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: Sat, 19 Dec 2009 17:49:28 -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/Dec/20/t12612702516no3jw5khocrol5.htm/, Retrieved Sun, 20 Dec 2009 01:51:03 +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/2009/Dec/20/t12612702516no3jw5khocrol5.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 «

3016 0 2155 0 2172 0 2150 0 2533 0 2058 0 2160 0 2260 0 2498 0 2695 0 2799 0 2946 0 2930 0 2318 0 2540 0 2570 0 2669 0 2450 0 2842 0 3440 0 2678 0 2981 0 2260 0 2844 0 2546 0 2456 0 2295 0 2379 0 2479 0 2057 0 2280 0 2351 0 2276 0 2548 1 2311 1 2201 1 2725 1 2408 1 2139 1 1898 1 2537 1 2068 1 2063 1 2520 1 2434 1 2190 1 2794 1 2070 1 2615 1 2265 1 2139 1 2428 1 2137 1 1823 1 2063 1 1806 1 1758 1 2243 1 1993 1 1932 1 2465 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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation y[t] = + 2517.66666666667 -282.916666666667x[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) 2517.66666666667 53.144233 47.3742 0 0 x -282.916666666667 78.440805 -3.6068 0.000639 0.00032 Multiple Linear Regression - Regression Statistics Multiple R 0.425034404876779 R-squared 0.180654245328958 Adjusted R-squared 0.166767029148093 F-TEST (value) 13.0086723628510 F-TEST (DF numerator) 1 F-TEST (DF denominator) 59 p-value 0.000639218028440691 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 305.290375342617 Sum Squared Residuals 5498930.58333334 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 3016 2517.66666666666 498.333333333337 2 2155 2517.66666666667 -362.666666666667 3 2172 2517.66666666667 -345.666666666667 4 2150 2517.66666666667 -367.666666666667 5 2533 2517.66666666667 15.3333333333333 6 2058 2517.66666666667 -459.666666666667 7 2160 2517.66666666667 -357.666666666667 8 2260 2517.66666666667 -257.666666666667 9 2498 2517.66666666667 -19.6666666666667 10 2695 2517.66666666667 177.333333333333 11 2799 2517.66666666667 281.333333333333 12 2946 2517.66666666667 428.333333333333 13 2930 2517.66666666667 412.333333333333 14 2318 2517.66666666667 -199.666666666667 15 2540 2517.66666666667 22.3333333333333 16 2570 2517.66666666667 52.3333333333333 17 2669 2517.66666666667 151.333333333333 18 2450 2517.66666666667 -67.6666666666667 19 2842 2517.66666666667 324.333333333333 20 3440 2517.66666666667 922.333333333333 21 2678 2517.66666666667 160.333333333333 22 2981 2517.66666666667 463.333333333333 23 2260 2517.66666666667 -257.666666666667 24 2844 2517.66666666667 326.333333333333 25 2546 2517.66666666667 28.3333333333333 26 2456 2517.66666666667 -61.6666666666667 27 2295 2517.66666666667 -222.666666666667 28 2379 2517.66666666667 -138.666666666667 29 2479 2517.66666666667 -38.6666666666667 30 2057 2517.66666666667 -460.666666666667 31 2280 2517.66666666667 -237.666666666667 32 2351 2517.66666666667 -166.666666666667 33 2276 2517.66666666667 -241.666666666667 34 2548 2234.75 313.25 35 2311 2234.75 76.25 36 2201 2234.75 -33.75 37 2725 2234.75 490.25 38 2408 2234.75 173.25 39 2139 2234.75 -95.75 40 1898 2234.75 -336.75 41 2537 2234.75 302.25 42 2068 2234.75 -166.75 43 2063 2234.75 -171.75 44 2520 2234.75 285.25 45 2434 2234.75 199.25 46 2190 2234.75 -44.75 47 2794 2234.75 559.25 48 2070 2234.75 -164.75 49 2615 2234.75 380.25 50 2265 2234.75 30.25 51 2139 2234.75 -95.75 52 2428 2234.75 193.25 53 2137 2234.75 -97.75 54 1823 2234.75 -411.75 55 2063 2234.75 -171.75 56 1806 2234.75 -428.75 57 1758 2234.75 -476.75 58 2243 2234.75 8.25 59 1993 2234.75 -241.75 60 1932 2234.75 -302.75 61 2465 2234.75 230.25 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.891595246791472 0.216809506417057 0.108404753208528 6 0.880971868877563 0.238056262244874 0.119028131122437 7 0.834107359907165 0.331785280185669 0.165892640092835 8 0.758485572954811 0.483028854090378 0.241514427045189 9 0.685013551721007 0.629972896557985 0.314986448278993 10 0.685041540024699 0.629916919950602 0.314958459975301 11 0.723206500122375 0.55358699975525 0.276793499877625 12 0.815621144471736 0.368757711056528 0.184378855528264 13 0.859226703591893 0.281546592816213 0.140773296408107 14 0.82044242729353 0.35911514541294 0.17955757270647 15 0.757219641865392 0.485560716269216 0.242780358134608 16 0.687155109170378 0.625689781659243 0.312844890829622 17 0.628349047097825 0.743301905804349 0.371650952902175 18 0.548644978700333 0.902710042599335 0.451355021299667 19 0.555721789177099 0.888556421645801 0.444278210822901 20 0.94724914447294 0.105501711054121 0.0527508555270605 21 0.931147516920578 0.137704966158845 0.0688524830794224 22 0.961903818415758 0.0761923631684841 0.0380961815842421 23 0.954888173378979 0.0902236532420423 0.0451118266210212 24 0.965110657255577 0.069778685488846 0.034889342744423 25 0.953004706652284 0.093990586695432 0.046995293347716 26 0.935946765217729 0.128106469564543 0.0640532347822714 27 0.919229899180141 0.161540201639718 0.0807701008198588 28 0.893865753034297 0.212268493931406 0.106134246965703 29 0.867955825509379 0.264088348981242 0.132044174490621 30 0.882096511959724 0.235806976080551 0.117903488040276 31 0.852683844354748 0.294632311290505 0.147316155645252 32 0.81195329000153 0.376093419996939 0.188046709998469 33 0.770461039473286 0.459077921053428 0.229538960526714 34 0.750245483545229 0.499509032909543 0.249754516454771 35 0.696225992522312 0.607548014955377 0.303774007477688 36 0.635300011672201 0.729399976655598 0.364699988327799 37 0.720613094324097 0.558773811351807 0.279386905675903 38 0.67481029834571 0.650379403308581 0.325189701654291 39 0.621494145499451 0.757011709001098 0.378505854500549 40 0.647758775875968 0.704482448248065 0.352241224124032 41 0.647477281908312 0.705045436183376 0.352522718091688 42 0.593687786655344 0.812624426689312 0.406312213344656 43 0.535721035920664 0.928557928158673 0.464278964079336 44 0.530528959157399 0.938942081685203 0.469471040842601 45 0.490978619695723 0.981957239391445 0.509021380304277 46 0.405985891713414 0.811971783426828 0.594014108286586 47 0.684802259307937 0.630395481384126 0.315197740692063 48 0.60894301772732 0.78211396454536 0.39105698227268 49 0.765731427836984 0.468537144326032 0.234268572163016 50 0.71218782190786 0.575624356184281 0.287812178092141 51 0.620902090490984 0.758195819018032 0.379097909509016 52 0.691182279331287 0.617635441337427 0.308817720668714 53 0.596001501661979 0.807996996676043 0.403998498338021 54 0.548767779915692 0.902464440168616 0.451232220084308 55 0.407223768590516 0.814447537181032 0.592776231409484 56 0.357421369222171 0.714842738444342 0.642578630777829 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 4 0.0769230769230769 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') }

Copyright

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.

Privacy Policy

We may request personal information to be submitted to our servers in order to be able to:

• personalize online software applications according to your needs
• enforce strict security rules with respect to the data that you upload (e.g. statistical data)
• manage user sessions of online applications
• alert you about important changes or upgrades in resources or applications

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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