Multiple regression model 2

*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: Tue, 21 Dec 2010 16:57:19 +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/21/t1292950528z0s1cuyl8iicgba.htm/, Retrieved Tue, 21 Dec 2010 17:55:31 +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/21/t1292950528z0s1cuyl8iicgba.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 «

1038.00 0 934.00 0 988.00 0 870.00 0 854.00 0 834.00 0 872.00 0 954.00 0 870.00 0 1238.00 0 1082.00 0 1053.00 0 934.00 0 787.00 0 1081.00 0 908.00 0 995.00 0 825.00 0 822.00 0 856.00 0 887.00 0 1094.00 0 990.00 0 936.00 0 1097.00 0 918.00 0 926.00 0 907.00 0 899.00 0 971.00 0 1087.00 0 1000.00 0 1071.00 0 1190.00 0 1116.00 0 1070.00 0 1314.00 0 1068.00 0 1185.00 0 1215.00 0 1145.00 0 1251.00 1 1363.00 1 1368.00 1 1535.00 1 1853.00 1 1866.00 1 2023.00 1 1373.00 1 1968.00 1 1424.00 1 1160.00 1 1243.00 1 1375.00 1 1539.00 1 1773.00 1 1906.00 1 2076.00 1 2004.00 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 6 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Multiple Linear Regression - Estimated Regression Equation Asielaanvragen[t] = + 1117.44351464435 + 612.225941422594Verandering[t] -88.6887029288698M1[t] -104.88870292887M2[t] -119.08870292887M3[t] -227.88870292887M4[t] -212.68870292887M5[t] -311.133891213389M6[t] -225.733891213389M7[t] -172.133891213389M8[t] -108.533891213389M9[t] + 127.866108786611M10[t] + 49.2661087866109M11[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) 1117.44351464435 89.505374 12.4847 0 0 Verandering 612.225941422594 51.250628 11.9457 0 0 M1 -88.6887029288698 118.874945 -0.7461 0.459423 0.229711 M2 -104.88870292887 118.874945 -0.8823 0.382178 0.191089 M3 -119.08870292887 118.874945 -1.0018 0.321682 0.160841 M4 -227.88870292887 118.874945 -1.917 0.061455 0.030728 M5 -212.68870292887 118.874945 -1.7892 0.080171 0.040086 M6 -311.133891213389 119.095697 -2.6125 0.012103 0.006051 M7 -225.733891213389 119.095697 -1.8954 0.064333 0.032167 M8 -172.133891213389 119.095697 -1.4453 0.155141 0.07757 M9 -108.533891213389 119.095697 -0.9113 0.36688 0.18344 M10 127.866108786611 119.095697 1.0736 0.288583 0.144292 M11 49.2661087866109 119.095697 0.4137 0.681039 0.34052 Multiple Linear Regression - Regression Statistics Multiple R 0.892748647069733 R-squared 0.797000146844838 Adjusted R-squared 0.744043663413057 F-TEST (value) 15.0500957615801 F-TEST (DF numerator) 12 F-TEST (DF denominator) 46 p-value 3.94029253669714e-12 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 177.167127554879 Sum Squared Residuals 1443856.78995816 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 1038 1028.75481171548 9.24518828452053 2 934 1012.55481171548 -78.554811715481 3 988 998.354811715481 -10.3548117154812 4 870 889.554811715481 -19.5548117154812 5 854 904.754811715481 -50.7548117154812 6 834 806.309623430962 27.6903765690375 7 872 891.709623430962 -19.7096234309623 8 954 945.309623430962 8.69037656903756 9 870 1008.90962343096 -138.909623430962 10 1238 1245.30962343096 -7.30962343096233 11 1082 1166.70962343096 -84.7096234309624 12 1053 1117.44351464435 -64.4435146443515 13 934 1028.75481171548 -94.7548117154816 14 787 1012.55481171548 -225.554811715481 15 1081 998.354811715481 82.6451882845188 16 908 889.554811715481 18.4451882845189 17 995 904.754811715481 90.2451882845188 18 825 806.309623430962 18.6903765690377 19 822 891.709623430962 -69.7096234309624 20 856 945.309623430962 -89.3096234309624 21 887 1008.90962343096 -121.909623430962 22 1094 1245.30962343096 -151.309623430962 23 990 1166.70962343096 -176.709623430962 24 936 1117.44351464435 -181.443514644351 25 1097 1028.75481171548 68.2451882845184 26 918 1012.55481171548 -94.5548117154812 27 926 998.354811715481 -72.3548117154812 28 907 889.554811715481 17.4451882845189 29 899 904.754811715481 -5.75481171548118 30 971 806.309623430962 164.690376569038 31 1087 891.709623430962 195.290376569038 32 1000 945.309623430962 54.6903765690376 33 1071 1008.90962343096 62.0903765690376 34 1190 1245.30962343096 -55.3096234309623 35 1116 1166.70962343096 -50.7096234309624 36 1070 1117.44351464435 -47.4435146443515 37 1314 1028.75481171548 285.245188284518 38 1068 1012.55481171548 55.4451882845188 39 1185 998.354811715481 186.645188284519 40 1215 889.554811715481 325.445188284519 41 1145 904.754811715481 240.245188284519 42 1251 1418.53556485356 -167.535564853556 43 1363 1503.93556485356 -140.935564853556 44 1368 1557.53556485356 -189.535564853556 45 1535 1621.13556485356 -86.1355648535565 46 1853 1857.53556485356 -4.53556485355654 47 1866 1778.93556485356 87.0644351464435 48 2023 1729.66945606695 293.330543933054 49 1373 1640.98075313808 -267.980753138076 50 1968 1624.78075313808 343.219246861925 51 1424 1610.58075313808 -186.580753138075 52 1160 1501.78075313808 -341.780753138076 53 1243 1516.98075313808 -273.980753138075 54 1375 1418.53556485356 -43.5355648535565 55 1539 1503.93556485356 35.0644351464435 56 1773 1557.53556485356 215.464435146444 57 1906 1621.13556485356 284.864435146443 58 2076 1857.53556485356 218.464435146444 59 2004 1778.93556485356 225.064435146444 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.0811360300197006 0.162272060039401 0.9188639699803 17 0.051505415782243 0.103010831564486 0.948494584217757 18 0.0176642633602434 0.0353285267204868 0.982335736639757 19 0.00623086152132235 0.0124617230426447 0.993769138478678 20 0.00290595966717274 0.00581191933434547 0.997094040332827 21 0.000963837129898598 0.0019276742597972 0.999036162870101 22 0.000820860516952931 0.00164172103390586 0.999179139483047 23 0.000465092038157293 0.000930184076314586 0.999534907961843 24 0.000359478959698126 0.000718957919396252 0.999640521040302 25 0.000215856714762181 0.000431713429524361 0.999784143285238 26 0.00012450152038837 0.000249003040776741 0.999875498479612 27 7.70518330326966e-05 0.000154103666065393 0.999922948166967 28 2.39447123954541e-05 4.78894247909082e-05 0.999976055287605 29 7.21779870049229e-06 1.44355974009846e-05 0.9999927822013 30 7.0476855730999e-06 1.40953711461998e-05 0.999992952314427 31 3.00614113271065e-05 6.01228226542129e-05 0.999969938588673 32 1.34845675676039e-05 2.69691351352078e-05 0.999986515432432 33 1.70739989380218e-05 3.41479978760437e-05 0.999982926001062 34 9.58458313345019e-06 1.91691662669004e-05 0.999990415416867 35 1.22738221957814e-05 2.45476443915628e-05 0.999987726177804 36 7.76830186977637e-05 0.000155366037395527 0.999922316981302 37 0.000424181202738651 0.000848362405477303 0.999575818797261 38 0.0240337708934346 0.0480675417868692 0.975966229106565 39 0.0262651070814819 0.0525302141629637 0.973734892918518 40 0.0409036080392553 0.0818072160785106 0.959096391960745 41 0.0307864558134012 0.0615729116268025 0.969213544186599 42 0.0162593732869586 0.0325187465739173 0.98374062671304 43 0.00915020326644869 0.0183004065328974 0.990849796733551 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 18 0.642857142857143 NOK 5% type I error level 23 0.821428571428571 NOK 10% type I error level 26 0.928571428571429 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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