Sleep in mammals 2

*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: Wed, 22 Dec 2010 18:41:17 +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/22/t1293043154tob5mqpjdwrynfc.htm/, Retrieved Wed, 22 Dec 2010 19:39:25 +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/22/t1293043154tob5mqpjdwrynfc.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:

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User-defined keywords:

Dataseries X:

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-999.00 6654.00 3.00 6.30 1.00 3.00 -999.00 3.39 1.00 -999.00 0.92 3.00 2.10 2547.00 4.00 9.10 10.55 4.00 15.80 0.02 1.00 5.20 160.00 4.00 10.90 3.30 1.00 8.30 52.16 1.00 11.00 0.43 4.00 3.20 465.00 5.00 7.60 0.55 2.00 -999.00 187.10 5.00 6.30 0.08 1.00 8.60 3.00 2.00 6.60 0.79 2.00 9.50 0.20 2.00 4.80 1.41 1.00 12.00 60.00 1.00 -999.00 529.00 5.00 3.30 27.66 5.00 11.00 0.12 2.00 -999.00 207.00 1.00 4.70 85.00 1.00 -999.00 36.33 1.00 10.40 0.10 3.00 7.40 1.04 4.00 2.10 521.00 5.00 -999.00 100.00 1.00 -999.00 35.00 4.00 7.70 0.01 4.00 17.90 0.01 1.00 6.10 62.00 1.00 8.20 0.12 1.00 8.40 1.35 3.00 11.90 0.02 3.00 10.80 0.05 3.00 13.80 1.70 1.00 14.30 3.50 1.00 -999.00 250.00 5.00 15.20 0.48 2.00 10.00 10.00 4.00 11.90 1.62 2.00 6.50 192.00 4.00 7.50 2.50 5.00 -999.00 4.29 2.00 10.60 0.28 3.00 7.40 4.24 1.00 8.40 6.80 2.00 5.70 0.75 2.00 4.90 3.60 3.00 -999.00 14.83 5.00 3.20 55.50 5.00 -999.00 1.40 2.00 8.10 0.06 2.00 11.00 0.90 2.00 4.90 2.00 3.00 13.20 etc...

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 6 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation SWS[t] = -168.238334738896 -0.105212324281577Wb[t] -11.3714898112225D[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) -168.238334738896 111.19493 -1.513 0.135617 0.067809 Wb -0.105212324281577 0.06038 -1.7425 0.086629 0.043314 D -11.3714898112225 37.669184 -0.3019 0.763807 0.381903 Multiple Linear Regression - Regression Statistics Multiple R 0.231053588405355 R-squared 0.0533857607149912 Adjusted R-squared 0.0212971424341435 F-TEST (value) 1.66369770888062 F-TEST (DF numerator) 2 F-TEST (DF denominator) 59 p-value 0.198200375520522 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 420.224485599023 Sum Squared Residuals 10418728.4795209 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 -999 -902.435609942173 -96.5643900578266 2 6.3 -202.458016496845 208.758016496845 3 -999 -179.966494329433 -819.033505670567 4 -999 -202.449599510902 -796.550400489098 5 2.1 -481.700083928962 483.800083928962 6 9.1 -214.834284004956 223.934284004956 7 15.8 -179.611928796604 195.411928796604 8 5.2 -230.558265868838 235.758265868838 9 10.9 -179.957025220247 190.857025220247 10 8.3 -185.097699384645 193.397699384645 11 11 -213.769535283227 224.769535283227 12 3.2 -274.019514585941 277.219514585941 13 7.6 -191.039181139695 198.639181139695 14 -999 -244.781009668091 -754.218990331909 15 6.3 -179.618241536061 185.918241536061 16 8.6 -191.296951334185 199.896951334185 17 6.6 -191.064432097523 197.664432097523 18 9.5 -191.002356826197 200.502356826197 19 4.8 -179.758173927355 184.558173927355 20 12 -185.922564007013 197.922564007013 21 -999 -280.753103339962 -718.246896660038 22 3.3 -228.005956684636 231.305956684636 23 11 -190.993939840254 201.993939840254 24 -999 -201.388775676405 -797.611224323595 25 4.7 -188.552872114052 193.252872114052 26 -999 -183.432188291268 -815.567811708732 27 10.4 -202.363325404991 212.763325404991 28 7.4 -213.833714801038 221.233714801038 29 2.1 -279.911404745709 282.011404745710 30 -999 -190.131056978276 -808.868943021724 31 -999 -217.406725333641 -781.59327466636 32 7.7 -213.725346107028 221.425346107028 33 17.9 -179.610876673361 197.510876673361 34 6.1 -186.132988655576 192.232988655576 35 8.2 -179.622450029032 187.822450029032 36 8.4 -202.494840810343 210.894840810343 37 11.9 -202.354908419049 214.254908419049 38 10.8 -202.358064788777 213.158064788777 39 13.8 -179.788685501397 193.588685501397 40 14.3 -179.978067685104 194.278067685104 41 -999 -251.398864865402 -747.601135134598 42 15.2 -191.031816276996 206.231816276996 43 10 -214.776417226601 224.776417226601 44 11.9 -191.151758326677 203.051758326677 45 6.5 -233.925060245848 240.425060245848 46 7.5 -225.358814605712 232.858814605712 47 -999 -191.432675232508 -807.567324767492 48 10.6 -202.382263623362 212.982263623362 49 7.4 -180.055924805072 187.455924805072 50 8.4 -191.696758166455 200.096758166455 51 5.7 -191.060223604552 196.760223604552 52 4.9 -202.731568539977 207.631568539977 53 -999 -226.656082564104 -772.343917435896 54 3.2 -230.935067792635 234.135067792635 55 -999 -191.128611615335 -807.871388384665 56 8.1 -190.987627100797 199.087627100797 57 11 -191.076005453194 202.076005453194 58 4.9 -202.563228821126 207.463228821126 59 13.2 -190.991835593769 204.191835593769 60 9.7 -214.165133622525 223.865133622525 61 12.8 -179.978067685104 192.778067685104 62 -999 -180.035934463458 -818.964065536542 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 6 0.711145230095977 0.577709539808047 0.288854769904023 7 0.896604869158122 0.206790261683755 0.103395130841878 8 0.828495767110768 0.343008465778465 0.171504232889232 9 0.830562669923595 0.338874660152811 0.169437330076405 10 0.796964942807064 0.406070114385871 0.203035057192936 11 0.714213818280304 0.571572363439393 0.285786181719696 12 0.660164651936076 0.679670696127847 0.339835348063924 13 0.58694210326677 0.826115793466459 0.413057896733229 14 0.813189317906464 0.373621364187072 0.186810682093536 15 0.759578094628825 0.480843810742349 0.240421905371175 16 0.698083216855145 0.60383356628971 0.301916783144855 17 0.629978974213935 0.74004205157213 0.370021025786065 18 0.558259987265906 0.883480025468187 0.441740012734094 19 0.483704536093 0.967409072186 0.516295463907 20 0.417234819222896 0.834469638445791 0.582765180777104 21 0.491675223707652 0.983350447415304 0.508324776292348 22 0.444993706275045 0.88998741255009 0.555006293724955 23 0.378424874851032 0.756849749702063 0.621575125148968 24 0.564650956414523 0.870698087170954 0.435349043585477 25 0.503584976914441 0.992830046171117 0.496415023085559 26 0.685801157139462 0.628397685721075 0.314198842860538 27 0.631450361503803 0.737099276992395 0.368549638496197 28 0.574694815139704 0.850610369720593 0.425305184860297 29 0.626488828085771 0.747022343828458 0.373511171914229 30 0.746367347901598 0.507265304196803 0.253632652098402 31 0.869828348500397 0.260343302999206 0.130171651499603 32 0.834093406759253 0.331813186481495 0.165906593240747 33 0.79341398651228 0.413172026975441 0.206586013487721 34 0.754515273345944 0.490969453308112 0.245484726654056 35 0.70223717569135 0.595525648617301 0.297762824308651 36 0.644347804120863 0.711304391758274 0.355652195879137 37 0.582839856221936 0.834320287556128 0.417160143778064 38 0.518777275269058 0.962445449461884 0.481222724730942 39 0.455586721097207 0.911173442194414 0.544413278902793 40 0.395106780661387 0.790213561322773 0.604893219338613 41 0.509724618172845 0.98055076365431 0.490275381827155 42 0.448419779305498 0.896839558610997 0.551580220694502 43 0.385612643492632 0.771225286985265 0.614387356507368 44 0.327757577665681 0.655515155331361 0.67224242233432 45 0.262390014163455 0.524780028326911 0.737609985836545 46 0.211249064061650 0.422498128123301 0.78875093593835 47 0.374801188662645 0.74960237732529 0.625198811337355 48 0.312273455900624 0.624546911801247 0.687726544099376 49 0.243595806115519 0.487191612231037 0.756404193884481 50 0.187575204587985 0.375150409175971 0.812424795412015 51 0.141737781669931 0.283475563339862 0.858262218330069 52 0.105822633533953 0.211645267067905 0.894177366466047 53 0.311656107810493 0.623312215620986 0.688343892189507 54 0.254086461396232 0.508172922792464 0.745913538603768 55 0.63992812209335 0.720143755813301 0.360071877906651 56 0.471633371430263 0.943266742860526 0.528366628569737 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 = 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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