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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: Mon, 24 Nov 2008 11:27:38 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Nov/24/t1227551307ax1i3ztjgs7yz9x.htm/, Retrieved Mon, 24 Nov 2008 18:28:27 +0000

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/2008/Nov/24/t1227551307ax1i3ztjgs7yz9x.htm/}, year = {2008}, } @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 = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

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Dataseries X:

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12300.00 0.00 12092.80 0.00 12380.80 0.00 12196.90 0.00 9455.00 0.00 13168.00 0.00 13427.90 0.00 11980.50 0.00 11884.80 0.00 11691.70 0.00 12233.80 0.00 14341.40 0.00 13130.70 0.00 12421.10 0.00 14285.80 0.00 12864.60 0.00 11160.20 0.00 14316.20 0.00 14388.70 0.00 14013.90 0.00 13419.00 0.00 12769.60 0.00 13315.50 0.00 15332.90 0.00 14243.00 0.00 13824.40 0.00 14962.90 0.00 13202.90 0.00 12199.00 0.00 15508.90 0.00 14199.80 0.00 15169.60 0.00 14058.00 0.00 13786.20 0.00 14147.90 0.00 16541.70 0.00 13587.50 0.00 15582.40 0.00 15802.80 0.00 14130.50 0.00 12923.20 0.00 15612.20 1.00 16033.70 1.00 16036.60 1.00 14037.80 1.00 15330.60 1.00 15038.30 1.00 17401.80 1.00 14992.50 1.00 16043.70 1.00 16929.60 1.00 15921.30 1.00 14417.20 1.00 15961.00 1.00 17851.90 1.00 16483.90 1.00 14215.50 1.00 17429.70 1.00 17839.50 1.00 17629.20 1.00

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 x[t] = + 15270.1496774194 + 2448.12580645161y[t] -2109.03483870968M1[t] -1766.89483870968M2[t] -887.394838709678M3[t] -2096.53483870968M4[t] -3728.85483870968M5[t] -1336.14M6[t] -1069M7[t] -1512.5M8[t] -2726.38M9[t] -2047.84M10[t] -1734.4M11[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) 15270.1496774194 510.020378 29.9403 0 0 y 2448.12580645161 313.895844 7.7992 0 0 M1 -2109.03483870968 701.892445 -3.0048 0.004253 0.002126 M2 -1766.89483870968 701.892445 -2.5173 0.015293 0.007646 M3 -887.394838709678 701.892445 -1.2643 0.21236 0.10618 M4 -2096.53483870968 701.892445 -2.987 0.004466 0.002233 M5 -3728.85483870968 701.892445 -5.3126 3e-06 1e-06 M6 -1336.14 699.079237 -1.9113 0.062077 0.031038 M7 -1069 699.079237 -1.5292 0.132929 0.066465 M8 -1512.5 699.079237 -2.1636 0.035615 0.017807 M9 -2726.38 699.079237 -3.9 0.000305 0.000152 M10 -2047.84 699.079237 -2.9293 0.005226 0.002613 M11 -1734.4 699.079237 -2.481 0.016738 0.008369 Multiple Linear Regression - Regression Statistics Multiple R 0.837890900854055 R-squared 0.70206116173402 Adjusted R-squared 0.625991671112919 F-TEST (value) 9.2292081358998 F-TEST (DF numerator) 12 F-TEST (DF denominator) 47 p-value 8.83679984742258e-09 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1105.34132769833 Sum Squared Residuals 57423634.183742 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 12300 13161.1148387097 -861.11483870969 2 12092.8 13503.2548387097 -1410.45483870968 3 12380.8 14382.7548387097 -2001.95483870968 4 12196.9 13173.6148387097 -976.714838709676 5 9455 11541.2948387097 -2086.29483870968 6 13168 13934.0096774194 -766.009677419355 7 13427.9 14201.1496774194 -773.249677419354 8 11980.5 13757.6496774194 -1777.14967741935 9 11884.8 12543.7696774194 -658.969677419356 10 11691.7 13222.3096774194 -1530.60967741935 11 12233.8 13535.7496774194 -1301.94967741936 12 14341.4 15270.1496774194 -928.749677419354 13 13130.7 13161.1148387097 -30.4148387096743 14 12421.1 13503.2548387097 -1082.15483870968 15 14285.8 14382.7548387097 -96.9548387096768 16 12864.6 13173.6148387097 -309.014838709677 17 11160.2 11541.2948387097 -381.094838709677 18 14316.2 13934.0096774194 382.190322580646 19 14388.7 14201.1496774194 187.550322580646 20 14013.9 13757.6496774194 256.250322580645 21 13419 12543.7696774194 875.230322580646 22 12769.6 13222.3096774194 -452.709677419355 23 13315.5 13535.7496774194 -220.249677419354 24 15332.9 15270.1496774194 62.7503225806451 25 14243 13161.1148387097 1081.88516129033 26 13824.4 13503.2548387097 321.145161290322 27 14962.9 14382.7548387097 580.145161290324 28 13202.9 13173.6148387097 29.2851612903226 29 12199 11541.2948387097 657.705161290322 30 15508.9 13934.0096774194 1574.89032258064 31 14199.8 14201.1496774194 -1.34967741935603 32 15169.6 13757.6496774194 1411.95032258065 33 14058 12543.7696774194 1514.23032258065 34 13786.2 13222.3096774194 563.890322580645 35 14147.9 13535.7496774194 612.150322580645 36 16541.7 15270.1496774194 1271.55032258065 37 13587.5 13161.1148387097 426.385161290326 38 15582.4 13503.2548387097 2079.14516129032 39 15802.8 14382.7548387097 1420.04516129032 40 14130.5 13173.6148387097 956.885161290322 41 12923.2 11541.2948387097 1381.90516129032 42 15612.2 16382.1354838710 -769.935483870967 43 16033.7 16649.2754838710 -615.575483870968 44 16036.6 16205.7754838710 -169.175483870968 45 14037.8 14991.8954838710 -954.095483870968 46 15330.6 15670.4354838710 -339.835483870968 47 15038.3 15983.8754838710 -945.575483870969 48 17401.8 17718.2754838710 -316.475483870969 49 14992.5 15609.2406451613 -616.740645161288 50 16043.7 15951.3806451613 92.31935483871 51 16929.6 16830.8806451613 98.7193548387086 52 15921.3 15621.7406451613 299.559354838709 53 14417.2 13989.4206451613 427.77935483871 54 15961 16382.1354838710 -421.135483870968 55 17851.9 16649.2754838710 1202.62451612903 56 16483.9 16205.7754838710 278.124516129033 57 14215.5 14991.8954838710 -776.395483870968 58 17429.7 15670.4354838710 1759.26451612903 59 17839.5 15983.8754838710 1855.62451612903 60 17629.2 17718.2754838710 -89.0754838709673 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.647059319474488 0.705881361051025 0.352940680525512 17 0.742957876071562 0.514084247856876 0.257042123928438 18 0.696594084519963 0.606811830960075 0.303405915480037 19 0.631636301049139 0.736727397901722 0.368363698950861 20 0.734339075805415 0.53132184838917 0.265660924194585 21 0.730852230198274 0.538295539603453 0.269147769801726 22 0.74138457459145 0.5172308508171 0.25861542540855 23 0.736255357445996 0.527489285108008 0.263744642554004 24 0.700140985148408 0.599718029703183 0.299859014851592 25 0.723331304749608 0.553337390500783 0.276668695250392 26 0.769004885042032 0.461990229915936 0.230995114957968 27 0.782373744617998 0.435252510764003 0.217626255382002 28 0.754057159120801 0.491885681758398 0.245942840879199 29 0.786439950174094 0.427120099651811 0.213560049825906 30 0.817948571611503 0.364102856776993 0.182051428388497 31 0.805114095100337 0.389771809799325 0.194885904899663 32 0.818110087280619 0.363779825438762 0.181889912719381 33 0.840602432533595 0.31879513493281 0.159397567466405 34 0.846348772157141 0.307302455685718 0.153651227842859 35 0.836245121307031 0.327509757385937 0.163754878692969 36 0.799442788412988 0.401114423174024 0.200557211587012 37 0.715576435223824 0.568847129552353 0.284423564776176 38 0.750136468699432 0.499727062601136 0.249863531300568 39 0.697376017964383 0.605247964071233 0.302623982035617 40 0.604894371788751 0.790211256422498 0.395105628211249 41 0.519285764739903 0.961428470520195 0.480714235260097 42 0.38648830066462 0.77297660132924 0.61351169933538 43 0.36982896699577 0.73965793399154 0.63017103300423 44 0.234466207190464 0.468932414380928 0.765533792809536 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 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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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