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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, 21 Dec 2010 19:11:04 +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/21/t129295855517cs0akbb9i9xww.htm/, Retrieved Tue, 21 Dec 2010 20:09:26 +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/21/t129295855517cs0akbb9i9xww.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}, }

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Dataseries X:

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25,4 23,4 11,5 9,9 8,1 27,9 25,4 23,4 11,5 9,9 26,1 27,9 25,4 23,4 11,5 18,8 26,1 27,9 25,4 23,4 14,1 18,8 26,1 27,9 25,4 11,5 14,1 18,8 26,1 27,9 15,8 11,5 14,1 18,8 26,1 12,4 15,8 11,5 14,1 18,8 4,5 12,4 15,8 11,5 14,1 -2,2 4,5 12,4 15,8 11,5 -4,2 -2,2 4,5 12,4 15,8 -9,4 -4,2 -2,2 4,5 12,4 -14,5 -9,4 -4,2 -2,2 4,5 -17,9 -14,5 -9,4 -4,2 -2,2 -15,1 -17,9 -14,5 -9,4 -4,2 -15,2 -15,1 -17,9 -14,5 -9,4 -15,7 -15,2 -15,1 -17,9 -14,5 -18 -15,7 -15,2 -15,1 -17,9 -18,1 -18 -15,7 -15,2 -15,1 -13,5 -18,1 -18 -15,7 -15,2 -9,9 -13,5 -18,1 -18 -15,7 -4,8 -9,9 -13,5 -18,1 -18 -1,7 -4,8 -9,9 -13,5 -18,1 -0,1 -1,7 -4,8 -9,9 -13,5 2,2 -0,1 -1,7 -4,8 -9,9 10,2 2,2 -0,1 -1,7 -4,8 7,6 10,2 2,2 -0,1 -1,7 10,8 7,6 10,2 2,2 -0,1 3,8 10,8 7,6 10,2 2,2 11 3,8 10,8 7,6 10,2 10,8 11 3,8 10,8 7,6 20,1 10,8 11 3,8 10,8 14,9 20,1 10,8 11 3,8 13 14,9 20,1 10,8 11 10,9 13 14,9 20,1 10,8 9,6 10,9 13 14,9 20,1 4 9,6 10,9 13 14,9 -1,1 4 9,6 10,9 13 -7,7 -1,1 4 9,6 10,9 -8,9 -7,7 -1,1 4 9,6 -8 -8,9 -7,7 - 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 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Ye[t] = -1.92302088502385 + 1.17077219512371`Ye-1`[t] + 0.192986133123134`Ye-2`[t] -0.75856833634634`Ye-3`[t] + 0.279150640338026`Ye-4`[t] + 2.42597534885396M1[t] + 2.08414450886024M2[t] + 2.76823136640609M3[t] + 0.787244547575236M4[t] + 0.448669555109071M5[t] + 2.10875014189562M6[t] + 2.54107952782004M7[t] + 3.63619152659933M8[t] -1.4954967014408M9[t] + 0.486246625640009M10[t] + 3.49851150920727M11[t] + 0.00449601425725426t + 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) -1.92302088502385 2.384285 -0.8065 0.424951 0.212475 `Ye-1` 1.17077219512371 0.145955 8.0215 0 0 `Ye-2` 0.192986133123134 0.197242 0.9784 0.334052 0.167026 `Ye-3` -0.75856833634634 0.207656 -3.653 0.000779 0.000389 `Ye-4` 0.279150640338026 0.154243 1.8098 0.078241 0.03912 M1 2.42597534885396 2.75884 0.8793 0.384741 0.19237 M2 2.08414450886024 2.764157 0.754 0.455503 0.227751 M3 2.76823136640609 2.776054 0.9972 0.324984 0.162492 M4 0.787244547575236 2.766462 0.2846 0.777521 0.38876 M5 0.448669555109071 2.777923 0.1615 0.872545 0.436273 M6 2.10875014189562 2.787292 0.7566 0.453979 0.22699 M7 2.54107952782004 2.748009 0.9247 0.360958 0.180479 M8 3.63619152659933 2.918006 1.2461 0.220347 0.110174 M9 -1.4954967014408 2.948789 -0.5072 0.614976 0.307488 M10 0.486246625640009 3.019172 0.1611 0.872905 0.436452 M11 3.49851150920727 3.024528 1.1567 0.25461 0.127305 t 0.00449601425725426 0.036684 0.1226 0.9031 0.45155 Multiple Linear Regression - Regression Statistics Multiple R 0.958437215457925 R-squared 0.91860189597474 Adjusted R-squared 0.884329010069368 F-TEST (value) 26.8025837833150 F-TEST (DF numerator) 16 F-TEST (DF denominator) 38 p-value 7.7715611723761e-16 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4.08094165586762 Sum Squared Residuals 632.855222346631 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 25.4 24.8741540318074 0.525845968192608 2 27.9 28.4636603949380 -0.563660394937972 3 26.1 23.884823842816 2.215176157184 4 18.8 22.0881643671574 -3.28816436715739 5 14.1 11.521953764734 2.57804623526601 6 11.5 8.33840188316596 3.16159811683404 7 15.8 9.8592624530671 5.9407375469329 8 12.4 17.0188984653756 -4.61889846537564 9 4.5 9.4011908255134 -4.9011908255134 10 -2.2 -2.50545853841261 0.305458538412611 11 -4.2 -5.07798170255863 0.877981702558626 12 -9.4 -7.16297099969426 -2.23702900030574 13 -14.5 -8.32936952262253 -6.17063047737747 14 -17.9 -15.9943430533023 -1.90565694669772 15 -15.1 -16.8843608555229 1.78436085552286 16 -15.2 -13.8217271807602 -1.37827281923985 17 -15.7 -12.5770581278830 -3.12294187211697 18 -18 -14.5902697566324 -3.40973024336757 19 -18.1 -16.0852348452157 -2.01476515478426 20 -13.5 -15.1952030537354 1.69520305373541 21 -9.9 -13.3510099298340 3.45100992983398 22 -4.8 -6.82844411282699 2.02844411282699 23 -1.7 -0.66332435185525 -1.03667564814475 24 -0.1 -0.990469828285689 0.890469828285689 25 2.2 1.04773784955574 1.15226215044426 26 10.2 2.78406330865110 7.4159366913489 27 7.6 12.9343494945208 -5.3343494945208 28 10.8 8.1596738985549 2.6403261014451 29 3.8 5.64380178062845 -1.84380178062845 30 11 3.93601143900503 7.06398856099497 31 10.8 8.29828337102829 2.50171662897171 32 20.1 16.7564975070327 3.34350249296727 33 14.9 15.0631429772159 -0.163142977215866 34 13 14.9177362196589 -1.91773621965886 35 10.9 7.59598639841947 3.30401360158053 36 9.6 7.81733194492033 1.78266805507967 37 4 8.31022508411245 -4.31022508411245 38 -1.1 2.22829128230821 -3.32829128230821 39 -7.7 -3.73486389396875 -3.96513610603125 40 -8.9 -10.5375936141867 1.63759361418674 41 -8 -11.2448527756834 3.2448527756834 42 -7.1 -5.17528180461411 -1.92471819538589 43 -5.3 -4.44318613162565 -0.856813868374348 44 -2.5 -2.08019291867295 -0.419807081327048 45 -2.4 -4.01332387289528 1.61332387289528 46 -2.9 -2.48383356841926 -0.416166431580736 47 -4.8 -1.65468034400559 -3.14531965599441 48 -7.2 -6.76389111694038 -0.436108883059623 49 1.7 -7.10274744285304 8.80274744285305 50 2.2 3.81832806740499 -1.61832806740499 51 13.4 8.10005141215481 5.29994858784519 52 12.3 11.9114825292346 0.388517470765397 53 13.7 14.556155358204 -0.856155358203993 54 4.4 9.29113823907555 -4.89113823907555 55 -2.5 3.07087515274601 -5.57087515274601 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 20 0.360360915840107 0.720721831680214 0.639639084159893 21 0.631424692687306 0.737150614625387 0.368575307312694 22 0.47494264445193 0.94988528890386 0.52505735554807 23 0.366354387217576 0.732708774435152 0.633645612782424 24 0.28052483254635 0.5610496650927 0.71947516745365 25 0.198689485001570 0.397378970003140 0.80131051499843 26 0.150104611147460 0.300209222294920 0.84989538885254 27 0.435771807719671 0.871543615439342 0.564228192280329 28 0.397665599347874 0.795331198695748 0.602334400652126 29 0.436228795471571 0.872457590943142 0.563771204528429 30 0.467146995014229 0.934293990028459 0.532853004985771 31 0.390996487073194 0.781992974146387 0.609003512926806 32 0.313838453647295 0.627676907294589 0.686161546352705 33 0.204497256465704 0.408994512931407 0.795502743534296 34 0.136491322618147 0.272982645236295 0.863508677381853 35 0.224531790061776 0.449063580123552 0.775468209938224 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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