WS 7 Multiple Regression analysis

*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: Sat, 21 Nov 2009 02:10:54 -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/21/t1258794747k1nj31fu7vu162i.htm/, Retrieved Sat, 21 Nov 2009 10:12:39 +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/21/t1258794747k1nj31fu7vu162i.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:

WS 7 Multiple Regression analysis

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

14.5 14.8 14.3 14.7 15.3 16 14.4 15.4 13.7 15 14.2 15.5 13.5 15.1 11.9 11.7 14.6 16.3 15.6 16.7 14.1 15 14.9 14.9 14.2 14.6 14.6 15.3 17.2 17.9 15.4 16.4 14.3 15.4 17.5 17.9 14.5 15.9 14.4 13.9 16.6 17.8 16.7 17.9 16.6 17.4 16.9 16.7 15.7 16 16.4 16.6 18.4 19.1 16.9 17.8 16.5 17.2 18.3 18.6 15.1 16.3 15.7 15.1 18.1 19.2 16.8 17.7 18.9 19.1 19 18 18.1 17.5 17.8 17.8 21.5 21.1 17.1 17.2 18.7 19.4 19 19.8 16.4 17.6 16.9 16.2 18.6 19.5 19.3 19.9 19.4 20 17.6 17.3 18.6 18.9 18.1 18.6 20.4 21.4 18.1 18.6 19.6 19.8 19.9 20.8 19.2 19.6 17.8 17.7 19.2 19.8 22 22.2 21.1 20.7 19.5 17.9 22.2 20.9 20.9 21.2 22.2 21.4 23.5 23 21.5 21.3 24.3 23.9 22.8 22.4 20.3 18.3 23.7 22.8 23.3 22.3 19.6 17.8 18 16.4 17.3 16 16.8 16.4 18.2 17.7 16.5 16.6 16 16.2 18.4 18.3

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] = -2.29101830970334 + 1.18227381282826X[t] -0.528396202113022M1[t] -1.09215623702356M2[t] -1.41384671982294M3[t] -1.40672834794418M4[t] -1.51707239523279M5[t] -1.67619740018946M6[t] -1.85649345552018M7[t] + 0.152145441079096M8[t] -1.98138135702689M9[t] -1.75420734980634M10[t] -1.10066825881478M11[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) -2.29101830970334 0.577156 -3.9695 0.000183 9.1e-05 X 1.18227381282826 0.031166 37.9353 0 0 M1 -0.528396202113022 0.324777 -1.627 0.108586 0.054293 M2 -1.09215623702356 0.324961 -3.3609 0.001305 0.000652 M3 -1.41384671982294 0.333002 -4.2458 7.1e-05 3.5e-05 M4 -1.40672834794418 0.326229 -4.3121 5.6e-05 2.8e-05 M5 -1.51707239523279 0.325948 -4.6543 1.6e-05 8e-06 M6 -1.67619740018946 0.3332 -5.0306 4e-06 2e-06 M7 -1.85649345552018 0.338322 -5.4874 1e-06 0 M8 0.152145441079096 0.339771 0.4478 0.655795 0.327897 M9 -1.98138135702689 0.345001 -5.7431 0 0 M10 -1.75420734980634 0.346507 -5.0625 4e-06 2e-06 M11 -1.10066825881478 0.34011 -3.2362 0.001907 0.000954 Multiple Linear Regression - Regression Statistics Multiple R 0.980495588337264 R-squared 0.961371598748837 Adjusted R-squared 0.954240201594776 F-TEST (value) 134.808310066057 F-TEST (DF numerator) 12 F-TEST (DF denominator) 65 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.583743276693048 Sum Squared Residuals 22.1491538504819 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 14.5 14.6782379180418 -0.178237918041825 2 14.3 13.9962505018485 0.303749498151452 3 15.3 15.2115159757259 0.0884840242741036 4 14.4 14.5092700599077 -0.109270059907701 5 13.7 13.9260164874878 -0.226016487487795 6 14.2 14.3580283889452 -0.158028388945250 7 13.5 13.7048228084832 -0.204822808483219 8 11.9 11.6937307414664 0.206269258533592 9 14.6 14.9986634823704 -0.398663482370433 10 15.6 15.6987470147223 -0.0987470147222814 11 14.1 14.3424206239058 -0.242420623905796 12 14.9 15.3248615014378 -0.424861501437754 13 14.2 14.4417831554763 -0.241783155476253 14 14.6 14.7056147895455 -0.105614789545495 15 17.2 17.4578362200996 -0.257836220099595 16 15.4 15.6915438727360 -0.29154387273596 17 14.3 14.3989260126191 -0.0989260126190978 18 17.5 17.1954855397331 0.304514460266929 19 14.5 14.6506418587458 -0.150641858745832 20 14.4 14.2947331296886 0.105266870311413 21 16.6 16.7720742016128 -0.172074201612825 22 16.7 17.1174755901162 -0.417475590116195 23 16.6 17.1798777746936 -0.57987777469362 24 16.9 17.4529543645286 -0.552954364528624 25 15.7 16.0969664934358 -0.39696649343582 26 16.4 16.2425707462222 0.157429253777763 27 18.4 18.8765647954935 -0.476564795493512 28 16.9 17.3467272106955 -0.44672721069553 29 16.5 16.5270188757100 -0.0270188757099678 30 18.3 18.0230772087129 0.276922791287143 31 15.1 15.1235513838771 -0.0235513838771379 32 15.7 15.7134617050825 -0.0134617050825008 33 18.1 18.4272575395724 -0.327257539572389 34 16.8 16.8810208275505 -0.0810208275505417 35 18.9 19.1897432565017 -0.289743256501670 36 19 18.9899103212054 0.0100896787946367 37 18.1 17.8703772126782 0.22962278732179 38 17.8 17.6612993216161 0.138700678383852 39 21.5 21.2411124211500 0.258887578849966 40 17.1 16.6373629229986 0.462637077001431 41 18.7 19.1280212639321 -0.428021263932143 42 19 19.4418057841068 -0.44180578410677 43 16.4 16.6605073405539 -0.26050734055388 44 16.9 17.0139628991936 -0.113962899193588 45 18.6 18.7819396834209 -0.181939683420869 46 19.3 19.4820232157727 -0.182023215772716 47 19.4 20.2537896880471 -0.853789688047104 48 17.6 18.1623186522256 -0.56231865222558 49 18.6 19.5255605506378 -0.925560550637774 50 18.1 18.6071183718788 -0.507118371878757 51 20.4 21.5957945649985 -1.19579456499851 52 18.1 18.2925462609581 -0.192546260958137 53 19.6 19.6009307890634 -0.000930789063447662 54 19.9 20.6240795969350 -0.724079596935033 55 19.2 19.0250549662104 0.174945033789598 56 17.8 18.7873736184360 -0.987373618435979 57 19.2 19.1366218272693 0.0633781727306502 58 22 22.2012529852777 -0.201252985277720 59 21.1 21.0813813570269 0.0186186429731163 60 19.5 18.8716829399225 0.628317060077465 61 22.2 21.8901081762943 0.309891823705701 62 20.9 21.6810302852322 -0.781030285232237 63 22.2 21.5957945649985 0.60420543500149 64 23.5 23.4945510374025 0.00544896259751321 65 21.5 21.3743415083058 0.125658491694158 66 24.3 24.2891284167026 0.0108715832973603 67 22.8 22.3354216421295 0.464578357870471 68 20.3 19.4967379061329 0.803262093867063 69 23.7 22.6834432657541 1.01655673424587 70 23.3 22.3194803665605 0.980519633439453 71 19.6 17.6527872998249 1.94721270017507 72 18 17.0982722206801 0.901727779319857 73 17.3 16.0969664934358 1.20303350656418 74 16.8 16.0061159836566 0.793884016343421 75 18.2 17.2213814575339 0.978618542466057 76 16.5 15.9279986353016 0.572001364698384 77 16 15.3447450628817 0.655254937118294 78 18.4 17.6683950648644 0.73160493513562 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.00973249266085412 0.0194649853217082 0.990267507339146 17 0.00316813748861622 0.00633627497723244 0.996831862511384 18 0.0141462552180820 0.0282925104361641 0.985853744781918 19 0.00437235940415554 0.00874471880831108 0.995627640595844 20 0.00130629874418729 0.00261259748837459 0.998693701255813 21 0.000477810631727827 0.000955621263455653 0.999522189368272 22 0.000253311448983821 0.000506622897967642 0.999746688551016 23 0.000126204986224539 0.000252409972449078 0.999873795013775 24 3.99824145091164e-05 7.99648290182327e-05 0.99996001758549 25 1.37223613160377e-05 2.74447226320754e-05 0.999986277638684 26 4.04688491923357e-06 8.09376983846715e-06 0.99999595311508 27 2.45605398836595e-06 4.9121079767319e-06 0.999997543946012 28 8.3617539185452e-07 1.67235078370904e-06 0.999999163824608 29 3.94283250540627e-07 7.88566501081254e-07 0.99999960571675 30 2.16129265549682e-07 4.32258531099365e-07 0.999999783870734 31 7.79334161734906e-08 1.55866832346981e-07 0.999999922066584 32 2.01028992086117e-08 4.02057984172234e-08 0.9999999798971 33 6.03859113494223e-09 1.20771822698845e-08 0.999999993961409 34 2.42324259855201e-09 4.84648519710403e-09 0.999999997576757 35 1.09233485250410e-09 2.18466970500819e-09 0.999999998907665 36 3.4271187090009e-09 6.8542374180018e-09 0.999999996572881 37 6.68598564873209e-09 1.33719712974642e-08 0.999999993314014 38 1.76701960503517e-09 3.53403921007034e-09 0.99999999823298 39 1.59424344158696e-09 3.18848688317391e-09 0.999999998405757 40 1.16794497268976e-08 2.33588994537951e-08 0.99999998832055 41 1.02323293318461e-08 2.04646586636922e-08 0.99999998976767 42 2.21494860165548e-08 4.42989720331096e-08 0.999999977850514 43 1.23356324898483e-08 2.46712649796967e-08 0.999999987664367 44 4.63360642107868e-09 9.26721284215737e-09 0.999999995366394 45 2.52194452470515e-09 5.04388904941031e-09 0.999999997478055 46 1.24834160879368e-09 2.49668321758737e-09 0.999999998751658 47 7.94686583862144e-09 1.58937316772429e-08 0.999999992053134 48 1.18727878670707e-08 2.37455757341414e-08 0.999999988127212 49 3.25961854170414e-07 6.51923708340828e-07 0.999999674038146 50 4.26473317970132e-07 8.52946635940265e-07 0.999999573526682 51 4.44654527463367e-05 8.89309054926733e-05 0.999955534547254 52 2.87118929357833e-05 5.74237858715666e-05 0.999971288107064 53 1.70232491362704e-05 3.40464982725408e-05 0.999982976750864 54 6.35280041356182e-05 0.000127056008271236 0.999936471995864 55 6.98944357101535e-05 0.000139788871420307 0.99993010556429 56 0.00326335854511175 0.0065267170902235 0.996736641454888 57 0.0204970877363935 0.040994175472787 0.979502912263607 58 0.0682010151446982 0.136402030289396 0.931798984855302 59 0.620329826398652 0.759340347202695 0.379670173601348 60 0.575239879778304 0.849520240443391 0.424760120221696 61 0.481990251912681 0.963980503825362 0.518009748087319 62 0.991550547067767 0.0168989058644659 0.00844945293223293 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 39 0.829787234042553 NOK 5% type I error level 43 0.914893617021277 NOK 10% type I error level 43 0.914893617021277 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/21/t1258794747k1nj31fu7vu162i/10yr1t1258794649.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258794747k1nj31fu7vu162i/10yr1t1258794649.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258794747k1nj31fu7vu162i/1b8sq1258794649.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258794747k1nj31fu7vu162i/1b8sq1258794649.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258794747k1nj31fu7vu162i/29t7p1258794649.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258794747k1nj31fu7vu162i/29t7p1258794649.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258794747k1nj31fu7vu162i/3ynk51258794649.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258794747k1nj31fu7vu162i/3ynk51258794649.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258794747k1nj31fu7vu162i/4dn2g1258794649.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258794747k1nj31fu7vu162i/4dn2g1258794649.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258794747k1nj31fu7vu162i/5jsv51258794649.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258794747k1nj31fu7vu162i/5jsv51258794649.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258794747k1nj31fu7vu162i/6g2vf1258794649.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258794747k1nj31fu7vu162i/6g2vf1258794649.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258794747k1nj31fu7vu162i/7yi9d1258794649.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258794747k1nj31fu7vu162i/7yi9d1258794649.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258794747k1nj31fu7vu162i/8yg0x1258794649.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258794747k1nj31fu7vu162i/8yg0x1258794649.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258794747k1nj31fu7vu162i/9xoh31258794649.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258794747k1nj31fu7vu162i/9xoh31258794649.ps (open in new window)

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') }

Copyright

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.

Privacy Policy

We may request personal information to be submitted to our servers in order to be able to:

• personalize online software applications according to your needs
• enforce strict security rules with respect to the data that you upload (e.g. statistical data)
• manage user sessions of online applications
• alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

FreeStatistics.org is powered by