Multiple Regression (szs effects)

*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, 18 Dec 2009 07:10:45 -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/18/t1261145504m1i5drs1h6rqniw.htm/, Retrieved Fri, 18 Dec 2009 15:11:56 +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/18/t1261145504m1i5drs1h6rqniw.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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100.0 114.1 141.7 100.0 93.5 110.3 153.4 117.5 88.2 103.9 145 95.5 89.2 101.6 137.7 100.2 91.4 94.6 148.3 104.9 92.5 95.9 152.2 115.9 91.4 104.7 169.4 125.1 88.2 102.8 168.6 129.9 87.1 98.1 161.1 136.8 84.9 113.9 174.1 136.0 92.5 80.9 179 107.6 93.5 95.7 190.6 117.9 93.5 113.2 190 119.3 91.4 105.9 181.6 123.9 90.3 108.8 174.8 113.7 91.4 102.3 180.5 131.9 93.5 99 196.8 159.6 93.5 100.7 193.8 124.3 92.5 115.5 197 138.3 91.4 100.7 216.3 104.9 89.2 109.9 221.4 132.0 86.0 114.6 217.9 118.1 88.2 85.4 229.7 114.0 87.1 100.5 227.4 106.5 87.1 114.8 204.2 110.4 86.0 116.5 196.6 115.0 84.9 112.9 198.8 95.5 84.9 102 207.5 105.8 86.0 106 190.7 109.1 86.0 105.3 201.6 105.6 84.9 118.8 210.5 118.2 86.0 106.1 223.5 107.2 82.8 109.3 223.8 102.1 77.4 117.2 231.2 126.5 80.6 92.5 244 111.7 78.5 104.2 234.7 99.3 75.3 112.5 250.2 88.1 75.3 122.4 265.7 117.7 75.3 113.3 287.6 96.0 77.4 100 283.3 95.7 78.5 110.7 295.4 117.2 76.3 112.8 312.3 113.2 73.1 109.8 333.8 101.7 68.8 117.3 347.7 129.8 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 31 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation wrk[t] = + 95.9818034995944 -0.162336402129562indpr[t] -0.0647428561585364grn[t] + 0.178268715937659bw[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) 95.9818034995944 7.727485 12.4208 0 0 indpr -0.162336402129562 0.073663 -2.2038 0.03167 0.015835 grn -0.0647428561585364 0.010282 -6.2969 0 0 bw 0.178268715937659 0.044613 3.9959 0.00019 9.5e-05 Multiple Linear Regression - Regression Statistics Multiple R 0.746019135974758 R-squared 0.556544551240525 Adjusted R-squared 0.532788009342696 F-TEST (value) 23.4270018605437 F-TEST (DF numerator) 3 F-TEST (DF denominator) 56 p-value 5.91810156436168e-10 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 5.030492271504 Sum Squared Residuals 1417.12773964504 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 100 86.1120288927127 13.8879711072873 2 93.5 89.0911183326592 4.40888166734084 3 88.2 86.7519995473916 1.44800045260843 4 89.2 88.4358590871539 0.764140912846139 5 91.4 89.7238025916873 1.67619740831269 6 92.5 91.2212240052148 1.27877599478517 7 91.4 90.3191587271743 1.08084127282568 8 88.2 91.5350820126481 -3.33508201264808 9 87.1 94.0136886638159 -6.9136886638159 10 84.9 90.4645014073577 -5.56450140735771 11 92.5 90.441531149827 2.05846885017309 12 93.5 89.1241030410283 4.37589695897173 13 93.5 86.5716379197688 6.92836208023122 14 91.4 89.1205697403595 2.27943025964049 15 90.3 87.2717046934977 3.02829530650228 16 91.4 91.2023476573016 0.197652342698408 17 93.5 95.6207926604181 -2.12079266041815 18 93.5 89.2461636726742 4.25383632732585 19 92.5 89.1321698045765 3.36783019542345 20 91.4 84.3310363199165 7.0689636800835 21 89.2 87.3384350558266 1.86156494417345 22 86 84.324118810839 1.67588118916096 23 88.2 87.5694743150071 0.630525684992893 24 87.1 83.9300878424829 3.16991215751707 25 87.1 83.8059595470651 3.29404045293489 26 86 84.842069463563 1.15793053643705 27 84.9 81.8078062668963 3.09219373310375 28 84.9 84.8501779756871 0.0498220243129133 29 86 85.8767991132265 0.123200886773470 30 86 84.6607969568074 1.33920304319263 31 84.9 84.1392299290618 0.76077007093819 32 86 83.398289230732 2.60171076926797 33 82.8 81.9502194357878 0.849780564212186 34 77.4 84.53842139227 -7.13842139226997 35 80.6 85.0810449701635 -4.48104497016354 36 78.5 81.573285549895 -3.07328554989509 37 75.3 77.2257695232606 -1.92576952326064 38 75.3 79.8918788634754 -4.59187886347536 39 75.3 76.0828404371352 -0.78284043713523 40 77.4 78.4668282521588 -1.06682825215880 41 78.5 79.7792175825139 -1.27921758251387 42 76.3 77.6310820052119 -1.33108200521189 43 73.1 74.676029570909 -1.57602957090897 44 68.8 77.5679317721818 -8.76793177218182 45 65.6 70.6108900205109 -5.01089002051085 46 69.9 72.5411542234386 -2.64115422343862 47 82.8 72.5341743489714 10.2658256510286 48 84.9 74.0539607457538 10.8460392542462 49 80.6 76.2888974911966 4.31110250880336 50 74.2 79.4199523730538 -5.21995237305377 51 71 82.596866713149 -11.5968667131490 52 74.2 87.5548046098363 -13.3548046098363 53 82.8 85.4265116323251 -2.62651163232511 54 86 85.0705158098905 0.929484190109497 55 86 87.0602579471919 -1.06025794719188 56 82.8 85.50616539791 -2.70616539790997 57 78.5 83.3580005193763 -4.85800051937632 58 79.6 85.5759413173148 -5.97594131731485 59 87.1 86.0635722157014 1.03642778429864 60 89.2 86.3000208450383 2.89997915496168 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 7 0.445034140966724 0.890068281933448 0.554965859033276 8 0.354710839918300 0.709421679836599 0.6452891600817 9 0.284078189082479 0.568156378164959 0.71592181091752 10 0.376360966678166 0.752721933356331 0.623639033321834 11 0.328608853344101 0.657217706688202 0.671391146655899 12 0.246729363695586 0.493458727391173 0.753270636304413 13 0.190222341557900 0.380444683115799 0.8097776584421 14 0.126493272715343 0.252986545430686 0.873506727284657 15 0.100643083350452 0.201286166700905 0.899356916649548 16 0.0688009544147705 0.137601908829541 0.93119904558523 17 0.101748562973606 0.203497125947212 0.898251437026394 18 0.0710283258188026 0.142056651637605 0.928971674181197 19 0.0478645456912701 0.0957290913825403 0.95213545430873 20 0.0525388571168908 0.105077714233782 0.94746114288311 21 0.042173498014149 0.084346996028298 0.95782650198585 22 0.0571533346517534 0.114306669303507 0.942846665348247 23 0.0405997815200276 0.0811995630400552 0.959400218479972 24 0.0340815463394675 0.068163092678935 0.965918453660533 25 0.0336097157270338 0.0672194314540676 0.966390284272966 26 0.0344598030760787 0.0689196061521574 0.965540196923921 27 0.0438072548104909 0.0876145096209818 0.956192745189509 28 0.0399457521194428 0.0798915042388857 0.960054247880557 29 0.0360810004259919 0.0721620008519838 0.963918999574008 30 0.0324759598393836 0.0649519196787671 0.967524040160616 31 0.0388959203377767 0.0777918406755534 0.961104079662223 32 0.0408203771738757 0.0816407543477513 0.959179622826124 33 0.0462178757137406 0.0924357514274812 0.95378212428626 34 0.0814773468241856 0.162954693648371 0.918522653175814 35 0.083841206929776 0.167682413859552 0.916158793070224 36 0.078001522840655 0.15600304568131 0.921998477159345 37 0.0713552107244577 0.142710421448915 0.928644789275542 38 0.059708769655306 0.119417539310612 0.940291230344694 39 0.0443210044077466 0.0886420088154933 0.955678995592253 40 0.0283178126698651 0.0566356253397302 0.971682187330135 41 0.0190037641990364 0.0380075283980728 0.980996235800964 42 0.0122120211649901 0.0244240423299803 0.98778797883501 43 0.00700308502731677 0.0140061700546335 0.992996914972683 44 0.0093548415661628 0.0187096831323256 0.990645158433837 45 0.0187740181364644 0.0375480362729287 0.981225981863536 46 0.0558834455520716 0.111766891104143 0.944116554447928 47 0.160503354554455 0.321006709108909 0.839496645445545 48 0.176360780890911 0.352721561781823 0.823639219109089 49 0.168360939992799 0.336721879985598 0.831639060007201 50 0.154786505559852 0.309573011119704 0.845213494440148 51 0.277203406939161 0.554406813878321 0.722796593060839 52 0.937814336854573 0.124371326290854 0.0621856631454272 53 0.898051548055673 0.203896903888654 0.101948451944327 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 5 0.106382978723404 NOK 10% type I error level 20 0.425531914893617 NOK

Charts produced by software:

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Parameters (Session):

par1 = 3 ; par2 = TRUE ; par3 = TRUE ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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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