Multiple regression model 4

*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 17:22:06 +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/t1292952039ox63qwqi3pw7xkt.htm/, Retrieved Tue, 21 Dec 2010 18:20:49 +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/t1292952039ox63qwqi3pw7xkt.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:

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1038,00 0 934,00 988,00 870,00 854,00 934,00 0 988,00 870,00 854,00 834,00 988,00 0 870,00 854,00 834,00 872,00 870,00 0 854,00 834,00 872,00 954,00 854,00 0 834,00 872,00 954,00 870,00 834,00 0 872,00 954,00 870,00 1238,00 872,00 0 954,00 870,00 1238,00 1082,00 954,00 0 870,00 1238,00 1082,00 1053,00 870,00 0 1238,00 1082,00 1053,00 934,00 1238,00 0 1082,00 1053,00 934,00 787,00 1082,00 0 1053,00 934,00 787,00 1081,00 1053,00 0 934,00 787,00 1081,00 908,00 934,00 0 787,00 1081,00 908,00 995,00 787,00 0 1081,00 908,00 995,00 825,00 1081,00 0 908,00 995,00 825,00 822,00 908,00 0 995,00 825,00 822,00 856,00 995,00 0 825,00 822,00 856,00 887,00 825,00 0 822,00 856,00 887,00 1094,00 822,00 0 856,00 887,00 1094,00 990,00 856,00 0 887,00 1094,00 990,00 936,00 887,00 0 1094,00 990,00 936,00 1097,00 1094,00 0 990,00 936,00 1097,00 918,00 990,00 0 936,00 1097,00 918,00 926,00 936,00 0 1097,00 918,00 926,00 907,00 1097,00 0 918,00 926,00 907,00 899,00 918,00 0 926,00 907,00 899,00 971,00 926,0 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 6 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Maandelijksewerkloosheid[t] = + 785.581646496084 + 316.837588957848x[t] + 0.113241666763825`y-1`[t] + 0.331362488209895`y-2`[t] + 0.0193980967903263`y-3`[t] -0.253615790411075`y-4`[t] -59.0113984962233M1[t] -35.8482054764646M2[t] -25.6599930393899M3[t] -136.285762455275M4[t] -141.100697932726M5[t] -153.268034800840M6[t] -123.621358861251M7[t] -197.682505736142M8[t] -180.794636617663M9[t] + 78.107982061271M10[t] + 15.0932390499574M11[t] + 4.08900526417693t + 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) 785.581646496084 187.243562 4.1955 0.000163 8.2e-05 x 316.837588957848 102.677091 3.0858 0.003832 0.001916 `y-1` 0.113241666763825 0.154518 0.7329 0.468255 0.234127 `y-2` 0.331362488209895 0.152241 2.1766 0.035969 0.017985 `y-3` 0.0193980967903263 0.151166 0.1283 0.898588 0.449294 `y-4` -0.253615790411075 0.146221 -1.7345 0.091161 0.04558 M1 -59.0113984962233 100.972532 -0.5844 0.562478 0.281239 M2 -35.8482054764646 102.743999 -0.3489 0.729136 0.364568 M3 -25.6599930393899 105.464578 -0.2433 0.809114 0.404557 M4 -136.285762455275 106.342184 -1.2816 0.207964 0.103982 M5 -141.100697932726 106.655141 -1.323 0.193966 0.096983 M6 -153.268034800840 117.242164 -1.3073 0.199184 0.099592 M7 -123.621358861251 113.945213 -1.0849 0.284976 0.142488 M8 -197.682505736142 113.423447 -1.7429 0.089663 0.044831 M9 -180.794636617663 109.898744 -1.6451 0.108419 0.05421 M10 78.107982061271 107.728175 0.725 0.472984 0.236492 M11 15.0932390499574 107.050948 0.141 0.888642 0.444321 t 4.08900526417693 2.565665 1.5937 0.119502 0.059751 Multiple Linear Regression - Regression Statistics Multiple R 0.907790108097507 R-squared 0.824082880359683 Adjusted R-squared 0.743256095660078 F-TEST (value) 10.195665748952 F-TEST (DF numerator) 17 F-TEST (DF denominator) 37 p-value 2.88513257729051e-09 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 148.271370356329 Sum Squared Residuals 813422.77289172 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 1038 964.101567569352 73.8984324306477 2 934 963.129988509344 -29.1299885093441 3 988 948.717527749679 39.2824722503214 4 870 813.682280029876 56.3177199701244 5 854 846.177661364638 7.82233863536176 6 834 774.614186129275 59.3858138707251 7 872 836.503797921011 35.4962020789889 8 954 883.289506786007 70.7104932139932 9 870 923.864500629006 -53.8645006290055 10 1238 1194.55406007125 43.445939928748 11 1082 1015.49761528195 66.502384718047 12 1053 991.885909581895 61.1140904181054 13 934 992.317118358785 -58.3171183587849 14 787 1040.33897500161 -253.338975001614 15 1081 1061.31709174386 19.6829082561369 16 908 899.619598440578 8.38040155942176 17 995 871.445943200952 123.554056799048 18 825 822.397083581267 2.60291641873282 19 822 900.64666682786 -78.6466668278594 20 856 914.454902562276 -58.4549025622758 21 887 882.531463708354 4.46853629164575 22 1094 1164.37270001152 -70.372700011518 23 990 1147.18008721217 -157.180087212171 24 936 1100.06776117793 -164.067761177928 25 1097 1029.18637198511 67.8136280148916 26 918 1032.63309464325 -114.633094643247 27 926 1014.08505205153 -88.0850520515253 28 907 954.81520671026 -47.8152067102606 29 899 980.986369596385 -81.9863695963852 30 971 928.412520675986 42.587479324014 31 1087 996.89885554267 90.10114445733 32 1000 984.62987556559 15.3701244344101 33 1071 931.787118852952 139.212881147048 34 1190 1238.27880505585 -48.2788050558488 35 1116 1220.55141847227 -104.551418472275 36 1070 1150.32408288937 -80.3240828893692 37 1314 1124.64869898646 189.351301013535 38 1068 1146.84990636917 -78.8499063691678 39 1185 1114.98022963238 70.0197703676242 40 1215 1036.54548044591 178.454519554090 41 1145 1042.67891907441 102.321080925588 42 1251 1288.36771636018 -37.3677163601832 43 1363 1380.8787309328 -17.8787309328007 44 1368 1395.62571508613 -27.6257150861273 45 1535 1624.81691680969 -89.8169168096881 46 1853 1777.79443486138 75.2055651386188 47 1866 1670.7708790336 195.229120966398 48 2023 1839.72224635081 183.277753649192 49 1373 1645.74624310029 -272.74624310029 50 1968 1492.04803547663 475.951964523373 51 1424 1464.90009882256 -40.9000988225573 52 1160 1355.33743437338 -195.337434373375 53 1243 1394.71110676361 -151.711106763612 54 1375 1442.20849325329 -67.2084932532887 55 1539 1568.07194877566 -29.0719487756588 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.113092285054002 0.226184570108004 0.886907714945998 22 0.0406324150817447 0.0812648301634895 0.959367584918255 23 0.0138374800061041 0.0276749600122081 0.986162519993896 24 0.0153647089178795 0.0307294178357590 0.98463529108212 25 0.0139018442199219 0.0278036884398438 0.986098155780078 26 0.00843910902341185 0.0168782180468237 0.991560890976588 27 0.00325489615046637 0.00650979230093274 0.996745103849534 28 0.00176641421060536 0.00353282842121073 0.998233585789395 29 0.000575107586278198 0.00115021517255640 0.999424892413722 30 0.000366114533177452 0.000732229066354905 0.999633885466823 31 0.000449908718232617 0.000899817436465234 0.999550091281767 32 0.000124382381039456 0.000248764762078912 0.99987561761896 33 0.000193358145939456 0.000386716291878912 0.99980664185406 34 0.0284704132159483 0.0569408264318965 0.971529586784052 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 7 0.5 NOK 5% type I error level 11 0.785714285714286 NOK 10% type I error level 13 0.928571428571429 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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