workshop 7 - model 1

*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: Sun, 22 Nov 2009 12:31:59 -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/22/t12589184294n9td5c0onx4xkf.htm/, Retrieved Sun, 22 Nov 2009 20:34:01 +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/22/t12589184294n9td5c0onx4xkf.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:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

269645 0 267037 0 258113 0 262813 0 267413 0 267366 0 264777 0 258863 0 254844 0 254868 0 277267 0 285351 0 286602 0 283042 0 276687 0 277915 0 277128 0 277103 0 275037 0 270150 0 267140 0 264993 0 287259 0 291186 0 292300 0 288186 0 281477 0 282656 0 280190 0 280408 0 276836 0 275216 0 274352 0 271311 0 289802 0 290726 0 292300 0 278506 0 269826 0 265861 0 269034 0 264176 0 255198 0 253353 0 246057 0 235372 0 258556 0 260993 0 254663 0 250643 0 243422 0 247105 0 248541 0 245039 0 237080 0 237085 0 225554 0 226839 0 247934 0 248333 1 246969 1 245098 1 246263 1 255765 1 264319 1 268347 1 273046 1 273963 1 267430 1 271993 1 292710 1 295881 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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 266427.050847458 -1033.43546284224x[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) 266427.050847458 2198.056901 121.2103 0 0 x -1033.43546284224 5172.89309 -0.1998 0.842233 0.421116 Multiple Linear Regression - Regression Statistics Multiple R 0.0238713545349506 R-squared 0.000569841567333308 Adjusted R-squared -0.0137077321245618 F-TEST (value) 0.0399116530322503 F-TEST (DF numerator) 1 F-TEST (DF denominator) 70 p-value 0.842232645431283 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 16883.5954151293 Sum Squared Residuals 19953905589.9244 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 269645 266427.050847458 3217.94915254196 2 267037 266427.050847458 609.949152542379 3 258113 266427.050847458 -8314.05084745762 4 262813 266427.050847458 -3614.05084745762 5 267413 266427.050847458 985.949152542378 6 267366 266427.050847458 938.949152542378 7 264777 266427.050847458 -1650.05084745762 8 258863 266427.050847458 -7564.05084745762 9 254844 266427.050847458 -11583.0508474576 10 254868 266427.050847458 -11559.0508474576 11 277267 266427.050847458 10839.9491525424 12 285351 266427.050847458 18923.9491525424 13 286602 266427.050847458 20174.9491525424 14 283042 266427.050847458 16614.9491525424 15 276687 266427.050847458 10259.9491525424 16 277915 266427.050847458 11487.9491525424 17 277128 266427.050847458 10700.9491525424 18 277103 266427.050847458 10675.9491525424 19 275037 266427.050847458 8609.94915254238 20 270150 266427.050847458 3722.94915254238 21 267140 266427.050847458 712.949152542378 22 264993 266427.050847458 -1434.05084745762 23 287259 266427.050847458 20831.9491525424 24 291186 266427.050847458 24758.9491525424 25 292300 266427.050847458 25872.9491525424 26 288186 266427.050847458 21758.9491525424 27 281477 266427.050847458 15049.9491525424 28 282656 266427.050847458 16228.9491525424 29 280190 266427.050847458 13762.9491525424 30 280408 266427.050847458 13980.9491525424 31 276836 266427.050847458 10408.9491525424 32 275216 266427.050847458 8788.94915254238 33 274352 266427.050847458 7924.94915254238 34 271311 266427.050847458 4883.94915254238 35 289802 266427.050847458 23374.9491525424 36 290726 266427.050847458 24298.9491525424 37 292300 266427.050847458 25872.9491525424 38 278506 266427.050847458 12078.9491525424 39 269826 266427.050847458 3398.94915254238 40 265861 266427.050847458 -566.050847457622 41 269034 266427.050847458 2606.94915254238 42 264176 266427.050847458 -2251.05084745762 43 255198 266427.050847458 -11229.0508474576 44 253353 266427.050847458 -13074.0508474576 45 246057 266427.050847458 -20370.0508474576 46 235372 266427.050847458 -31055.0508474576 47 258556 266427.050847458 -7871.05084745762 48 260993 266427.050847458 -5434.05084745762 49 254663 266427.050847458 -11764.0508474576 50 250643 266427.050847458 -15784.0508474576 51 243422 266427.050847458 -23005.0508474576 52 247105 266427.050847458 -19322.0508474576 53 248541 266427.050847458 -17886.0508474576 54 245039 266427.050847458 -21388.0508474576 55 237080 266427.050847458 -29347.0508474576 56 237085 266427.050847458 -29342.0508474576 57 225554 266427.050847458 -40873.0508474576 58 226839 266427.050847458 -39588.0508474576 59 247934 266427.050847458 -18493.0508474576 60 248333 265393.615384615 -17060.6153846154 61 246969 265393.615384615 -18424.6153846154 62 245098 265393.615384615 -20295.6153846154 63 246263 265393.615384615 -19130.6153846154 64 255765 265393.615384615 -9628.61538461538 65 264319 265393.615384615 -1074.61538461539 66 268347 265393.615384615 2953.38461538461 67 273046 265393.615384615 7652.38461538462 68 273963 265393.615384615 8569.38461538462 69 267430 265393.615384615 2036.38461538461 70 271993 265393.615384615 6599.38461538462 71 292710 265393.615384615 27316.3846153846 72 295881 265393.615384615 30487.3846153846 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.0354627183568103 0.0709254367136206 0.96453728164319 6 0.0094682924091266 0.0189365848182532 0.990531707590873 7 0.00212963813939298 0.00425927627878597 0.997870361860607 8 0.00117371646525504 0.00234743293051007 0.998826283534745 9 0.00143302309839171 0.00286604619678343 0.998566976901608 10 0.00109421068593121 0.00218842137186243 0.998905789314069 11 0.00282181832646105 0.0056436366529221 0.997178181673539 12 0.0148938128172048 0.0297876256344095 0.985106187182795 13 0.0338157794851491 0.0676315589702982 0.96618422051485 14 0.0374604192725389 0.0749208385450778 0.962539580727461 15 0.0257332075620856 0.0514664151241711 0.974266792437914 16 0.0182505602243058 0.0365011204486115 0.981749439775694 17 0.0121117193134624 0.0242234386269247 0.987888280686538 18 0.00783350534409378 0.0156670106881876 0.992166494655906 19 0.00453880357102051 0.00907760714204102 0.99546119642898 20 0.00233880074035785 0.00467760148071570 0.997661199259642 21 0.00120525012773768 0.00241050025547535 0.998794749872262 22 0.000643925048678761 0.00128785009735752 0.999356074951321 23 0.00108505211976411 0.00217010423952822 0.998914947880236 24 0.00262723369152092 0.00525446738304185 0.99737276630848 25 0.00597669769214798 0.0119533953842960 0.994023302307852 26 0.00798094384139588 0.0159618876827918 0.992019056158604 27 0.00659914525941592 0.0131982905188318 0.993400854740584 28 0.00593442949186078 0.0118688589837216 0.99406557050814 29 0.00475061671632172 0.00950123343264344 0.995249383283678 30 0.00393421496710734 0.00786842993421468 0.996065785032893 31 0.00284781764878067 0.00569563529756134 0.99715218235122 32 0.00198942923281205 0.00397885846562409 0.998010570767188 33 0.00137872439849714 0.00275744879699429 0.998621275601503 34 0.0009201420968414 0.0018402841936828 0.999079857903159 35 0.00238758063318223 0.00477516126636446 0.997612419366818 36 0.00762712216504952 0.0152542443300990 0.99237287783495 37 0.0328435667243912 0.0656871334487825 0.96715643327561 38 0.0459838502916263 0.0919677005832526 0.954016149708374 39 0.0501041289316111 0.100208257863222 0.949895871068389 40 0.0541302359707232 0.108260471941446 0.945869764029277 41 0.0657443097977227 0.131488619595445 0.934255690202277 42 0.0774209777338352 0.154841955467670 0.922579022266165 43 0.0962355168930104 0.192471033786021 0.90376448310699 44 0.117878962438013 0.235757924876026 0.882121037561987 45 0.165303674210645 0.330607348421291 0.834696325789355 46 0.306480224913597 0.612960449827194 0.693519775086403 47 0.310090708632903 0.620181417265806 0.689909291367097 48 0.333038694182424 0.666077388364847 0.666961305817576 49 0.343446068454199 0.686892136908397 0.656553931545801 50 0.351986417613577 0.703972835227154 0.648013582386423 51 0.369273976734586 0.738547953469172 0.630726023265414 52 0.369524171574982 0.739048343149964 0.630475828425018 53 0.370449592863613 0.740899185727225 0.629550407136387 54 0.370498380540162 0.740996761080325 0.629501619459838 55 0.378133428356017 0.756266856712034 0.621866571643983 56 0.373365511279968 0.746731022559937 0.626634488720032 57 0.429868180644137 0.859736361288274 0.570131819355863 58 0.490094805041194 0.980189610082387 0.509905194958806 59 0.415551496776682 0.831102993553363 0.584448503223318 60 0.402108833493497 0.804217666986994 0.597891166506503 61 0.423014803348505 0.84602960669701 0.576985196651495 62 0.514664447599857 0.970671104800286 0.485335552400143 63 0.671163298238754 0.657673403522492 0.328836701761246 64 0.726999975803457 0.546000048393086 0.273000024196543 65 0.692333589132915 0.61533282173417 0.307666410867085 66 0.615475919867385 0.769048160265229 0.384524080132615 67 0.480255162145382 0.960510324290764 0.519744837854618 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 18 0.285714285714286 NOK 5% type I error level 28 0.444444444444444 NOK 10% type I error level 34 0.53968253968254 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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