regression PS

*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 18:55:16 +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/t1292353034o0sfsdpbvcspwir.htm/, Retrieved Tue, 14 Dec 2010 19:57:14 +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/t1292353034o0sfsdpbvcspwir.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:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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6654000 5712000 -999.0 3.3 38.6 645.0 3 5 3 1000 6600 2.0 8.3 4.5 42.0 3 1 3 3385 44500 -999.0 12.5 14.0 60.0 1 1 1 .920 5700 -999.0 16.5 -999.0 25.0 5 2 3 2547000 4603000 1.8 3.9 69.0 624.0 3 5 4 10550 179500 .7 9.8 27.0 180.0 4 4 4 .023 .300 3.9 19.7 19.0 35.0 1 1 1 160000 169000 1.0 6.2 30.4 392.0 4 5 4 3300 25600 3.6 14.5 28.0 63.0 1 2 1 52160 440000 1.4 9.7 50.0 230.0 1 1 1 .425 6400 1.5 12.5 7.0 112.0 5 4 4 465000 423000 .7 3.9 30.0 281.0 5 5 5 .550 2400 2.7 10.3 -999.0 -999.0 2 1 2 187100 419000 -999.0 3.1 40.0 365.0 5 5 5 .075 1200 2.1 8.4 3.5 42.0 1 1 1 3000 25000 .0 8.6 50.0 28.0 2 2 2 .785 3500 4.1 10.7 6.0 42.0 2 2 2 .200 5000 1.2 10.7 10.4 120.0 2 2 2 1410 17500 1.3 6.1 34.0 -999.0 1 2 1 60000 81000 6.1 18.1 7.0 -999.0 1 1 1 529000 680000 .3 -999.0 28.0 400.0 5 5 5 27660 115000 .5 3.8 20.0 148.0 5 5 5 .120 1000 3.4 14.4 3.9 16.0 3 1 2 207000 406000 -999.0 12.0 39.3 252.0 1 4 1 85000 325000 1.5 6.2 41.0 310.0 1 3 1 36330 119500 -999.0 13.0 16.2 63.0 1 1 1 .101 4000 3.4 13 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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation PS[t] = -244.529665049594 -0.000242637461065961bowgth[t] + 0.000196998343894375brwght[t] + 0.301538779457337TS[t] + 0.184093912577121LIFESPAN[t] -0.157429661772659DRAAGTIJD[t] -30.6168396497268PRED[t] -103.669940902568Exposure[t] + 160.603410887734OverallD[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) -244.529665049594 116.124698 -2.1058 0.03998 0.01999 bowgth -0.000242637461065961 0.000159 -1.528 0.132457 0.066229 brwght 0.000196998343894375 0.000159 1.2351 0.222238 0.111119 TS 0.301538779457337 0.206867 1.4576 0.150839 0.07542 LIFESPAN 0.184093912577121 0.209186 0.88 0.382806 0.191403 DRAAGTIJD -0.157429661772659 0.187617 -0.8391 0.405182 0.202591 PRED -30.6168396497268 95.92979 -0.3192 0.750861 0.37543 Exposure -103.669940902568 61.459279 -1.6868 0.097519 0.048759 OverallD 160.603410887734 122.57462 1.3103 0.195761 0.097881 Multiple Linear Regression - Regression Statistics Multiple R 0.437155435075075 R-squared 0.191104874415678 Adjusted R-squared 0.0690074969689877 F-TEST (value) 1.56518410478651 F-TEST (DF numerator) 8 F-TEST (DF denominator) 53 p-value 0.157740646773758 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 384.691125735455 Sum Squared Residuals 7843324.89763942 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 -999 -955.615810302327 -43.3841896976729 2 2 39.5368080521380 -37.5368080521380 3 -999 -213.367166403626 -785.632833596374 4 -999 -304.891015454242 -694.108984545758 5 1.8 -7.88810908830689 9.6881090883069 6 0.7 -126.873489633856 127.573489633856 7 3.9 -214.284921063081 218.184921063081 8 1 -302.708790302711 303.708790302711 9 3.6 -318.031648471931 321.631648471931 10 1.4 -168.268933787950 169.668933787950 11 1.5 -181.193527064841 182.693527064841 12 0.7 -179.981549641668 180.681549641668 13 2.7 -111.285538026651 113.985538026651 14 -999 -124.964976073713 -874.035023926287 15 2.1 -221.411446252281 223.511446252281 16 0 -180.309459561999 180.309459561999 17 4.1 -193.488118024287 197.588118024287 18 1.2 -204.661978968459 205.861978968459 19 1.3 -153.406811725476 154.706811725476 20 6.1 -52.7956751155638 58.8956751155638 21 0.3 -466.397332262899 466.697332262899 22 0.5 -115.474920326501 115.974920326501 23 3.4 -116.105083803601 119.505083803601 24 -999 -528.286402890337 -470.713597109663 25 1.5 -421.538443245452 423.038443245452 26 -999 -206.502494754286 -792.497505245714 27 3.4 -17.2755528283292 20.6755528283292 28 0.8 -72.2123797964895 73.0123797964895 29 0.8 -153.880299253587 154.680299253587 30 -999 -219.910684546733 -779.089315453267 31 -999 -513.208337581271 -485.791662418729 32 1.4 37.2978341518032 -35.8978341518032 33 2 -215.665595366524 217.665595366524 34 1.9 5.56923844040173 -3.66923844040173 35 2.4 -433.675306389444 436.075306389444 36 2.8 -144.588685339426 147.388685339426 37 1.3 12.7215901662120 -11.4215901662120 38 2 10.6483158240167 -8.64831582401667 39 5.6 -243.120102538073 248.720102538073 40 3.1 -259.999697581963 263.099697581963 41 1 -443.238365651673 444.238365651673 42 1.8 -203.547912960806 205.347912960806 43 0.9 -138.792281541852 139.692281541852 44 1.8 -82.5257571507456 84.3257571507456 45 1.9 -160.990784048345 162.890784048345 46 0.9 -110.203130405062 111.103130405062 47 -999 -188.841246077261 -810.15875392274 48 2.6 43.6738670574933 -41.0738670574933 49 2.4 -212.739029859733 215.139029859733 50 1.2 -279.538545242627 280.738545242627 51 0.9 -221.6163672933 222.5163672933 52 0.5 -91.3351637930795 91.8351637930795 53 -999 -116.900441475076 -882.099558524924 54 0.6 -110.882335594233 111.482335594233 55 -999 -198.287367821307 -800.712632178693 56 2.2 42.3760908930892 -40.1760908930892 57 2.3 -92.3213774887169 94.6213774887169 58 0.5 15.2209938684948 -14.7209938684948 59 2.6 -224.074809130191 226.674809130191 60 0.6 -50.7200754632581 51.3200754632581 61 6.6 -244.712693142038 251.312693142038 62 -999 -581.906770846459 -417.093229153541 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 12 0.738338079559527 0.523323840880946 0.261661920440473 13 0.706152229702804 0.587695540594392 0.293847770297196 14 0.931539562463506 0.136920875072987 0.0684604375364935 15 0.905051805092775 0.18989638981445 0.094948194907225 16 0.852702708362963 0.294594583274074 0.147297291637037 17 0.790664940145131 0.418670119709737 0.209335059854869 18 0.728653357518112 0.542693284963776 0.271346642481888 19 0.705103488120435 0.589793023759131 0.294896511879565 20 0.663953060517205 0.672093878965589 0.336046939482794 21 0.607221239578175 0.78555752084365 0.392778760421825 22 0.518437610700273 0.963124778599454 0.481562389299727 23 0.463500128903553 0.927000257807106 0.536499871096447 24 0.521583640646114 0.956832718707772 0.478416359353886 25 0.541915498084073 0.916169003831854 0.458084501915927 26 0.773264387518016 0.453471224963968 0.226735612481984 27 0.712184843038033 0.575630313923933 0.287815156961967 28 0.634968238140517 0.730063523718965 0.365031761859483 29 0.570093223542002 0.859813552915995 0.429906776457998 30 0.854514200233432 0.290971599533136 0.145485799766568 31 0.872425034899589 0.255149930200822 0.127574965100411 32 0.822144200623933 0.355711598752134 0.177855799376067 33 0.782858684414224 0.434282631171552 0.217141315585776 34 0.785261126785605 0.429477746428789 0.214738873214395 35 0.79041605527593 0.419167889448139 0.209583944724069 36 0.73318987640567 0.533620247188659 0.266810123594329 37 0.662372641460726 0.675254717078548 0.337627358539274 38 0.601323200947907 0.797353598104185 0.398676799052093 39 0.521845532732993 0.956308934534014 0.478154467267007 40 0.438933411080906 0.877866822161811 0.561066588919094 41 0.394232256878251 0.788464513756502 0.605767743121749 42 0.350226636135575 0.70045327227115 0.649773363864425 43 0.278223101395908 0.556446202791816 0.721776898604092 44 0.204669113247342 0.409338226494684 0.795330886752658 45 0.139520873755176 0.279041747510352 0.860479126244824 46 0.399583346961828 0.799166693923656 0.600416653038172 47 0.573012999739444 0.853974000521112 0.426987000260556 48 0.449834944589286 0.899669889178573 0.550165055410714 49 0.314433862522383 0.628867725044765 0.685566137477617 50 0.205830408578058 0.411660817156116 0.794169591421942 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 = 3 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 3 ; 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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