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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: Wed, 29 Dec 2010 20:50:14 +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/29/t1293655696g1diz2flen64n6t.htm/, Retrieved Wed, 29 Dec 2010 21:48:25 +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/29/t1293655696g1diz2flen64n6t.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}, }

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Dataseries X:

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12 -2 3 16 0 6 11 0 8 17 2 6 10 -2 3 23 3 7 9 -4 3 24 1 4 8 -4 7 27 1 3 7 -7 4 31 0 0 6 -9 -4 40 1 6 5 -13 -6 47 -1 3 4 -8 8 43 2 1 3 -13 2 60 2 6 2 -15 -1 64 0 5 1 -15 -2 65 1 7 12 -15 0 65 1 4 11 -10 10 55 3 3 10 -12 3 57 3 6 9 -11 6 57 1 6 8 -11 7 57 1 5 7 -17 -4 65 -2 2 6 -18 -5 69 1 3 5 -19 -7 70 1 -2 4 -22 -10 71 -1 -4 3 -24 -21 71 -4 0 2 -24 -22 73 -2 1 1 -20 -16 68 -1 4 12 -25 -25 65 -5 -3 11 -22 -22 57 -4 -3 10 -17 -22 41 -5 0 9 -9 -19 21 0 6 8 -11 -21 21 -2 -1 7 -13 -31 17 -4 0 6 -11 -28 9 -6 -1 5 -9 -23 11 -2 1 4 -7 -17 6 -2 -4 3 -3 -12 -2 -2 -1 2 -3 -14 0 1 -1 1 -6 -18 5 -2 0 12 -4 -16 3 0 3 11 -8 -22 7 -1 0 10 -1 -9 4 2 8 9 -2 -10 8 3 8 8 -2 -10 9 2 8 7 -1 0 14 3 8 6 1 3 12 4 11 5 2 2 12 5 13 4 2 4 7 5 5 3 -1 -3 15 4 12 2 1 0 14 5 13 1 -1 -1 19 6 9 12 -8 -7 39 4 11 11 1 2 12 6 7 10 2 3 11 6 12 9 -2 -3 17 3 11 8 -2 -5 16 5 10 7 -2 0 25 5 13 6 -2 -3 24 5 14 5 -6 -7 28 3 10 4 -4 -7 25 5 13 3 -5 -7 31 5 12 2 -2 -4 24 6 13 1 -1 -3 24 6 17

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' @ www.wessa.org Multiple Linear Regression - Estimated Regression Equation werkloosheid[t] = + 1.9989505883349 -0.128143998980092maand[t] -3.92249416334768indicator[t] + 0.97268311331247economie[t] + 1.1112397730813`financiën`[t] + 0.894075712318706spaarvermogen[t] -0.0222883901599848t + 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) 1.9989505883349 0.648241 3.0837 0.003244 0.001622 maand -0.128143998980092 0.045273 -2.8305 0.006553 0.003276 indicator -3.92249416334768 0.030266 -129.602 0 0 economie 0.97268311331247 0.037166 26.1714 0 0 `financiën` 1.1112397730813 0.15361 7.2341 0 0 spaarvermogen 0.894075712318706 0.057103 15.6573 0 0 t -0.0222883901599848 0.018955 -1.1758 0.244913 0.122456 Multiple Linear Regression - Regression Statistics Multiple R 0.998871733521904 R-squared 0.997744740029054 Adjusted R-squared 0.997489427579512 F-TEST (value) 3907.93610661126 F-TEST (DF numerator) 6 F-TEST (DF denominator) 53 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.16205798068679 Sum Squared Residuals 71.5700737753262 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 16 16.5664261509587 -0.566426150958654 2 17 15.9131885458085 1.08681145419152 3 23 21.0059324001616 1.99406759983842 4 24 24.0520696525584 -0.0520696525583974 5 27 27.1545820023096 -0.154582002309649 6 31 32.316403851198 -1.31640385119796 7 40 38.9614769272072 1.0385230727928 8 47 47.9072362796744 -0.907236279674364 9 43 43.5637525527371 -0.563752552737141 10 60 61.9163588600144 -1.91635886001435 11 64 63.8325981971111 0.167401802888893 12 65 65.8651618903374 -0.865161890337453 13 65 63.6964286010653 1.30357139893473 14 55 55.2450483601156 -0.24504836011558 15 57 59.0693376393999 -2.06933763939988 16 57 55.9482688786471 1.05173112135288 17 57 56.132731888461 0.867268111539013 18 65 63.05809177473 1.94190822527002 19 69 70.3415534651479 -1.3415534651479 20 70 67.9541584490972 2.04584155090279 21 71 72.898816237223 -1.89881623722294 22 71 70.3927294563321 0.607270543667845 23 73 72.6424572103211 0.357542789678896 24 68 66.6879017556627 1.31209824433726 25 65 65.4108630950918 -0.410863095091768 26 57 57.7785253268875 -0.778525326887539 27 41 39.8428974828441 1.15710251715593 28 21 22.4075022641389 -1.40750226413889 29 21 19.9319704406359 1.06802955936413 30 17 16.8275794091827 0.172420590817256 31 9 8.88994077276361 0.110059227236392 32 11 12.2473341384133 -1.24733413841331 33 6 5.87392153881935 0.126078461180648 34 -2 -2.16455680223279 0.164556802232788 35 0 -0.670348100793724 0.670348100793724 36 5 4.87261393789435 0.127386062105646 37 3 2.44582614200165 0.554173857998346 38 7 8.61209281430023 -1.61209281430023 39 4 4.39169477054225 -0.391694770542249 40 8 8.55860120247886 -0.558601202478862 41 9 7.55321703821768 1.44678296178232 42 14 14.5746493898961 -0.574649389896102 43 12 13.5470329219957 -1.54703292199568 44 12 11.6571024518744 0.342897548125645 45 7 6.55571858876975 0.444281411230251 46 15 16.7675651075952 -1.76756510759524 47 14 13.9517972150574 0.0482027849425886 48 19 18.4648949610669 0.535105038933129 49 39 38.2200549241596 0.779945075840381 50 12 10.4237877795506 1.57621222044937 51 11 12.0502108999291 -1.05021089992905 52 17 17.7821494507025 -0.782149450702457 53 16 17.2710426667415 -1.27104266674151 54 25 24.9225409790801 0.0774590209199105 55 24 23.0044229602815 0.995577039718506 56 28 29.110740373805 -1.11074037380501 57 25 26.2763143390485 -1.27631433904848 58 31 29.4105883988976 1.58941160110244 59 24 22.672326343012 1.32767365698795 60 24 23.4046737510718 0.595326248928235 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.0697152137359669 0.139430427471934 0.930284786264033 11 0.206085560318639 0.412171120637278 0.793914439681361 12 0.303796225835462 0.607592451670924 0.696203774164538 13 0.204305282225973 0.408610564451947 0.795694717774027 14 0.324142074791732 0.648284149583463 0.675857925208268 15 0.69493831290327 0.610123374193462 0.305061687096731 16 0.740159864786945 0.51968027042611 0.259840135213055 17 0.668530139099675 0.66293972180065 0.331469860900325 18 0.70589014799277 0.588219704014459 0.294109852007229 19 0.731133814420138 0.537732371159724 0.268866185579862 20 0.83975618113576 0.320487637728479 0.160243818864239 21 0.932211029784599 0.135577940430803 0.0677889702154014 22 0.902191081792552 0.195617836414896 0.097808918207448 23 0.8635181949432 0.272963610113598 0.136481805056799 24 0.831674186196856 0.336651627606289 0.168325813803144 25 0.8263930159049 0.347213968190199 0.173606984095099 26 0.851391622120106 0.297216755759788 0.148608377879894 27 0.838762514403761 0.322474971192478 0.161237485596239 28 0.900366822769171 0.199266354461657 0.0996331772308285 29 0.891437291741217 0.217125416517567 0.108562708258783 30 0.854206936169205 0.29158612766159 0.145793063830795 31 0.835946846814353 0.328106306371293 0.164053153185647 32 0.819534682346368 0.360930635307265 0.180465317653632 33 0.762397001190435 0.475205997619129 0.237602998809565 34 0.71163796647755 0.5767240670449 0.28836203352245 35 0.653009913286306 0.693980173427387 0.346990086713694 36 0.611101739752077 0.777796520495847 0.388898260247923 37 0.598013036236227 0.803973927527545 0.401986963763773 38 0.607142262905578 0.785715474188845 0.392857737094422 39 0.52034507825543 0.95930984348914 0.47965492174457 40 0.482559259828192 0.965118519656383 0.517440740171808 41 0.7417351209646 0.516529758070799 0.258264879035399 42 0.688231036980248 0.623537926039504 0.311768963019752 43 0.679346143155952 0.641307713688095 0.320653856844048 44 0.651029102300791 0.697941795398417 0.348970897699208 45 0.55058734729775 0.898825305404499 0.449412652702249 46 0.478641822120555 0.95728364424111 0.521358177879445 47 0.418956166091634 0.837912332183268 0.581043833908366 48 0.305405772912246 0.610811545824491 0.694594227087754 49 0.252024447090524 0.504048894181049 0.747975552909476 50 0.244804022716422 0.489608045432844 0.755195977283578 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 = 0 ; par3 = 0 ; par4 = 12 ;

Parameters (R input):

par1 = 4 ; par2 = Do not include Seasonal Dummies ; par3 = 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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