Multiple Regression- Ps: 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, 14 Dec 2010 09:50:13 +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/14/t129232024680b1pjqfhaxggsd.htm/, Retrieved Tue, 14 Dec 2010 10:51:03 +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/14/t129232024680b1pjqfhaxggsd.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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No (this computation is public)

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Dataseries X:

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6.3 2 4.5 1 6.6 42 3 1 3 2.1 1.8 69 2547 4603 624 3 5 4 9.1 0.7 27 10.55 179.5 180 4 4 4 15.8 3.9 19 0.023 0.3 35 1 1 1 5.2 1 30.4 160 169 392 4 5 4 10.9 3.6 28 3.3 25.6 63 1 2 1 8.3 1.4 50 52.16 440 230 1 1 1 11 1.5 7 0.42 6.4 112 5 4 4 3.2 0.7 30 465 423 281 5 5 5 6.3 2.1 3.5 0.075 1.2 42 1 1 1 6.6 4.1 6 0.785 3.5 42 2 2 2 9.5 1.2 10.4 0.2 5 120 2 2 2 3.3 0.5 20 27.66 115 148 5 5 5 11 3.4 3.9 0.12 1 16 3 1 2 4.7 1.5 41 85 325 310 1 3 1 10.4 3.4 9 0.101 4 28 5 1 3 7.4 0.8 7.6 1.04 5.5 68 5 3 4 2.1 0.8 46 521 655 336 5 5 5 17.9 2 24 0.1 0.25 50 1 1 1 6.1 1.9 100 62 1320 267 1 1 1 11.9 1.3 3.2 0.023 0.4 19 4 1 3 13.8 5.6 5 1.7 6.3 12 2 1 1 14.3 14.3 6.5 3.5 10.8 120 2 1 1 15.2 1.8 12 0.48 15.5 140 2 2 2 10 0.9 20.2 10 115 170 4 4 4 11.9 1.8 13 1.62 11.4 17 2 1 2 6.5 1.9 27 192 180 115 4 4 4 7.5 0.9 18 2.5 12.1 31 5 5 5 10.6 2.6 4.7 0.28 1.9 21 3 1 3 7.4 2.4 9.8 4.235 50.4 52 1 1 1 8.4 1.2 29 6.8 179 164 2 3 2 5.7 0.9 7 0.75 12.3 225 2 2 2 4.9 0.5 6 3.6 21 225 3 2 3 3.2 0.6 20 5 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 7 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation PS[t] = + 3.1953114478424 + 0.090823714491886SWS[t] -0.00941744275009553L[t] + 0.00306860442319590BW[t] -0.000795427276824133BRW[t] -0.000926904983833428Tg[t] + 1.80501265303085P[t] + 0.374434799750786S[t] -2.89072374549107D[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) 3.1953114478424 1.84695 1.73 0.093899 0.046949 SWS 0.090823714491886 0.121899 0.7451 0.462026 0.231013 L -0.00941744275009553 0.036499 -0.258 0.798153 0.399077 BW 0.00306860442319590 0.004331 0.7086 0.484065 0.242032 BRW -0.000795427276824133 0.002586 -0.3075 0.760556 0.380278 Tg -0.000926904983833428 0.005299 -0.1749 0.862313 0.431157 P 1.80501265303085 0.752305 2.3993 0.022842 0.011421 S 0.374434799750786 0.46588 0.8037 0.427884 0.213942 D -2.89072374549107 0.953311 -3.0323 0.004969 0.002484 Multiple Linear Regression - Regression Statistics Multiple R 0.680451393267708 R-squared 0.463014098599965 Adjusted R-squared 0.319817858226622 F-TEST (value) 3.23342356889252 F-TEST (DF numerator) 8 F-TEST (DF denominator) 30 p-value 0.0090051591885767 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.99725666621076 Sum Squared Residuals 119.6710257217 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 2 0.801312654211155 1.19868734578884 2 1.8 2.0365496751474 -0.236549675147398 3 0.7 0.64518280801302 0.0548171919869793 4 3.9 3.70750870713747 0.192491292862533 5 1 0.903836876775719 0.0961631232242814 6 3.6 3.51612848817098 0.0838715118290233 7 1.4 2.36388210654043 -0.963882106540434 8 1.5 2.98074241129233 -1.48074241129233 9 0.7 0.477017606398694 0.222982393601306 10 2.1 2.98360913008506 -0.883609130085062 11 4.1 2.27638557125173 1.82361442874827 12 1.2 2.42305073193597 -1.22305073193597 13 0.5 -0.393479088979977 0.893479088979977 14 3.4 4.1504118739016 -0.750411873901599 15 1.5 2.98863802600793 -1.48863802600793 16 3.4 4.7536228026311 -1.3536228026311 17 0.8 2.31709401230088 -1.51709401230088 18 0.8 0.162755381821027 0.637244618178973 19 2 3.83752377296687 -1.83752377296687 20 1.9 0.989121376670687 0.910878623329313 21 1.3 3.15043322119469 -1.85043322119469 22 5.6 5.48441043027081 0.115589569729190 23 14.3 5.41753445035364 8.88246554964636 24 1.8 2.89964711929473 -1.09964711929473 25 0.9 0.8498491385171 0.0501508614829003 26 1.8 2.33684539285956 -0.536845392859563 27 1.9 1.02569053323377 0.874309466766228 28 0.9 0.11990665999224 0.78009334000776 29 2.6 1.21096525565310 1.38903474434690 30 2.4 2.98854664924295 -0.588546649242949 31 1.2 2.36347963433092 -1.16347963433092 32 0.9 2.00849601222656 -1.10849601222656 33 0.5 0.861368696220661 -0.361368696220661 34 0.6 -0.367637864848339 0.967637864848339 35 2.3 2.30008576373919 -8.5763739192668e-05 36 0.5 0.497990807171823 0.00200919282817660 37 2.6 4.71067736583368 -2.11067736583368 38 0.6 0.402815505695254 0.197184494304746 39 6.6 5.41800030473758 1.18199969526242 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 12 0.171626708098684 0.343253416197367 0.828373291901316 13 0.0750712231122462 0.150142446224492 0.924928776887754 14 0.0325524904675182 0.0651049809350363 0.967447509532482 15 0.0118644030997789 0.0237288061995578 0.988135596900221 16 0.00443858894792217 0.00887717789584434 0.995561411052078 17 0.00296665469916431 0.00593330939832863 0.997033345300836 18 0.000984371014804933 0.00196874202960987 0.999015628985195 19 0.000792581141189964 0.00158516228237993 0.99920741885881 20 0.000283170652607621 0.000566341305215242 0.999716829347392 21 0.000285519278133202 0.000571038556266405 0.999714480721867 22 0.000487861980646209 0.000975723961292417 0.999512138019354 23 0.993512987542587 0.0129740249148252 0.00648701245741258 24 0.982793106938453 0.0344137861230949 0.0172068930615475 25 0.957719644480838 0.0845607110383247 0.0422803555191624 26 0.916859815779786 0.166280368440427 0.0831401842202136 27 0.86868591397197 0.262628172056058 0.131314086028029 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 7 0.4375 NOK 5% type I error level 10 0.625 NOK 10% type I error level 12 0.75 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 = 2 ; 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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This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

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