sleep in mammals

*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: Tue, 21 Dec 2010 19:11:59 +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/21/t12929586212kzzlyxhijj6d1x.htm/, Retrieved Tue, 21 Dec 2010 20:10:21 +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/21/t12929586212kzzlyxhijj6d1x.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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Dataseries X:

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-999,00 -999,00 38,60 6654,00 5712,00 645,00 3,00 5,00 3,00 3,30 6,30 2,00 4,50 1,00 6600,00 42,00 3,00 1,00 3,00 8,30 -999,00 -999,00 14,00 3,39 44,50 60,00 1,00 1,00 1,00 12,50 -999,00 -999,00 -999,00 0,92 5,70 25,00 5,00 2,00 3,00 16,50 2,10 1,80 69,00 2547,00 4603,00 624,00 3,00 5,00 4,00 3,90 9,10 0,70 27,00 10,55 179,50 180,00 4,00 4,00 4,00 9,80 15,80 3,90 19,00 0,02 0,30 35,00 1,00 1,00 1,00 19,70 5,20 1,00 30,40 160,00 169,00 392,00 4,00 5,00 4,00 6,20 10,90 3,60 28,00 3,30 25,60 63,00 1,00 2,00 1,00 14,50 8,30 1,40 50,00 52,16 440,00 230,00 1,00 1,00 1,00 9,70 11,00 1,50 7,00 0,43 6,40 112,00 5,00 4,00 4,00 12,50 3,20 0,70 30,00 465,00 423,00 281,00 5,00 5,00 5,00 3,90 7,60 2,70 -999,00 0,55 2,40 -999,00 2,00 1,00 2,00 10,30 -999,00 -999,00 40,00 187,10 419,00 365,00 5,00 5,00 5,00 3,10 6,30 2,10 3,50 0,08 1,20 42,00 1,00 1,00 1,00 8,40 8,60 0,00 50,00 3,00 25,00 28,00 2,00 2,00 2,00 8,60 6,60 4,10 6,00 0,79 3500,00 42,00 2,00 2,00 2,00 10,70 9,50 1,20 10,40 0,20 5,00 120,00 2,00 2, 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 5 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation TS[t] = + 34.3623416950708 + 0.997337133245564SWS[t] -0.826836682048261PS[t] -0.0603303939819822L[t] + 0.0318126126570365Wb[t] -0.00602942557266054Wbr[t] + 0.0505446567493215Tg[t] -36.4418346082895P[t] -22.2453149809266S[t] + 45.6701835467499D[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) 34.3623416950708 55.213315 0.6224 0.536427 0.268214 SWS 0.997337133245564 0.134795 7.3989 0 0 PS -0.826836682048261 0.142513 -5.8018 0 0 L -0.0603303939819822 0.096716 -0.6238 0.535492 0.267746 Wb 0.0318126126570365 0.036817 0.8641 0.391515 0.195758 Wbr -0.00602942557266054 0.024183 -0.2493 0.804091 0.402046 Tg 0.0505446567493215 0.085304 0.5925 0.55607 0.278035 P -36.4418346082895 43.88123 -0.8305 0.410073 0.205036 S -22.2453149809266 29.432912 -0.7558 0.453181 0.22659 D 45.6701835467499 58.506465 0.7806 0.438577 0.219288 Multiple Linear Regression - Regression Statistics Multiple R 0.758466158770888 R-squared 0.575270914000666 Adjusted R-squared 0.501760110654627 F-TEST (value) 7.82566490659452 F-TEST (DF numerator) 9 F-TEST (DF denominator) 52 p-value 3.50571223939333e-07 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 176.519122961762 Sum Squared Residuals 1620268.04010186 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 3.3 -11.9955409957943 15.2955409957943 2 8.3 6.52061674852568 1.77938325147432 3 12.5 -146.956985885365 159.456985885365 4 16.5 -164.128281529472 180.628281529472 5 3.9 77.7474462580329 -73.8474462580329 6 9.8 -2.48608148908987 12.2860814890899 7 19.7 34.5002522230462 -14.8002522230462 8 6.2 -13.5410144728643 19.7410144728643 9 14.5 8.44011403950065 6.05988596049935 10 9.7 36.0808524811404 -26.3808524811404 11 12.5 -39.2031237426272 51.7031237426272 12 3.9 -3.47424077292195 7.37424077292195 13 10.3 45.7000055732159 -35.4000055732159 14 3.1 -181.591044795955 184.691044795955 15 8.4 27.7992714626102 -19.3992714626102 16 8.6 15.2489418445866 -6.64894184458662 17 10.7 -7.79616002757208 18.4961600275721 18 10.7 22.2250464646873 -11.5250464646873 19 6.1 -49.7936134270408 55.8936134270408 20 18.1 -21.2263340713524 39.3263340713524 21 -999 -996.052861259797 -2.94713874020323 22 3.8 -21.3841400740765 25.1841400740765 23 14.4 2.86256778891819 11.5374322110818 24 12 -201.216986981437 213.216986981437 25 6.2 -5.75821860230515 11.9582186023051 26 13 -146.342378238904 159.342378238904 27 13.8 -24.6691938181456 38.4691938181456 28 8.2 -22.204767720574 30.404767720574 29 2.9 -2.45664589425919 5.35664589425919 30 10.8 -143.046868792969 153.846868792969 31 -999 -172.378571731787 -826.621428268213 32 9.1 -2.20547744780346 11.3054774478035 33 19.9 38.6221511252355 -18.7221511252355 34 8 27.3340666522057 -19.3340666522057 35 10.6 52.8694300272936 -42.2694300272936 36 11.2 108.403244560721 -97.2032445607211 37 13.2 14.9191788197142 -1.71917881971419 38 12.8 13.873086430901 -1.07308643090101 39 19.4 -5.64251196487524 25.0425119648752 40 17.4 2.32170593252762 15.0782940674724 41 -999 -1002.07453500624 3.07453500624458 42 17 28.2737291826044 -11.2737291826044 43 10.9 -1.47764428151898 12.3776442815190 44 13.7 41.0114954729491 -27.3114954729491 45 8.4 -3.58738088885917 11.9873808888592 46 8.4 -23.4991002819954 31.8991002819954 47 12.5 -159.743631532462 172.243631532462 48 13.2 48.9994083315792 -35.7994083315792 49 9.8 28.6093491204509 -18.8093491204509 50 9.6 -0.854676600010684 10.4546766000107 51 6.6 24.1690107914671 -17.5690107914671 52 5.4 33.0287650337228 -27.6287650337228 53 2.6 -194.616665994192 197.216665994192 54 3.8 -20.8910258833457 24.6910258833457 55 11 -158.249548194037 169.249548194037 56 10.3 -50.318109078764 60.618109078764 57 13.3 42.4168561649980 -29.1168561649979 58 5.4 53.9215238271743 -48.5215238271743 59 15.8 -14.9239482109909 30.7239482109909 60 10.3 22.6678973149941 -12.3678973149941 61 19.4 -7.1732023545494 26.5732023545494 62 -999 -220.705501628845 -778.294498371155 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 13 4.16801205372821e-06 8.33602410745642e-06 0.999995831987946 14 1.25546308987227e-07 2.51092617974454e-07 0.99999987445369 15 1.84722947368898e-09 3.69445894737795e-09 0.99999999815277 16 4.68965879079796e-11 9.37931758159592e-11 0.999999999953103 17 6.29727962316913e-13 1.25945592463383e-12 0.99999999999937 18 8.10391050064924e-15 1.62078210012985e-14 0.999999999999992 19 9.28543729192027e-17 1.85708745838405e-16 1 20 8.75316005089924e-17 1.75063201017985e-16 1 21 1.46987941491156e-18 2.93975882982313e-18 1 22 2.27548396957985e-20 4.5509679391597e-20 1 23 3.73571810586561e-22 7.47143621173122e-22 1 24 8.0697960900013e-24 1.61395921800026e-23 1 25 1.77787424560019e-25 3.55574849120039e-25 1 26 4.18166621544073e-27 8.36333243088147e-27 1 27 5.5588729728587e-29 1.11177459457174e-28 1 28 8.34998549637248e-31 1.66999709927450e-30 1 29 1.20029360022974e-32 2.40058720045949e-32 1 30 3.20543568152003e-34 6.41087136304007e-34 1 31 0.758999474758771 0.482001050482458 0.241000525241229 32 0.709799332586127 0.580401334827747 0.290200667413873 33 0.642440065298908 0.715119869402184 0.357559934701092 34 0.586651602015634 0.826696795968732 0.413348397984366 35 0.555966415653154 0.888067168693692 0.444033584346846 36 0.677087283394027 0.645825433211947 0.322912716605973 37 0.657573521588333 0.684852956823335 0.342426478411667 38 0.696814401526296 0.606371196947409 0.303185598473704 39 0.689570922259443 0.620858155481114 0.310429077740557 40 0.781162684711438 0.437674630577125 0.218837315288562 41 0.731358256950796 0.537283486098407 0.268641743049204 42 0.723922446830877 0.552155106338246 0.276077553169123 43 0.661395095627986 0.677209808744029 0.338604904372014 44 0.572894841299078 0.854210317401844 0.427105158700922 45 0.459794565654661 0.919589131309322 0.540205434345339 46 0.440810772228564 0.881621544457127 0.559189227771436 47 0.383869614464437 0.767739228928874 0.616130385535563 48 0.261401851952303 0.522803703904606 0.738598148047697 49 0.155761111819717 0.311522223639435 0.844238888180283 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 18 0.486486486486487 NOK 5% type I error level 18 0.486486486486487 NOK 10% type I error level 18 0.486486486486487 NOK

Charts produced by software:

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Parameters (Session):

par1 = 10 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 10 ; 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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