H1: multiple linear regression export poland (included seas. dummies and lin. trend)

*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, 04 Dec 2008 01:08:30 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/04/t1228378769ltpu04gktht2a5h.htm/, Retrieved Thu, 04 Dec 2008 08:19:29 +0000

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/2008/Dec/04/t1228378769ltpu04gktht2a5h.htm/}, year = {2008}, } @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 = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

Feedback Forum:

2008-11-27 13:41:43 [a2386b643d711541400692649981f2dc]  [reply]  test Post a new message

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

156.3 0 151.5 0 159.1 0 166.9 0 160.5 0 162.8 0 178.9 0 148.5 0 184.1 0 197 0 186.8 0 139.2 0 162.7 0 187.5 0 235.8 0 219.4 0 212.4 1 220.2 1 197.5 1 185.6 1 232.4 1 223.8 1 219.4 1 191.4 1 210.4 1 212.6 1 274.4 1 256 1 227.6 1 261.7 1 237 1 234.9 1 310.6 1 274.2 1 288.1 1 242.5 1 271.7 1 282.2 1 317.4 1 280.3 1 322.6 1 328.2 1 280.7 1 288.8 1 347.9 1 360.1 1 348 1 275.7 1 332.6 1 340.8 1 390.5 1 351.2 1 377.4 1 413.5 1 366.9 1 364.8 1 388 1 429.8 1 423.6 1 326.4 1

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 10 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation Poland[t] = + 139.424285714286 + 119.519642857143Dummy[t] + 15.6039285714285M1[t] + 23.7839285714286M2[t] + 64.3039285714286M3[t] + 43.6239285714286M4[t] + 25.06M5[t] + 42.24M6[t] + 17.16M7[t] + 9.48000000000002M8[t] + 57.56M9[t] + 61.94M10[t] + 58.14M11[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) 139.424285714286 31.25218 4.4613 5.1e-05 2.5e-05 Dummy 119.519642857143 18.415523 6.4902 0 0 M1 15.6039285714285 39.15194 0.3985 0.692031 0.346016 M2 23.7839285714286 39.15194 0.6075 0.546458 0.273229 M3 64.3039285714286 39.15194 1.6424 0.107178 0.053589 M4 43.6239285714286 39.15194 1.1142 0.27085 0.135425 M5 25.06 38.978316 0.6429 0.523399 0.2617 M6 42.24 38.978316 1.0837 0.284035 0.142018 M7 17.16 38.978316 0.4402 0.661778 0.330889 M8 9.48000000000002 38.978316 0.2432 0.808899 0.40445 M9 57.56 38.978316 1.4767 0.146421 0.07321 M10 61.94 38.978316 1.5891 0.118746 0.059373 M11 58.14 38.978316 1.4916 0.142486 0.071243 Multiple Linear Regression - Regression Statistics Multiple R 0.721228828916513 R-squared 0.520171023660284 Adjusted R-squared 0.397661497786315 F-TEST (value) 4.24596389504767 F-TEST (DF numerator) 12 F-TEST (DF denominator) 47 p-value 0.000160712427105358 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 61.6301293542771 Sum Squared Residuals 178518.823678571 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 156.3 155.028214285714 1.27178571428553 2 151.5 163.208214285714 -11.7082142857143 3 159.1 203.728214285714 -44.6282142857142 4 166.9 183.048214285714 -16.1482142857143 5 160.5 164.484285714286 -3.98428571428569 6 162.8 181.664285714286 -18.8642857142857 7 178.9 156.584285714286 22.3157142857143 8 148.5 148.904285714286 -0.404285714285711 9 184.1 196.984285714286 -12.8842857142857 10 197 201.364285714286 -4.36428571428569 11 186.8 197.564285714286 -10.7642857142857 12 139.2 139.424285714286 -0.224285714285711 13 162.7 155.028214285714 7.67178571428575 14 187.5 163.208214285714 24.2917857142857 15 235.8 203.728214285714 32.0717857142857 16 219.4 183.048214285714 36.3517857142857 17 212.4 284.003928571429 -71.6039285714286 18 220.2 301.183928571429 -80.9839285714286 19 197.5 276.103928571429 -78.6039285714286 20 185.6 268.423928571429 -82.8239285714286 21 232.4 316.503928571429 -84.1039285714286 22 223.8 320.883928571429 -97.0839285714286 23 219.4 317.083928571429 -97.6839285714286 24 191.4 258.943928571429 -67.5439285714286 25 210.4 274.547857142857 -64.1478571428571 26 212.6 282.727857142857 -70.1278571428572 27 274.4 323.247857142857 -48.8478571428572 28 256 302.567857142857 -46.5678571428571 29 227.6 284.003928571429 -56.4039285714286 30 261.7 301.183928571429 -39.4839285714286 31 237 276.103928571429 -39.1039285714286 32 234.9 268.423928571429 -33.5239285714286 33 310.6 316.503928571429 -5.90392857142855 34 274.2 320.883928571429 -46.6839285714286 35 288.1 317.083928571429 -28.9839285714286 36 242.5 258.943928571429 -16.4439285714285 37 271.7 274.547857142857 -2.84785714285712 38 282.2 282.727857142857 -0.527857142857138 39 317.4 323.247857142857 -5.84785714285716 40 280.3 302.567857142857 -22.2678571428571 41 322.6 284.003928571429 38.5960714285714 42 328.2 301.183928571429 27.0160714285714 43 280.7 276.103928571429 4.59607142857143 44 288.8 268.423928571429 20.3760714285714 45 347.9 316.503928571429 31.3960714285714 46 360.1 320.883928571429 39.2160714285714 47 348 317.083928571429 30.9160714285714 48 275.7 258.943928571429 16.7560714285714 49 332.6 274.547857142857 58.0521428571429 50 340.8 282.727857142857 58.0721428571429 51 390.5 323.247857142857 67.2521428571429 52 351.2 302.567857142857 48.6321428571428 53 377.4 284.003928571429 93.3960714285714 54 413.5 301.183928571429 112.316071428571 55 366.9 276.103928571429 90.7960714285714 56 364.8 268.423928571429 96.3760714285714 57 388 316.503928571429 71.4960714285714 58 429.8 320.883928571429 108.916071428571 59 423.6 317.083928571429 106.516071428571 60 326.4 258.943928571429 67.4560714285714 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.175395833959053 0.350791667918106 0.824604166040947 17 0.0792271034518703 0.158454206903741 0.92077289654813 18 0.0349780494520449 0.0699560989040898 0.965021950547955 19 0.0177198624474239 0.0354397248948478 0.982280137552576 20 0.00766190352579117 0.0153238070515823 0.992338096474209 21 0.00341931491824822 0.00683862983649644 0.996580685081752 22 0.00181846924041758 0.00363693848083517 0.998181530759582 23 0.00102517764864939 0.00205035529729877 0.99897482235135 24 0.000473685057528678 0.000947370115057356 0.999526314942471 25 0.00021553478730659 0.00043106957461318 0.999784465212693 26 0.000100859026354991 0.000201718052709983 0.999899140973645 27 8.34177356437657e-05 0.000166835471287531 0.999916582264356 28 3.67325881668643e-05 7.34651763337286e-05 0.999963267411833 29 3.38920834732144e-05 6.77841669464287e-05 0.999966107916527 30 8.78912553144288e-05 0.000175782510628858 0.999912108744686 31 7.46598983885768e-05 0.000149319796777154 0.999925340101611 32 0.000137903558630254 0.000275807117260508 0.99986209644137 33 0.000668575318899064 0.00133715063779813 0.9993314246811 34 0.0019058835947833 0.0038117671895666 0.998094116405217 35 0.00615604855975582 0.0123120971195116 0.993843951440244 36 0.00754303732743711 0.0150860746548742 0.992456962672563 37 0.0099303460657664 0.0198606921315328 0.990069653934234 38 0.0122381268094604 0.0244762536189207 0.98776187319054 39 0.0161065142045448 0.0322130284090896 0.983893485795455 40 0.0153935816812134 0.0307871633624269 0.984606418318787 41 0.0358850094933194 0.0717700189866388 0.96411499050668 42 0.0800985154513261 0.160197030902652 0.919901484548674 43 0.120226819974099 0.240453639948198 0.879773180025901 44 0.168655967792752 0.337311935585504 0.831344032207248 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 14 0.482758620689655 NOK 5% type I error level 22 0.758620689655172 NOK 10% type I error level 24 0.827586206896552 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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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