review 7

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R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Tue, 24 Nov 2009 14:51:11 -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/Nov/24/t12590995393cybi4ez96hzge8.htm/, Retrieved Tue, 24 Nov 2009 22:52:31 +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/Nov/24/t12590995393cybi4ez96hzge8.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:

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Dataseries X:

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6,3 2,3 6,1 6,2 6,3 6,5 1,9 6,3 6,1 6,2 6,6 2 6,5 6,3 6,1 6,5 2,3 6,6 6,5 6,3 6,2 2,8 6,5 6,6 6,5 6,2 2,4 6,2 6,5 6,6 5,9 2,3 6,2 6,2 6,5 6,1 2,7 5,9 6,2 6,2 6,1 2,7 6,1 5,9 6,2 6,1 2,9 6,1 6,1 5,9 6,1 3 6,1 6,1 6,1 6,1 2,2 6,1 6,1 6,1 6,4 2,3 6,1 6,1 6,1 6,7 2,8 6,4 6,1 6,1 6,9 2,8 6,7 6,4 6,1 7 2,8 6,9 6,7 6,4 7 2,2 7 6,9 6,7 6,8 2,6 7 7 6,9 6,4 2,8 6,8 7 7 5,9 2,5 6,4 6,8 7 5,5 2,4 5,9 6,4 6,8 5,5 2,3 5,5 5,9 6,4 5,6 1,9 5,5 5,5 5,9 5,8 1,7 5,6 5,5 5,5 5,9 2 5,8 5,6 5,5 6,1 2,1 5,9 5,8 5,6 6,1 1,7 6,1 5,9 5,8 6 1,8 6,1 6,1 5,9 6 1,8 6 6,1 6,1 5,9 1,8 6 6 6,1 5,5 1,3 5,9 6 6 5,6 1,3 5,5 5,9 6 5,4 1,3 5,6 5,5 5,9 5,2 1,2 5,4 5,6 5,5 5,2 1,4 5,2 5,4 5,6 5,2 2,2 5,2 5,2 5,4 5,5 2,9 5,2 5,2 5,2 5,8 3,1 5,5 5,2 5,2 5,8 3,5 5,8 5,5 5,2 5,5 3,6 5,8 5,8 5,5 5,3 4,4 5,5 5,8 5,8 5,1 4,1 5,3 5,5 5,8 5,2 5,1 5,1 5,3 5,5 5,8 5,8 5,2 5,1 5,3 5,8 5,9 5,8 5,2 5,1 5,5 5,4 5,8 5,8 5,2 5 5,5 5,5 5,8 5,8 4,9 4,8 5 5,5 5,8 5,3 3,2 4,9 5 5,5 6,1 2,7 5,3 4,9 5 6,5 2,1 6,1 5,3 4,9 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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation WMan>25[t] = + 0.735025720431746 -0.0210343049789478Infl[t] + 1.53127463437046`Yt-1`[t] -0.87884453464065`Yt-2`[t] + 0.233796372880887`Yt-3`[t] + 0.189859756972755M1[t] + 0.174504533469675M2[t] -0.0105409561502874M3[t] + 0.0117568591029149M4[t] -0.0614529939498516M5[t] -0.0384070699885562M6[t] -0.143835756622776M7[t] + 0.191929657849674M8[t] -0.237988285451912M9[t] -0.0344461062204082M10[t] -0.0984258641635606M11[t] + 0.000182769755273578t + 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) 0.735025720431746 0.579241 1.2689 0.211795 0.105897 Infl -0.0210343049789478 0.020598 -1.0212 0.313303 0.156652 `Yt-1` 1.53127463437046 0.16145 9.4845 0 0 `Yt-2` -0.87884453464065 0.260262 -3.3768 0.001644 0.000822 `Yt-3` 0.233796372880887 0.174767 1.3378 0.188532 0.094266 M1 0.189859756972755 0.122122 1.5547 0.127903 0.063951 M2 0.174504533469675 0.130647 1.3357 0.189201 0.0946 M3 -0.0105409561502874 0.1385 -0.0761 0.939713 0.469856 M4 0.0117568591029149 0.138498 0.0849 0.932774 0.466387 M5 -0.0614529939498516 0.133945 -0.4588 0.648866 0.324433 M6 -0.0384070699885562 0.132947 -0.2889 0.774157 0.387078 M7 -0.143835756622776 0.131778 -1.0915 0.281584 0.140792 M8 0.191929657849674 0.127343 1.5072 0.139622 0.069811 M9 -0.237988285451912 0.135333 -1.7585 0.086304 0.043152 M10 -0.0344461062204082 0.13279 -0.2594 0.796655 0.398328 M11 -0.0984258641635606 0.12832 -0.767 0.447565 0.223783 t 0.000182769755273578 0.001993 0.0917 0.927386 0.463693 Multiple Linear Regression - Regression Statistics Multiple R 0.960363514089563 R-squared 0.922298079194454 Adjusted R-squared 0.891217310872236 F-TEST (value) 29.6742368024135 F-TEST (DF numerator) 16 F-TEST (DF denominator) 40 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.180375424468064 Sum Squared Residuals 1.30141175008137 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 6.3 6.24154564974555 0.0584543502544519 2 6.5 6.60554666103937 -0.105546661039375 3 6.6 6.52568689333466 0.0743131066653372 4 6.5 6.56597501793455 -0.0659750179345478 5 6.2 6.28817813982265 -0.0881781398226484 6 6.2 5.97170225597181 0.228297744028186 7 5.9 6.10883349269487 -0.208833492694868 8 6.1 5.90684665275561 0.193153347244389 9 6.1 6.04701976647558 0.0529802335244167 10 6.1 6.00063003567418 0.099369964325824 11 6.1 5.98148889156458 0.118511108435421 12 6.1 6.09692496946657 0.00307503053342833 13 6.4 6.2848640656967 0.115135934303295 14 6.7 6.71855684977056 -0.0185568497705628 15 6.9 6.72942315982481 0.170576840175186 16 7 6.86464422317945 0.135355776820546 17 7 6.85173519124251 0.14826480875749 18 6.8 6.82542498407961 -0.0254249840796129 19 6.4 6.43309691661887 -0.0330969166188734 20 5.9 6.33861444552023 -0.43861444552023 21 5.5 5.45012392456667 0.0498760754333326 22 5.5 5.38934616847113 0.110653831528873 23 5.6 5.56860252969064 0.0313974703093559 24 5.8 5.73102693888996 0.0689730611100418 25 5.9 6.13312964753433 -0.233129647534329 26 6.1 6.11659195708563 -0.0165919570856334 27 6.1 6.20527270719873 -0.105272707198725 28 6 6.07326059206927 -0.0732605920692655 29 6 5.89386531991090 0.106134680089095 30 5.9 6.00497846709154 -0.104978467091538 31 5.5 5.73374260197693 -0.233742601976932 32 5.6 5.54506538592054 0.0549346140794619 33 5.4 5.59661585237944 -0.196615852379442 34 5.2 5.3147863023736 -0.114786302373605 35 5.2 5.13967607053206 0.0603239294679375 36 5.2 5.35046689281969 -0.150466892819691 37 5.5 5.47902613148628 0.0209738685137202 38 5.8 5.91902920705382 -0.119029207053820 39 5.8 5.92148179511649 -0.121481795116494 40 5.5 5.74834450109915 -0.248344501099146 41 5.3 5.26924649537162 0.0307535046283756 42 5.1 5.25618391409998 -0.156183914099981 43 5.2 4.92927876043186 0.270721239568141 44 5.8 5.53264002696332 0.267359973036681 45 5.8 5.88492247550114 -0.084922475501142 46 5.5 5.59523749348109 -0.0952374934810924 47 5 5.21023250821271 -0.210232508212714 48 4.9 4.82158119882378 0.0784188011762216 49 5.3 5.26143450553714 0.0385654944628619 50 6.1 5.84027532505061 0.259724674949391 51 6.5 6.5181354445253 -0.0181354445253040 52 6.8 6.54777566571759 0.252224334282413 53 6.6 6.79697485365231 -0.196974853652312 54 6.4 6.34171037875706 0.0582896212429455 55 6.4 6.19504822827747 0.204951771722533 56 6.6 6.6768334888403 -0.0768334888403017 57 6.7 6.52131798107717 0.178682018922835 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 20 0.492579542751354 0.985159085502707 0.507420457248646 21 0.328504893616433 0.657009787232867 0.671495106383567 22 0.484608631307898 0.969217262615796 0.515391368692102 23 0.485120309768121 0.970240619536242 0.514879690231879 24 0.477950289256308 0.955900578512616 0.522049710743692 25 0.640447559412129 0.719104881175742 0.359552440587871 26 0.527190048967293 0.945619902065413 0.472809951032707 27 0.467190626800216 0.934381253600433 0.532809373199784 28 0.397257061499041 0.794514122998083 0.602742938500959 29 0.592279926467327 0.815440147065347 0.407720073532673 30 0.844681729036644 0.310636541926712 0.155318270963356 31 0.820714459297493 0.358571081405015 0.179285540702507 32 0.835212288403651 0.329575423192698 0.164787711596349 33 0.742878210279851 0.514243579440298 0.257121789720149 34 0.63775558575543 0.724488828489139 0.362244414244570 35 0.623366764594652 0.753266470810696 0.376633235405348 36 0.562052774481022 0.875894451037956 0.437947225518978 37 0.414051754613009 0.828103509226017 0.585948245386991 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 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = 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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