model 4

*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: Fri, 20 Nov 2009 01:59:37 -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/20/t1258707619uoqspu2f9evyo0q.htm/, Retrieved Fri, 20 Nov 2009 10:00:35 +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/20/t1258707619uoqspu2f9evyo0q.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:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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105.8 93.7 105.9 106 106.1 105.7 105.7 104.5 105.8 105.9 106 106.1 105.6 95.4 105.7 105.8 105.9 106 105.4 86.5 105.6 105.7 105.8 105.9 105.4 102.9 105.4 105.6 105.7 105.8 105.5 101.9 105.4 105.4 105.6 105.7 105.6 103.7 105.5 105.4 105.4 105.6 105.7 100.7 105.6 105.5 105.4 105.4 105.9 94.2 105.7 105.6 105.5 105.4 106.1 93.6 105.9 105.7 105.6 105.5 106 104.7 106.1 105.9 105.7 105.6 105.8 101 106 106.1 105.9 105.7 105.8 97.6 105.8 106 106.1 105.9 105.7 105.8 105.8 105.8 106 106.1 105.5 93.7 105.7 105.8 105.8 106 105.3 91.2 105.5 105.7 105.8 105.8 105.2 106.3 105.3 105.5 105.7 105.8 105.2 103.4 105.2 105.3 105.5 105.7 105 107.4 105.2 105.2 105.3 105.5 105.1 101.2 105 105.2 105.2 105.3 105.1 96.9 105.1 105 105.2 105.2 105.2 96.3 105.1 105.1 105 105.2 104.9 109.8 105.2 105.1 105.1 105 104.8 97.9 104.9 105.2 105.1 105.1 104.5 105.1 104.8 104.9 105.2 105.1 104.5 107.9 104.5 104.8 104.9 105.2 104.4 95 104.5 104.5 104.8 104.9 104.4 95.2 104.4 104.5 104.5 104.8 104.2 105.8 104.4 104.4 104.5 1 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 Werkl[t] = + 13.181305483574 -0.0167499771012351Infl[t] + 1.01704809359358`Yt-1`[t] + 0.0183717956239474`Yt-2`[t] -0.304695129059736`Yt-3`[t] + 0.159093233761395`Yt-4`[t] + 0.0623924437488247M1[t] + 0.205812380211141M2[t] -0.0775331339962117M3[t] -0.106742976619106M4[t] + 0.0578994848837974M5[t] + 0.227318039355702M6[t] + 0.177074745524402M7[t] + 0.165127828048767M8[t] + 0.204067321450513M9[t] + 0.271447808716314M10[t] + 0.142836066402679M11[t] -0.00332475677410949t + 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) 13.181305483574 6.770538 1.9469 0.058971 0.029485 Infl -0.0167499771012351 0.004804 -3.487 0.00125 0.000625 `Yt-1` 1.01704809359358 0.151537 6.7115 0 0 `Yt-2` 0.0183717956239474 0.220522 0.0833 0.934042 0.467021 `Yt-3` -0.304695129059736 0.221958 -1.3728 0.177875 0.088938 `Yt-4` 0.159093233761395 0.147438 1.0791 0.287366 0.143683 M1 0.0623924437488247 0.085715 0.7279 0.471132 0.235566 M2 0.205812380211141 0.092299 2.2298 0.031743 0.015871 M3 -0.0775331339962117 0.09766 -0.7939 0.432177 0.216089 M4 -0.106742976619106 0.100624 -1.0608 0.295473 0.147736 M5 0.0578994848837974 0.089024 0.6504 0.519361 0.25968 M6 0.227318039355702 0.089078 2.5519 0.014858 0.007429 M7 0.177074745524402 0.095133 1.8613 0.070444 0.035222 M8 0.165127828048767 0.087082 1.8962 0.065552 0.032776 M9 0.204067321450513 0.090057 2.266 0.029232 0.014616 M10 0.271447808716314 0.087615 3.0982 0.003653 0.001827 M11 0.142836066402679 0.093264 1.5315 0.133925 0.066962 t -0.00332475677410949 0.003697 -0.8993 0.374174 0.187087 Multiple Linear Regression - Regression Statistics Multiple R 0.996509035112443 R-squared 0.993030257060732 Adjusted R-squared 0.989912214166848 F-TEST (value) 318.478703102129 F-TEST (DF numerator) 17 F-TEST (DF denominator) 38 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.102457087339735 Sum Squared Residuals 0.398903280353396 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 105.8 105.811705379203 -0.0117053792030353 2 105.7 105.761465623687 -0.0614656236867831 3 105.6 105.538238344935 0.0617616550653452 4 105.4 105.565796742347 -0.165796742346709 5 105.4 105.261728213864 0.138271786136022 6 105.5 105.455457819068 0.0445421809319375 7 105.6 105.518474321476 0.0815256785244096 8 105.7 105.625175920699 0.074824079300987 9 105.9 105.842737984500 0.057262015499536 10 106.1 106.107530310004 -0.00753031000418853 11 106 105.982192853406 0.0178071465936141 12 105.8 105.754946792834 0.0450532071662002 13 105.8 105.636597224612 0.163402775388063 14 105.7 105.697956392603 0.00204360739653135 15 105.5 105.557285737623 -0.057285737623412 16 105.3 105.329560635946 -0.0295606359461054 17 105.2 105.061339221509 0.138660778491294 18 105.2 105.215658486752 -0.0156584867517507 19 105 105.122373727239 -0.122373727238677 20 105.1 105.006193158452 0.0938068415484304 21 105.1 105.195953923473 -0.0959539234729413 22 105.2 105.332835845600 -0.132835845599708 23 104.9 105.014191305346 -0.114191305346402 24 104.8 104.779987284535 0.0200127154652182 25 104.5 104.580769275428 -0.0807692754280743 26 104.5 104.474330773686 0.0256692263135833 27 104.4 104.380965211401 0.0190347885987440 28 104.4 104.318875022566 0.0811249774335682 29 104.2 104.253077820331 -0.0530778203313235 30 104.1 104.174206610681 -0.0742066106810689 31 103.9 103.964175116303 -0.0641751163027591 32 103.8 103.967070447466 -0.167070447465852 33 103.9 103.875856909242 0.0241430907584613 34 104.2 104.113284933038 0.086715066961893 35 104.1 104.114426143602 -0.0144261436018154 36 103.8 103.976443007382 -0.17644300738184 37 103.6 103.592759953810 0.00724004619013386 38 103.7 103.640656406459 0.059343593540604 39 103.5 103.592840711749 -0.0928407117491103 40 103.4 103.400419689951 -0.000419689951405759 41 103.1 103.268445238279 -0.168445238278550 42 103.1 103.063735969874 0.0362640301264214 43 103.1 103.016707228416 0.083292771584335 44 103.2 103.276259497012 -0.0762594970123955 45 103.3 103.285451182785 0.014548817214944 46 103.5 103.446348911358 0.0536510886420031 47 103.6 103.489189697645 0.110810302354604 48 103.5 103.388622915250 0.111377084750422 49 103.3 103.378168166947 -0.0781681669470875 50 103.2 103.225590803564 -0.0255908035639357 51 103.1 103.030669994292 0.0693300057084329 52 103.2 103.085347909189 0.114652090810652 53 103 103.055409506017 -0.0554095060174416 54 103 102.990941113626 0.00905888637446086 55 103.1 103.078269606567 0.0217303934326917 56 103.4 103.325300976371 0.0746990236288304 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.747515140273827 0.504969719452346 0.252484859726173 22 0.724596359982256 0.550807280035488 0.275403640017744 23 0.675975286593944 0.648049426812112 0.324024713406056 24 0.759624611212188 0.480750777575625 0.240375388787812 25 0.74028073563245 0.519438528735099 0.259719264367549 26 0.791306721315375 0.417386557369249 0.208693278684625 27 0.742245505581885 0.515508988836231 0.257754494418115 28 0.732950625853426 0.534098748293149 0.267049374146574 29 0.966131009154233 0.067737981691533 0.0338689908457665 30 0.949839455727235 0.100321088545529 0.0501605442727646 31 0.937656429036802 0.124687141926397 0.0623435709631984 32 0.934563929953443 0.130872140093114 0.0654360700465571 33 0.884327938712213 0.231344122575574 0.115672061287787 34 0.819234270766169 0.361531458467662 0.180765729233831 35 0.771134674933003 0.457730650133994 0.228865325066997 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 1 0.0666666666666667 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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