*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, 01 Dec 2010 19:23:20 +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/01/t1291231462xj5i0qhl8i0mxu1.htm/, Retrieved Wed, 01 Dec 2010 20:24:22 +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/01/t1291231462xj5i0qhl8i0mxu1.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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2 1 2 14 3 6 3 6 2 4 2 4 2 2 4 18 5 10 4 8 1 2 2 4 2 3 6 11 3 6 2 4 2 4 4 8 1 4 4 12 3 3 2 2 2 2 3 3 2 5 10 16 4 8 4 8 1 2 3 6 2 6 12 18 5 10 4 8 1 2 2 4 2 7 14 14 4 8 4 8 2 4 4 8 2 8 16 14 4 8 4 8 3 6 3 6 2 9 18 15 4 8 3 6 2 4 2 4 2 10 20 15 4 8 3 6 2 4 2 4 1 11 11 17 4 4 5 5 2 2 2 2 2 12 24 19 5 10 4 8 1 2 1 2 1 13 13 10 2 2 2 2 4 4 2 2 2 14 28 16 4 8 3 6 2 4 1 2 2 15 30 18 5 10 5 10 2 4 2 4 1 16 16 14 4 4 4 4 3 3 3 3 1 17 17 14 4 4 3 3 3 3 2 2 2 18 36 17 4 8 4 8 1 2 2 4 1 19 19 14 4 4 2 2 1 1 3 3 2 20 40 16 5 10 3 6 2 4 2 4 1 21 21 18 4 4 4 4 1 1 1 1 2 22 44 11 3 6 2 4 3 6 3 6 2 23 46 14 3 6 5 10 2 4 4 8 2 24 48 12 3 6 3 6 3 6 3 6 1 25 25 17 5 5 4 4 2 2 2 2 2 26 52 9 2 4 3 6 4 8 4 8 1 27 27 16 4 4 4 4 2 2 2 2 2 28 56 14 4 8 4 8 2 4 4 8 2 29 58 15 4 8 4 8 2 4 3 6 1 30 30 11 3 3 2 2 2 2 4 4 2 31 62 16 4 8 4 8 2 4 2 4 1 32 32 13 3 3 4 4 3 3 3 3 2 33 66 17 4 8 4 8 2 4 1 2 2 34 68 15 4 8 3 6 2 4 2 4 1 35 35 14 4 4 4 4 3 3 3 3 1 36 36 16 4 4 4 4 2 2 2 2 1 37 37 9 2 2 3 3 4 4 4 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 R Framework error message Warning: there are blank lines in the 'Data X' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values. Multiple Linear Regression - Estimated Regression Equation PSS[t] = + 14.7010144744564 -0.213486826461162G[t] + 0.0485974878790153T[t] -0.0288204218007257`T-G`[t] + 0.696344101971695HPP[t] -0.142272713875854`HPP-G`[t] -0.655973025889067TGYW[t] + 1.06170320950822`TGYW-G`[t] -0.789069557634572POP[t] -0.157775203711889`POP-G`[t] -0.294494920037662IDT[t] -0.584187019346881`IDT-G `[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) 14.7010144744564 0.619659 23.7244 0 0 G -0.213486826461162 0.01374 -15.5372 0 0 T 0.0485974878790153 0.017017 2.8558 0.006081 0.00304 `T-G` -0.0288204218007257 0.01082 -2.6636 0.010168 0.005084 HPP 0.696344101971695 0.156934 4.4372 4.5e-05 2.3e-05 `HPP-G` -0.142272713875854 0.100438 -1.4165 0.162365 0.081182 TGYW -0.655973025889067 0.145994 -4.4932 3.7e-05 1.9e-05 `TGYW-G` 1.06170320950822 0.101758 10.4336 0 0 POP -0.789069557634572 0.110111 -7.1661 0 0 `POP-G` -0.157775203711889 0.110529 -1.4275 0.159206 0.079603 IDT -0.294494920037662 0.134578 -2.1883 0.032995 0.016497 `IDT-G ` -0.584187019346881 0.094525 -6.1802 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.99123303097312 R-squared 0.98254292169216 Adjusted R-squared 0.978986850185008 F-TEST (value) 276.300102434920 F-TEST (DF numerator) 11 F-TEST (DF denominator) 54 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.801797935945067 Sum Squared Residuals 34.7155162246316 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 14 14.7677158202741 -0.767715820274149 2 18 18.1543231711774 -0.154323171177378 3 11 10.3564577982390 0.643542201760957 4 12 12.5105751029876 -0.51057510298765 5 16 16.2525254710587 -0.252525471058658 6 18 18.1181497482876 -0.118149748287631 7 14 13.666949835824 0.333050164175989 8 14 14.0161554737746 -0.0161554737746486 9 15 15.1071676487146 -0.107167648714623 10 15 15.0981242929922 -0.0981242929921869 11 17 15.2989584438735 1.70104155612650 12 19 19.5267585726844 -0.526758572684439 13 10 11.1194897262880 -1.11948972628803 14 16 16.5248198288339 -0.524819828833866 15 18 18.3995729748547 -0.39957297485472 16 14 13.1665868899148 0.833413110085201 17 14 13.6593157117585 0.340684288241517 18 17 17.5978308053984 -0.597830805398411 19 14 14.3081472436043 -0.308147243604294 20 16 15.4194894099878 0.580510590012188 21 18 16.9165256217683 1.08347437823174 22 11 10.5428830331858 0.457116966814171 23 14 14.5778908631724 -0.57789086317241 24 12 11.9922297148683 0.0077702851316808 25 17 15.7241785734463 1.27582142655375 26 9 8.99485540541368 0.00514459458631516 27 16 15.209661317507 0.790338682493012 28 14 13.4770393656529 0.522960634347149 29 15 14.9308649686618 0.0691350313381611 30 11 12.1460968816386 -1.14609688163863 31 16 16.3756472159484 -0.375647215948391 32 13 12.9289485590716 0.0710514409284098 33 17 17.8204294632349 -0.820429463234943 34 15 14.8810837556537 0.118916244346281 35 14 13.5423511454023 0.4576488545977 36 16 15.3876549122116 0.612345087788406 37 9 10.2425056170170 -1.24250561701704 38 15 15.0214788607490 -0.0214788607490249 39 17 16.7150990443889 0.284900955611112 40 13 13.019002265736 -0.0190022657359885 41 15 14.5396954812566 0.46030451874342 42 16 16.2761703030016 -0.276170303001593 43 16 15.133321001509 0.866678998491 44 12 12.2194285906646 -0.219428590664604 45 12 11.8195085731143 0.180491426885667 46 3 3.14523108604716 -0.145231086047158 47 4 4.34565707400495 -0.345657074004954 48 4 6.20001989471674 -2.20001989471674 49 5 6.31841452002216 -1.31841452002216 50 4 4.04033402058695 -0.0403340205869518 51 3 4.07603987631705 -1.07603987631705 52 3 4.47411808649622 -1.47411808649622 53 4 4.67418624008053 -0.674186240080527 54 3 3.74735705978176 -0.74735705978176 55 4 3.7166330890825 0.283366910917499 56 4 3.29903041767677 0.700969582323229 57 4 3.67035405093384 0.329645949066157 58 3 2.77438143743493 0.225618562565073 59 3 2.61371006879986 0.386289931200144 60 3 2.5889476795104 0.411052320489598 61 3 3.14973924232481 -0.149739242324807 62 4 2.78656573322439 1.21343426677561 63 4 3.78484745566502 0.215152544334983 64 4 3.62140566148015 0.378594338519852 65 4 2.60626164266918 1.39373835733082 66 3 1.86310115834165 1.13689884165835 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 15 1.00489494034282e-45 2.00978988068565e-45 1 16 1.83697553139090e-60 3.67395106278181e-60 1 17 3.49914216649658e-74 6.99828433299317e-74 1 18 2.87745481376475e-88 5.7549096275295e-88 1 19 7.88047576183506e-102 1.57609515236701e-101 1 20 4.41833035673249e-120 8.83666071346498e-120 1 21 4.89965276183681e-138 9.79930552367363e-138 1 22 1.34370497216944e-146 2.68740994433888e-146 1 23 4.70916751899335e-162 9.4183350379867e-162 1 24 5.54879927060798e-178 1.10975985412160e-177 1 25 1.59002359740615e-196 3.1800471948123e-196 1 26 1.14650321024298e-203 2.29300642048595e-203 1 27 8.15242740362624e-223 1.63048548072525e-222 1 28 1.99638093890283e-235 3.99276187780566e-235 1 29 1.09407494592744e-249 2.18814989185488e-249 1 30 6.03313659772278e-258 1.20662731954456e-257 1 31 3.5188664351616e-288 7.0377328703232e-288 1 32 7.22277340874178e-290 1.44455468174836e-289 1 33 2.32677969909686e-308 4.65355939819372e-308 1 34 5.61209167111072e-320 1.12241833422214e-319 1 35 0 0 1 36 0 0 1 37 0 0 1 38 0 0 1 39 0 0 1 40 0 0 1 41 0 0 1 42 0 0 1 43 0 0 1 44 0 0 1 45 1 4.02811470584559e-128 2.01405735292280e-128 46 1 4.784238973527e-118 2.3921194867635e-118 47 1 9.31144006844364e-100 4.65572003422182e-100 48 1 2.25907481145191e-88 1.12953740572596e-88 49 1 1.42351471209035e-75 7.11757356045177e-76 50 1 1.12677186633582e-60 5.63385933167909e-61 51 1 1.03964351399275e-44 5.19821756996373e-45 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 37 1 NOK 5% type I error level 37 1 NOK 10% type I error level 37 1 NOK

Charts produced by software:

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Parameters (Session):

par1 = 4 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 4 ; 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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