*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: Thu, 19 Nov 2009 11:44:30 -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/19/t1258656794q1arr2mjtg4irhk.htm/, Retrieved Thu, 19 Nov 2009 19:53:26 +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/19/t1258656794q1arr2mjtg4irhk.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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103.8 122.5 80.2 19 103.5 122.4 74.8 18 104.1 121.9 77.8 19 101.9 122.2 73 19 102 123.7 72 22 100.7 122.6 75.8 23 99 115.7 72.6 20 96.5 116.1 71.9 14 101.8 120.5 74.8 14 100.5 122.6 72.9 14 103.3 119.9 72.9 15 102.3 120.7 79.9 11 100.4 120.2 74 17 103 122.1 76 16 99 119.3 69.6 20 104.8 121.7 77.3 24 104.5 113.5 75.2 23 104.8 123.7 75.8 20 103.8 123.4 77.6 21 106.3 126.4 76.7 19 105.2 124.1 77 23 108.2 125.6 77.9 23 106.2 124.8 76.7 23 103.9 123 71.9 23 104.9 126.9 73.4 27 106.2 127.3 72.5 26 107.9 129 73.7 17 106.9 126.2 69.5 24 110.3 125.4 74.7 26 109.8 126.3 72.5 24 108.3 126.3 72.1 27 110.9 128.4 70.7 27 109.8 127.2 71.4 26 109.3 128.5 69.5 24 109 129 73.5 23 107.9 128.9 72.4 23 108.4 128.3 74.5 24 107.2 124.6 72.2 17 109.5 126.2 73 21 109.9 129.1 73.3 19 108 127.3 71.3 22 114.7 129.2 73.6 22 115.6 130.4 71.3 18 107.6 125.9 71.2 16 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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 R Framework error message Warning: there are blank lines in the 'Data X' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values. Multiple Linear Regression - Estimated Regression Equation dzcg[t] = + 35.827194618634 + 0.620492354829152totid[t] -0.175207770002832ndzcg[t] + 0.0505564905142856`indc `[t] -0.267758201308649M1[t] -2.10353433741009M2[t] -4.31529303020741M3[t] -4.15092239169755M4[t] -3.98514743986063M5[t] -3.03513796721337M6[t] -2.9433276410124M7[t] -2.40598674775383M8[t] -0.370837857517617M9[t] -1.06772121231664M10[t] -1.31099541995592M11[t] -0.195264491163186t + 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) 35.827194618634 15.343124 2.3351 0.024059 0.01203 totid 0.620492354829152 0.131304 4.7256 2.3e-05 1.1e-05 ndzcg -0.175207770002832 0.190627 -0.9191 0.362938 0.181469 `indc ` 0.0505564905142856 0.07609 0.6644 0.509807 0.254904 M1 -0.267758201308649 1.76059 -0.1521 0.8798 0.4399 M2 -2.10353433741009 1.877751 -1.1202 0.268554 0.134277 M3 -4.31529303020741 1.875068 -2.3014 0.026054 0.013027 M4 -4.15092239169755 1.845966 -2.2486 0.029478 0.014739 M5 -3.98514743986063 1.85268 -2.151 0.036881 0.018441 M6 -3.03513796721337 1.845947 -1.6442 0.107101 0.05355 M7 -2.9433276410124 1.850447 -1.5906 0.1187 0.05935 M8 -2.40598674775383 1.840687 -1.3071 0.197814 0.098907 M9 -0.370837857517617 1.851996 -0.2002 0.842198 0.421099 M10 -1.06772121231664 1.844407 -0.5789 0.565545 0.282773 M11 -1.31099541995592 1.834468 -0.7146 0.478519 0.239259 t -0.195264491163186 0.032669 -5.9771 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.89732527534081 R-squared 0.80519264976546 Adjusted R-squared 0.740256866353947 F-TEST (value) 12.3998296080108 F-TEST (DF numerator) 15 F-TEST (DF denominator) 45 p-value 2.39483988195843e-11 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.89887556448711 Sum Squared Residuals 378.156579227121 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 80.2 79.2688998518525 0.931100148147502 2 74.8 77.0186758046253 -2.21867580462526 3 77.8 75.1221084090779 2.67789159092207 4 73 73.6735690447996 -0.673569044799629 5 72 73.5949865574949 -1.59498655749488 6 75.8 73.7863765152185 2.01362348478153 7 72.6 73.6853494885234 -1.08534948852337 8 71.9 72.102772952459 -0.202772952459035 9 74.8 76.4603526441141 -1.6603526441141 10 72.9 74.393628419868 -1.49362841986805 11 72.9 76.2160857841091 -3.31608578410913 12 79.9 76.3689321800133 3.53106781998670 13 74 75.1179168414532 -1.11791684145322 14 76 74.3167050832247 1.68329491677528 15 69.6 70.1205201980127 -0.520520198012685 16 77.3 73.4702093174188 3.82979068258122 17 75.2 74.6407192951527 0.559280704847296 18 75.8 73.6428232575138 2.15717674248622 19 77.6 73.0219955592375 4.57800444076245 20 76.7 74.2885665573687 2.41143344263126 21 77 76.0511131991934 0.94888680080664 22 77.9 76.7576307627144 1.14236923728564 23 76.7 75.2182735702559 1.48172642974415 24 71.9 75.2222460689466 -3.32224606894663 25 73.4 74.89863139035 -1.49863139035005 26 72.5 73.5535912258479 -1.0535912258479 27 73.7 71.4485434214636 2.25145657853643 28 69.5 71.641634403589 -2.14163440358901 29 74.7 73.9630980677127 0.736901932287297 30 72.5 74.1487968977511 -1.64879689775108 31 72.1 73.266273672088 -1.166273672088 32 70.7 74.8536938797332 -4.15369387973323 33 71.4 76.1707295219833 -4.7707295219833 34 69.5 74.6394524165743 -5.13945241657427 35 73.5 73.8766056358074 -0.376605635807353 36 72.4 74.3273157512883 -1.92731575128830 37 74.5 74.330220388747 0.169779611252972 38 72.2 71.8489622510979 0.351037748902109 39 73 70.790965013297 2.20903498670295 40 73.3 70.3990525885386 2.9009474114614 41 71.3 69.6576710325849 1.64232896741509 42 73.6 74.2368200284189 -0.636820028418914 43 71.3 74.2793336967424 -2.97933369674238 44 71.2 70.3447932441887 0.85520675581127 45 81.4 75.4990942842871 5.9009057157129 46 76.1 73.6087678405234 2.49123215947656 47 71.1 71.6113117970483 -0.511311797048289 48 75.7 72.5244903700094 3.17550962999062 49 70 71.4030066836362 -1.40300668363621 50 68.5 67.2620656352042 1.23793436479577 51 56.7 63.3178629581488 -6.61786295814876 52 57.9 61.815534645654 -3.91553464565398 53 58.8 60.1435250470548 -1.3435250470548 54 59.3 61.1851833010978 -1.88518330109776 55 61.3 60.6470475834087 0.652952416591306 56 62.9 61.8101733662503 1.08982663374973 57 61.4 61.8187103504221 -0.41871035042214 58 64.5 61.5005205603199 2.99947943968011 59 63.8 61.0777232127794 2.72227678722063 60 61.6 63.0570156297424 -1.45701562974238 61 64.7 61.781324843961 2.91867515603901 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 19 0.23925991950688 0.47851983901376 0.76074008049312 20 0.294213364505212 0.588426729010424 0.705786635494788 21 0.176763341045642 0.353526682091285 0.823236658954358 22 0.113087670523094 0.226175341046189 0.886912329476906 23 0.0894249561984708 0.178849912396942 0.910575043801529 24 0.270174427906442 0.540348855812884 0.729825572093558 25 0.196886163865332 0.393772327730664 0.803113836134668 26 0.128081803939589 0.256163607879179 0.87191819606041 27 0.18250092619244 0.36500185238488 0.81749907380756 28 0.212573525787618 0.425147051575235 0.787426474212382 29 0.156324486811328 0.312648973622656 0.843675513188672 30 0.222705341608857 0.445410683217713 0.777294658391143 31 0.209565888691486 0.419131777382972 0.790434111308514 32 0.257345844495958 0.514691688991916 0.742654155504042 33 0.285060572506748 0.570121145013496 0.714939427493252 34 0.472244810966617 0.944489621933233 0.527755189033383 35 0.373255935356234 0.746511870712468 0.626744064643766 36 0.305368434230863 0.610736868461727 0.694631565769137 37 0.351961377056051 0.703922754112102 0.648038622943949 38 0.405638335770558 0.811276671541117 0.594361664229442 39 0.355171179373265 0.71034235874653 0.644828820626735 40 0.270591876390886 0.541183752781772 0.729408123609114 41 0.183869841285086 0.367739682570173 0.816130158714914 42 0.111205806399792 0.222411612799585 0.888794193600208 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 0 0 OK

Charts produced by software:

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Parameters (Session):

par1 = 3 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 3 ; 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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