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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: Wed, 02 Dec 2009 11:37:08 -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/Dec/02/t1259779126midcyhsa5gecrn5.htm/, Retrieved Wed, 02 Dec 2009 19:38:59 +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/Dec/02/t1259779126midcyhsa5gecrn5.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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No (this computation is public)

User-defined keywords:

Dataseries X:

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656 677 825 696 627 0 785 656 677 825 696 0 412 785 656 677 825 0 352 412 785 656 677 0 839 352 412 785 656 0 729 839 352 412 785 0 696 729 839 352 412 0 641 696 729 839 352 0 695 641 696 729 839 0 638 695 641 696 729 0 762 638 695 641 696 0 635 762 638 695 641 0 721 635 762 638 695 0 854 721 635 762 638 0 418 854 721 635 762 0 367 418 854 721 635 0 824 367 418 854 721 0 687 824 367 418 854 0 601 687 824 367 418 0 676 601 687 824 367 0 740 676 601 687 824 0 691 740 676 601 687 0 683 691 740 676 601 0 594 683 691 740 676 0 729 594 683 691 740 0 731 729 594 683 691 0 386 731 729 594 683 0 331 386 731 729 594 0 707 331 386 731 729 0 715 707 331 386 731 0 657 715 707 331 386 0 653 657 715 707 331 0 642 653 657 715 707 0 643 642 653 657 715 0 718 643 642 653 657 0 654 718 643 642 653 0 632 654 718 643 642 0 731 632 654 718 643 0 392 731 632 654 718 0 344 392 731 632 654 0 792 344 392 731 632 0 852 792 344 392 731 0 649 852 792 344 392 0 629 649 852 792 344 0 685 629 649 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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y(t)[t] = + 498.427859024053 + 0.130784812235800`Y(t-1)`[t] + 0.0162915608389134`Y(t-2)`[t] + 0.263994243417347`Y(t-3)`[t] -0.219932791022093`Y(t-4)`[t] + 59.7224027781905X[t] + 47.4989221017373M1[t] + 150.105502994404M2[t] -201.549014116771M3[t] -255.564897907489M4[t] + 196.293610116600M5[t] + 211.074911954083M6[t] + 48.6418087775556M7[t] -47.9260020233859M8[t] + 65.6461246792301M9[t] + 32.5833805008135M10[t] + 89.4593062550886M11[t] -0.262984632943971t + 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) 498.427859024053 216.524119 2.302 0.026911 0.013456 `Y(t-1)` 0.130784812235800 0.166603 0.785 0.437315 0.218657 `Y(t-2)` 0.0162915608389134 0.159149 0.1024 0.919004 0.459502 `Y(t-3)` 0.263994243417347 0.167897 1.5724 0.124158 0.062079 `Y(t-4)` -0.219932791022093 0.171296 -1.2839 0.206939 0.103469 X 59.7224027781905 31.475611 1.8974 0.065391 0.032695 M1 47.4989221017373 41.654504 1.1403 0.261295 0.130647 M2 150.105502994404 37.212849 4.0337 0.000255 0.000128 M3 -201.549014116771 40.935964 -4.9235 1.7e-05 8e-06 M4 -255.564897907489 67.716821 -3.774 0.000549 0.000274 M5 196.293610116600 78.488621 2.5009 0.016816 0.008408 M6 211.074911954083 75.453002 2.7974 0.008041 0.004021 M7 48.6418087775556 82.446848 0.59 0.558698 0.279349 M8 -47.9260020233859 65.654753 -0.73 0.469885 0.234942 M9 65.6461246792301 47.533881 1.381 0.175335 0.087668 M10 32.5833805008135 41.874409 0.7781 0.441316 0.220658 M11 89.4593062550886 40.880254 2.1883 0.034864 0.017432 t -0.262984632943971 0.709166 -0.3708 0.712819 0.356409 Multiple Linear Regression - Regression Statistics Multiple R 0.955072487884467 R-squared 0.912163457113825 Adjusted R-squared 0.872868161612115 F-TEST (value) 23.2130448560728 F-TEST (DF numerator) 17 F-TEST (DF denominator) 38 p-value 5.32907051820075e-15 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 52.8072951092583 Sum Squared Residuals 105967.195836739 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 656 693.487785516207 -37.4877855162073 2 785 809.553644535133 -24.5536445351328 3 412 406.722782724199 5.27721727580146 4 352 332.768964644308 19.2310353556923 5 839 809.114493120692 29.885506879308 6 729 759.50633739721 -30.5063373972103 7 696 656.553186816552 39.4468131834482 8 641 695.375584892178 -54.3755848921782 9 695 664.80730477753 30.1926952224705 10 638 653.12871696042 -15.1287169604194 11 762 695.904766785386 66.0952332146137 12 635 647.823166297527 -12.8231662975268 13 721 653.545543566417 67.454456433583 14 854 810.339060723886 43.6609392761136 15 418 416.418078238534 1.58192176146643 16 367 357.918778665335 9.08122133466464 17 824 811.938170453296 12.0618295467042 18 687 741.041725910909 -54.0417259109090 19 601 650.300352599864 -49.3003525998645 20 676 671.852061062623 4.14793893737662 21 740 656.892492972561 83.1075070274392 22 691 640.586146643345 50.4138533566552 23 683 730.547080143013 -47.5470801430132 24 594 639.380896528041 -45.3808965280408 25 729 647.835236668273 81.1647633317275 26 731 775.049586477908 -44.0495864779083 27 386 403.856989735548 -17.8569897355479 28 331 359.70318547452 -28.7031854745202 29 707 769.322017402124 -62.3220174021237 30 715 740.601508600154 -25.6015086001542 31 657 646.434455678669 10.5655443213312 32 653 653.506612652956 -0.506612652955813 33 642 684.76492946806 -42.7649294680594 34 643 632.864273032367 10.1357269676335 35 718 701.128916702317 16.8710832976826 36 654 619.207572779306 34.7924272206937 37 632 661.978404272587 -29.9784042725873 38 731 779.98171023471 -48.9817102347105 39 392 407.262899658113 -15.2628996581132 40 344 318.528669679799 25.4713303202008 41 792 789.297634460038 2.70236553996208 42 852 750.35815779628 101.641842203721 43 649 664.693270449246 -15.6932704492463 44 629 671.11684680186 -42.1168468018602 45 685 755.53527278185 -70.5352727818503 46 617 662.42086336387 -45.4208633638693 47 715 750.419236369283 -35.4192363692831 48 715 691.588364395126 23.4116356048739 49 629 710.153029976516 -81.1530299765161 50 916 842.075998028362 73.924001971638 51 531 504.739249643607 26.2607503563933 52 357 382.080401536038 -25.0804015360375 53 917 899.32768456385 17.6723154361493 54 828 819.492270295447 8.50772970455288 55 708 693.018734455669 14.9812655443313 56 858 765.148894590382 92.8511054096175 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.471905859998609 0.943811719997218 0.528094140001391 22 0.340217032930881 0.680434065861762 0.659782967069119 23 0.280392888246322 0.560785776492643 0.719607111753678 24 0.185921447974251 0.371842895948501 0.81407855202575 25 0.317779027795748 0.635558055591497 0.682220972204252 26 0.629153389950879 0.741693220098243 0.370846610049121 27 0.528467146690236 0.943065706619529 0.471532853309764 28 0.430621900210985 0.86124380042197 0.569378099789015 29 0.495048703451873 0.990097406903746 0.504951296548127 30 0.465944415781926 0.931888831563851 0.534055584218074 31 0.338859073490985 0.677718146981971 0.661140926509015 32 0.228766218526325 0.45753243705265 0.771233781473675 33 0.169889857489507 0.339779714979013 0.830110142510493 34 0.0916101058331298 0.183220211666260 0.90838989416687 35 0.0815887870019564 0.163177574003913 0.918411212998044 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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