mul lin regr inv

*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: Thu, 18 Dec 2008 09:55:59 -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/Dec/18/t1229619412ks0qz7ghz47kxtq.htm/, Retrieved Thu, 18 Dec 2008 17:57:01 +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/2008/Dec/18/t1229619412ks0qz7ghz47kxtq.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}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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93.0 0 99.2 0 112.2 0 112.1 0 103.3 0 108.2 0 90.4 0 72.8 0 111.0 0 117.9 0 111.3 0 110.5 0 94.8 0 100.4 0 132.1 0 114.6 0 101.9 0 130.2 0 84.0 0 86.4 0 122.3 0 120.9 0 110.2 0 112.6 0 102.0 0 105.0 0 130.5 0 115.5 0 103.7 0 130.9 0 89.1 0 93.8 0 123.8 0 111.9 0 118.3 0 116.9 0 103.6 1 116.6 1 141.3 1 107.0 1 125.2 1 136.4 1 91.6 1 95.3 1 132.3 1 130.6 1 131.9 1 118.6 1 114.3 1 111.3 1 126.5 1 112.1 1 119.3 1 142.4 1 101.1 1 97.4 1 129.1 1 136.9 1 129.8 1 123.9 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 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation INV[t] = + 111.855 + 11.6125INVA[t] -14.9599999999999M1[t] -10M2[t] + 12.0200000000000M3[t] -4.23999999999999M4[t] -5.82M5[t] + 13.1200000000000M6[t] -25.26M7[t] -27.36M8[t] + 7.2M9[t] + 7.14000000000001M10[t] + 3.80000000000000M11[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) 111.855 2.951941 37.892 0 0 INVA 11.6125 1.693054 6.8589 0 0 M1 -14.9599999999999 4.06333 -3.6817 0.000597 0.000298 M2 -10 4.06333 -2.461 0.017582 0.008791 M3 12.0200000000000 4.06333 2.9582 0.004832 0.002416 M4 -4.23999999999999 4.06333 -1.0435 0.302064 0.151032 M5 -5.82 4.06333 -1.4323 0.158669 0.079335 M6 13.1200000000000 4.06333 3.2289 0.002269 0.001134 M7 -25.26 4.06333 -6.2166 0 0 M8 -27.36 4.06333 -6.7334 0 0 M9 7.2 4.06333 1.7719 0.082886 0.041443 M10 7.14000000000001 4.06333 1.7572 0.0854 0.0427 M11 3.80000000000000 4.06333 0.9352 0.354469 0.177234 Multiple Linear Regression - Regression Statistics Multiple R 0.928358869984951 R-squared 0.861850191479734 Adjusted R-squared 0.826577899942645 F-TEST (value) 24.4341990248491 F-TEST (DF numerator) 12 F-TEST (DF denominator) 47 p-value 3.33066907387547e-16 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 6.42468932935464 Sum Squared Residuals 1940.00175 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 93 96.8949999999997 -3.89499999999972 2 99.2 101.855 -2.65500000000003 3 112.2 123.875 -11.6750000000000 4 112.1 107.615 4.48500000000002 5 103.3 106.035 -2.73500000000003 6 108.2 124.975 -16.775 7 90.4 86.595 3.805 8 72.8 84.495 -11.6950000000001 9 111 119.055 -8.05500000000002 10 117.9 118.995 -1.09499999999997 11 111.3 115.655 -4.35500000000001 12 110.5 111.855 -1.35500000000000 13 94.8 96.895 -2.09500000000008 14 100.4 101.855 -1.45499999999999 15 132.1 123.875 8.225 16 114.6 107.615 6.98499999999999 17 101.9 106.035 -4.13499999999999 18 130.2 124.975 5.225 19 84 86.595 -2.59500000000000 20 86.4 84.495 1.90500000000001 21 122.3 119.055 3.245 22 120.9 118.995 1.90499999999999 23 110.2 115.655 -5.455 24 112.6 111.855 0.744999999999993 25 102 96.895 5.10499999999992 26 105 101.855 3.145 27 130.5 123.875 6.625 28 115.5 107.615 7.885 29 103.7 106.035 -2.33500000000000 30 130.9 124.975 5.92500000000001 31 89.1 86.595 2.50499999999999 32 93.8 84.495 9.305 33 123.8 119.055 4.745 34 111.9 118.995 -7.09500000000001 35 118.3 115.655 2.64499999999999 36 116.9 111.855 5.045 37 103.6 108.5075 -4.90750000000007 38 116.6 113.4675 3.1325 39 141.3 135.4875 5.81250000000002 40 107 119.2275 -12.2275 41 125.2 117.6475 7.55250000000001 42 136.4 136.5875 -0.187499999999984 43 91.6 98.2075 -6.6075 44 95.3 96.1075 -0.80749999999999 45 132.3 130.6675 1.63250000000002 46 130.6 130.6075 -0.00750000000001372 47 131.9 127.2675 4.63250000000001 48 118.6 123.4675 -4.8675 49 114.3 108.5075 5.79249999999993 50 111.3 113.4675 -2.16750000000000 51 126.5 135.4875 -8.9875 52 112.1 119.2275 -7.1275 53 119.3 117.6475 1.65250000000001 54 142.4 136.5875 5.81250000000002 55 101.1 98.2075 2.8925 56 97.4 96.1075 1.29250000000002 57 129.1 130.6675 -1.5675 58 136.9 130.6075 6.2925 59 129.8 127.2675 2.53250000000001 60 123.9 123.4675 0.432500000000012 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.915678365423827 0.168643269152347 0.0843216345761733 17 0.858680749608797 0.282638500782406 0.141319250391203 18 0.97870558215901 0.0425888356819791 0.0212944178409896 19 0.965989265494376 0.0680214690112474 0.0340107345056237 20 0.9704535585668 0.0590928828663985 0.0295464414331993 21 0.96518376727175 0.0696324654564999 0.0348162327282499 22 0.94007869266901 0.119842614661981 0.0599213073309905 23 0.936005495893123 0.127989008213755 0.0639945041068774 24 0.898873419638507 0.202253160722986 0.101126580361493 25 0.8759219653905 0.248156069218998 0.124078034609499 26 0.830388337142988 0.339223325714024 0.169611662857012 27 0.810823483619967 0.378353032760066 0.189176516380033 28 0.877012340586284 0.245975318827432 0.122987659413716 29 0.868263514480526 0.263472971038947 0.131736485519474 30 0.864823053344502 0.270353893310995 0.135176946655498 31 0.808006499321109 0.383987001357782 0.191993500678891 32 0.862153197388058 0.275693605223884 0.137846802611942 33 0.836812024917328 0.326375950165344 0.163187975082672 34 0.881883688999445 0.236232622001109 0.118116311000555 35 0.865598043688543 0.268803912622914 0.134401956311457 36 0.806147054403364 0.387705891193273 0.193852945596636 37 0.822883831277005 0.354232337445990 0.177116168722995 38 0.777528967130398 0.444942065739203 0.222471032869602 39 0.915418328023575 0.169163343952851 0.0845816719764255 40 0.922099255741884 0.155801488516233 0.0779007442581163 41 0.912639736351544 0.174720527296912 0.087360263648456 42 0.881253373149309 0.237493253701382 0.118746626850691 43 0.928761382369514 0.142477235260971 0.0712386176304856 44 0.839831799692888 0.320336400614224 0.160168200307112 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 1 0.0344827586206897 OK 10% type I error level 4 0.137931034482759 NOK

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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