -0.582041703774555 34 112.85 114.176324985431 -1.32632498543131 35 113.06 113.916907057097 -0.856907057096523 36 112.99 113.704469167464 -0.714469167463717 37 113.32 113.789270445073 -0.46927044507291 38 113.74 114.254978518651 -0.514978518650945 39 113.91 114.600936814876 -0.690936814876401 40 114.52 114.770186146934 -0.250186146934460 41 114.96 115.044425943638 -0.0844259436381378 42 114.91 115.076050609667 -0.166050609667156 43 115.3 115.253310367669 0.0466896323311486 44 115.44 115.357320793612 0.0826792063875177 45 115.52 115.591320793612 -0.0713207936124928 46 116.08 115.724352962033 0.355647037967329 47 115.94 115.454882903980 0.485117096020317 48 115.56 115.232392884629 0.327607115371302 49 115.88 115.849957037302 0.0300429626980139 50 116.66 116.285508721725 0.374491278274537 51 117.41 116.782248963724 0.627751036276228 52 117.68 117.343531354791 0.336468645208758 53 117.85 117.557458373186 0.292541626814202 54 118.21 117.589083039215 0.620916960785181 55 118.92 118.168427985944 0.751572014055861 56 119.03 118.282490541606 0.747509458394033 57 119.17 118.606959709070 0.56304029093032 58 118.95 118.277593910453 0.672406089546919 59 118.92 119.144014510556 -0.224014510555646 60 118.9 119.323609679932 -0.423609679932279 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.627181854495576 0.745636291008848 0.372818145504424 17 0.760669476644624 0.478661046710752 0.239330523355376 18 0.71791528702387 0.564169425952261 0.282084712976130 19 0.66540748956459 0.669185020870821 0.334592510435410 20 0.581231197837836 0.837537604324327 0.418768802162164 21 0.499049840808313 0.998099681616626 0.500950159191687 22 0.469776676239497 0.939553352478994 0.530223323760503 23 0.546828687028798 0.906342625942405 0.453171312971202 24 0.648934016060533 0.702131967878934 0.351065983939467 25 0.627183784366929 0.745632431266143 0.372816215633071 26 0.571726990828027 0.856546018343946 0.428273009171973 27 0.555437785379433 0.889124429241134 0.444562214620567 28 0.521995796868149 0.956008406263702 0.478004203131851 29 0.647899456759136 0.704201086481727 0.352100543240864 30 0.586302977627375 0.82739404474525 0.413697022372625 31 0.545114456145094 0.909771087709813 0.454885543854906 32 0.482847211769255 0.96569442353851 0.517152788230745 33 0.390302123570833 0.780604247141665 0.609697876429167 34 0.63950039606008 0.720999207879839 0.360499603939919 35 0.605465385548611 0.789069228902778 0.394534614451389 36 0.522174460573231 0.955651078853537 0.477825539426769 37 0.431371134878631 0.862742269757262 0.568628865121369 38 0.398719991226755 0.79743998245351 0.601280008773245 39 0.518670973467479 0.962658053065041 0.481329026532521 40 0.461514795466123 0.923029590932246 0.538485204533877 41 0.388334213298095 0.77666842659619 0.611665786701905 42 0.391739810707263 0.783479621414527 0.608260189292737 43 0.411863178150485 0.82372635630097 0.588136821849515 44 0.453254633154413 0.906509266308827 0.546745366845587 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 0 0 OK 5% type I error level 0 0 OK 10% type I error level 0 0 OK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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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