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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: Tue, 28 Dec 2010 00:49:34 +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/Dec/28/t1293497257d2g5rsm3b7v5rpp.htm/, Retrieved Tue, 28 Dec 2010 01:47:38 +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/Dec/28/t1293497257d2g5rsm3b7v5rpp.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 «

99 94.6 106.3 95.9 128.9 104.7 111.1 102.8 102.9 98.1 130 113.9 87 80.9 87.5 95.7 117.6 113.2 103.4 105.9 110.8 108.8 112.6 102.3 102.5 99 112.4 100.7 135.6 115.5 105.1 100.7 127.7 109.9 137 114.6 91 85.4 90.5 100.5 122.4 114.8 123.3 116.5 124.3 112.9 120 102 118.1 106 119 105.3 142.7 118.8 123.6 106.1 129.6 109.3 151.6 117.2 110.4 92.5 99.2 104.2 130.5 112.5 136.2 122.4 129.7 113.3 128 100 121.6 110.7 135.8 112.8 143.8 109.8 147.5 117.3 136.2 109.1 156.6 115.9 123.3 96 104.5 99.8 139.8 116.8 136.5 115.7 112.1 99.4 118.5 94.3 94.4 91 102.3 93.2 111.4 103.1 99.2 94.1 87.8 91.8 115.8 102.7 79.7 82.6 72.7 89.1 104.5 104.5 103 105.1 95.1 95.1 104.2 88.7 78.3 86.3

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 5 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 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 ipi[t] = -83.6948607837712 + 2.01157944981591`tip `[t] -14.6973798833694M1[t] -8.59150522082137M2[t] -9.0930245904434M3[t] -11.9610838018231M4[t] -11.4142195211682M5[t] -8.72060225971292M6[t] + 2.29366396537288M7[t] -26.1061509349583M8[t] -23.313673168531M9[t] -27.4420937616331M10[t] -19.1181103452043M11[t] + 0.119620211242018t + 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) -83.6948607837712 13.818476 -6.0567 0 0 `tip ` 2.01157944981591 0.132403 15.1928 0 0 M1 -14.6973798833694 3.904156 -3.7645 0.000463 0.000232 M2 -8.59150522082137 4.117864 -2.0864 0.042394 0.021197 M3 -9.0930245904434 4.38877 -2.0719 0.043789 0.021894 M4 -11.9610838018231 4.16177 -2.874 0.006068 0.003034 M5 -11.4142195211682 4.146825 -2.7525 0.008378 0.004189 M6 -8.72060225971292 4.524442 -1.9274 0.05998 0.02999 M7 2.29366396537288 4.307948 0.5324 0.596939 0.29847 M8 -26.1061509349583 4.074633 -6.407 0 0 M9 -23.313673168531 4.507242 -5.1725 5e-06 2e-06 M10 -27.4420937616331 4.556273 -6.0229 0 0 M11 -19.1181103452043 4.217408 -4.5331 4e-05 2e-05 t 0.119620211242018 0.049506 2.4163 0.019618 0.009809 Multiple Linear Regression - Regression Statistics Multiple R 0.954042074610755 R-squared 0.910196280127594 Adjusted R-squared 0.885356953354376 F-TEST (value) 36.6433554515236 F-TEST (DF numerator) 13 F-TEST (DF denominator) 47 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 6.43555143585808 Sum Squared Residuals 1946.56714732802 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 99 92.0227954966864 6.9772045033136 2 106.3 100.863343655237 5.4366563447628 3 128.9 118.183343655237 10.7166563447628 4 111.1 111.612903700449 -0.512903700449282 5 102.9 102.824964778211 0.0750352217886005 6 130 137.421157558 -7.42115755800011 7 87 82.1729221504029 4.82707784959712 8 87.5 83.6641033185892 3.8358966814108 9 117.6 121.778841668037 -4.17884166803694 10 103.4 103.085511302521 0.314488697479326 11 110.8 117.362695334658 -6.56269533465769 12 112.6 123.525159467301 -10.9251594673006 13 102.5 102.309187610781 0.190812389219359 14 112.4 111.954367549258 0.445632450742226 15 135.6 141.343844248153 -5.74384424815325 16 105.1 108.82402939074 -3.72402939074011 17 127.7 127.997044820943 -0.297044820943388 18 137 140.264705707775 -3.26470570777545 19 91 92.6604722094787 -1.66047220947870 20 90.5 94.7551272126098 -4.25512721260978 21 122.4 126.432811322647 -4.03281132264659 22 123.3 125.843696005474 -2.54369600547356 23 124.3 127.045613613807 -2.74561361380716 24 120 124.35712816726 -4.35712816726001 25 118.1 117.825686294396 0.274313705603763 26 119 122.643075553315 -3.64307555331518 27 142.7 149.41749896745 -6.71749896744997 28 123.6 121.122000954650 2.47799904534977 29 129.6 128.225539685958 1.37446031404194 30 151.6 146.930254812201 4.66974518779895 31 110.4 108.378128838076 2.02187116192414 32 99.2 103.633413711833 -4.43341371183287 33 130.5 123.241621122974 7.25837887702577 34 136.2 139.147457294292 -2.94745729429167 35 129.7 129.285687928638 0.414312071362261 36 128 121.769411802532 6.23058819746759 37 121.6 128.715552243435 -7.11555224343524 38 135.8 139.165363961839 -3.36536396183872 39 143.8 132.748726454011 11.0512735459890 40 147.5 145.087133327493 2.41286667250735 41 136.2 129.258666330899 6.94133366910091 42 156.6 145.750644062345 10.8493559376554 43 123.3 116.854099447336 6.44590055266422 44 104.5 96.217906667547 8.28209333245291 45 139.8 133.326855292087 6.47314470791315 46 136.5 127.105317515429 9.39468248457073 47 112.1 102.760176111101 9.33982388889919 48 118.5 111.738851473486 6.76114852651406 49 94.4 90.522879616966 3.87712038303399 50 102.3 101.173849280351 1.12615071964888 51 111.4 120.706586675149 -9.3065866751486 52 99.2 99.8539326266677 -0.653932626667735 53 87.8 95.893784383988 -8.09378438398807 54 115.8 120.633237859679 -4.83323785967879 55 79.7 91.3343773547068 -11.6343773547068 56 72.7 76.129449089421 -3.42944908942106 57 104.5 110.019870594255 -5.51987059425538 58 103 107.218017882285 -4.21801788228482 59 95.1 95.5458270117966 -0.4458270117966 60 104.2 101.909449089421 2.29055091057893 61 78.3 82.5038987377355 -4.20389873773546 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.350705546926428 0.701411093852856 0.649294453073572 18 0.315356652003748 0.630713304007496 0.684643347996252 19 0.193911504748982 0.387823009497964 0.806088495251018 20 0.117899730709766 0.235799461419532 0.882100269290234 21 0.0723104433869092 0.144620886773818 0.92768955661309 22 0.0488036576448555 0.097607315289711 0.951196342355144 23 0.0508296289876381 0.101659257975276 0.949170371012362 24 0.0572240356388942 0.114448071277788 0.942775964361106 25 0.0328110219184523 0.0656220438369047 0.967188978081548 26 0.0195470257336247 0.0390940514672495 0.980452974266375 27 0.0170149422603178 0.0340298845206355 0.982985057739682 28 0.0173783347151543 0.0347566694303086 0.982621665284846 29 0.0108035581028501 0.0216071162057002 0.98919644189715 30 0.0158955917171871 0.0317911834343742 0.984104408282813 31 0.0107090896129871 0.0214181792259743 0.989290910387013 32 0.0110174183631066 0.0220348367262133 0.988982581636893 33 0.00708325732107652 0.0141665146421530 0.992916742678923 34 0.00996502651086717 0.0199300530217343 0.990034973489133 35 0.0131732453467699 0.0263464906935397 0.98682675465323 36 0.0248521414605858 0.0497042829211716 0.975147858539414 37 0.217157684447213 0.434315368894426 0.782842315552787 38 0.460941861253163 0.921883722506326 0.539058138746837 39 0.557276361544705 0.88544727691059 0.442723638455295 40 0.984645938845046 0.0307081223099071 0.0153540611549535 41 0.978938433520451 0.0421231329590978 0.0210615664795489 42 0.950935195904115 0.09812960819177 0.049064804095885 43 0.94648119613933 0.107037607721339 0.0535188038606695 44 0.861130064584313 0.277739870831374 0.138869935415687 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 13 0.464285714285714 NOK 10% type I error level 16 0.571428571428571 NOK

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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