ws 7

*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: Tue, 23 Nov 2010 20:49:21 +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/Nov/23/t12905452758uj4tbqjr0ej8e1.htm/, Retrieved Tue, 23 Nov 2010 21:48:04 +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/Nov/23/t12905452758uj4tbqjr0ej8e1.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}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

102.89 167.16 100.70 106.88 97.69 102.64 179.84 99.62 107.45 101.69 103.33 174.44 99.83 107.65 102.72 103.56 180.35 100.74 107.72 101.85 103.60 193.17 100.84 108.10 114.94 104.24 195.16 100.85 108.38 106.20 105.31 202.43 99.71 108.62 106.76 105.40 189.91 100.80 108.79 107.24 105.89 195.98 100.06 109.03 106.50 105.89 212.09 100.57 109.34 106.77 105.54 205.81 99.79 109.73 108.24 106.15 204.31 99.90 109.76 104.43 106.14 196.07 100.12 109.96 100.90 105.85 199.98 100.40 110.49 103.91 106.27 199.10 100.51 111.37 103.81 106.51 198.31 100.70 111.56 104.59 106.82 195.72 100.62 111.90 104.94 106.53 223.04 99.70 111.96 111.64 107.14 238.41 99.48 112.25 111.27 107.39 259.73 99.36 112.39 106.82 107.33 326.54 99.39 112.30 106.07 107.53 335.15 99.45 112.49 111.35 107.42 321.81 99.28 112.77 112.59 108.25 368.62 99.40 113.15 108.59 108.26 369.59 99.10 113.15 106.83 108.93 425.00 99.48 113.28 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 R Framework error message The field 'Names of X columns' contains a hard return which cannot be interpreted. Please, resubmit your request without hard returns in the 'Names of X columns'. Multiple Linear Regression - Estimated Regression Equation Bier[t] = + 69.8633744517073 -0.00683435744293085Tarwe[t] + 0.297906175405562suiker[t] + 0.0895655954552326minerwater[t] -0.0559117429109895`fruit `[t] + 0.301835836738048t + 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) 69.8633744517073 28.616018 2.4414 0.018069 0.009035 Tarwe -0.00683435744293085 0.00218 -3.1355 0.002821 0.00141 suiker 0.297906175405562 0.133131 2.2377 0.029551 0.014775 minerwater 0.0895655954552326 0.255794 0.3501 0.727642 0.363821 `fruit ` -0.0559117429109895 0.022358 -2.5008 0.015581 0.00779 t 0.301835836738048 0.084159 3.5865 0.00074 0.00037 Multiple Linear Regression - Regression Statistics Multiple R 0.991103313689328 R-squared 0.982285778405966 Adjusted R-squared 0.980582487868078 F-TEST (value) 576.698899310532 F-TEST (DF numerator) 5 F-TEST (DF denominator) 52 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.734513116633436 Sum Squared Residuals 28.0544949623413 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 102.89 103.132683638906 -0.242683638906177 2 102.64 102.853526571595 -0.213526571595034 3 103.33 103.215152259253 0.114847740747191 4 103.56 103.802604471137 -0.24260447113661 5 103.6 103.348764674565 0.251235325435013 6 104.24 104.153726201515 0.0862737984848322 7 105.31 104.056448386560 1.25355161344014 8 105.4 104.756956624306 0.643043375694419 9 105.89 104.859727774228 1.03027222577168 10 105.89 105.216063426023 0.673936573977261 11 105.54 105.281192530834 0.258807469165562 12 106.15 105.841760291386 0.308239708613978 13 106.14 106.48073216361 -0.340732163609888 14 105.85 106.718434811289 -0.868434811288836 15 106.27 107.143463460163 -0.873463460162977 16 106.51 107.480706916274 -0.97070691627391 17 106.82 107.787294437193 -0.967294437192651 18 106.53 107.259107205440 -0.729107205440385 19 107.14 107.437020977250 -0.297020977250447 20 107.39 107.818746011574 -0.428746011574177 21 107.33 107.706788516404 -0.376788516404455 22 107.53 107.689458366650 -0.159458366649669 23 107.42 107.987568287375 -0.567568287375306 24 108.25 108.262918491175 -0.0129184911753782 25 108.26 108.567157816095 -0.30715781609545 26 108.93 108.297571081250 0.632428918750427 27 109.43 108.564018942331 0.865981057668588 28 109.61 109.581657776669 0.0283422233314187 29 109.74 110.042753165678 -0.302753165677895 30 110.12 110.287302695253 -0.167302695252599 31 110.16 110.635668114295 -0.475668114295267 32 110.44 111.235478746547 -0.795478746546753 33 111.23 111.843514754071 -0.613514754071378 34 112.86 112.393226492119 0.466773507881204 35 112.77 112.976475489634 -0.206475489634281 36 113.04 113.380262739529 -0.340262739529257 37 112.79 113.543551552498 -0.753551552497622 38 113.87 113.806687789089 0.063312210911412 39 114.28 114.171104066483 0.108895933517175 40 115.51 114.500567842858 1.00943215714189 41 116.76 114.408476741746 2.35152325825364 42 116.91 114.961828225906 1.94817177409439 43 116.47 115.741261338299 0.728738661700558 44 116.94 116.305667501602 0.634332498398377 45 117.24 116.78833702778 0.451662972220061 46 116.82 116.873497620107 -0.0534976201070794 47 117.48 116.699665343874 0.780334656125546 48 117.11 117.127057241067 -0.0170572410669104 49 117.31 117.608394248431 -0.298394248430646 50 117.77 117.737342144220 0.0326578557795465 51 118.37 118.019290701756 0.350709298243679 52 117.91 118.187043278759 -0.277043278759200 53 118.12 117.718336598076 0.401663401924421 54 118.02 118.200664764272 -0.180664764271798 55 117.77 118.993943475454 -1.22394347545425 56 117.85 118.871608312618 -1.02160831261753 57 118.68 119.265792669255 -0.585792669254667 58 118.9 119.463947207674 -0.563947207673924 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.0496990253031775 0.099398050606355 0.950300974696823 10 0.0222756820580731 0.0445513641161461 0.977724317941927 11 0.0564725395864933 0.112945079172987 0.943527460413507 12 0.0941182559770203 0.188236511954041 0.90588174402298 13 0.0766250365206111 0.153250073041222 0.923374963479389 14 0.0399444132636314 0.0798888265272627 0.960055586736369 15 0.0575262014697434 0.115052402939487 0.942473798530256 16 0.0344679143784245 0.0689358287568489 0.965532085621576 17 0.0228079669946299 0.0456159339892597 0.97719203300537 18 0.0382155980381344 0.0764311960762687 0.961784401961866 19 0.0248468396196000 0.0496936792392001 0.9751531603804 20 0.0166701843084037 0.0333403686168075 0.983329815691596 21 0.0114028351402277 0.0228056702804555 0.988597164859772 22 0.00666737999275523 0.0133347599855105 0.993332620007245 23 0.0078581376272185 0.015716275254437 0.992141862372782 24 0.00704218197155988 0.0140843639431198 0.99295781802844 25 0.00570483905101195 0.0114096781020239 0.994295160948988 26 0.00409940757513739 0.00819881515027479 0.995900592424863 27 0.00509648246836754 0.0101929649367351 0.994903517531633 28 0.00295873944358895 0.00591747888717789 0.99704126055641 29 0.00153954833773910 0.00307909667547821 0.99846045166226 30 0.000750297593806008 0.00150059518761202 0.999249702406194 31 0.000383009087513662 0.000766018175027324 0.999616990912486 32 0.000275270399288779 0.000550540798577559 0.999724729600711 33 0.000631697535094076 0.00126339507018815 0.999368302464906 34 0.0119296005931846 0.0238592011863691 0.988070399406815 35 0.0134119722703183 0.0268239445406365 0.986588027729682 36 0.0176538812980499 0.0353077625960999 0.98234611870195 37 0.106031732314648 0.212063464629295 0.893968267685352 38 0.27556054225684 0.55112108451368 0.72443945774316 39 0.88713782419094 0.225724351618119 0.112862175809059 40 0.996938389905658 0.00612322018868453 0.00306161009434226 41 0.998678266203408 0.00264346759318382 0.00132173379659191 42 0.999233083538432 0.00153383292313501 0.000766916461567504 43 0.999036886084385 0.00192622783123081 0.000963113915615406 44 0.997098621419335 0.00580275716133079 0.00290137858066540 45 0.994679421162514 0.0106411576749724 0.0053205788374862 46 0.991797467895607 0.0164050642087860 0.00820253210439301 47 0.98199747757775 0.0360050448445007 0.0180025224222503 48 0.967347507450653 0.0653049850986936 0.0326524925493468 49 0.960372262097357 0.0792554758052866 0.0396277379026433 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 12 0.292682926829268 NOK 5% type I error level 28 0.682926829268293 NOK 10% type I error level 34 0.829268292682927 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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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