ws7

*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: Fri, 20 Nov 2009 07:41:25 -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/20/t1258728335vg35zpgfbtd770s.htm/, Retrieved Fri, 20 Nov 2009 15:45:47 +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/20/t1258728335vg35zpgfbtd770s.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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10284.5 1.038351422 1.4 12792 0.933031106 1.3 12823.61538 0.932783124 1.3 13845.66667 0.953755367 1.2 15335.63636 1.009865664 1.1 11188.5 0.979532493 1.4 13633.25 0.98651077 1.2 12298.46667 0.964661281 1.5 15353.63636 0.946761816 1.1 12696.15385 0.959068881 1.3 12213.93333 0.985710058 1.5 13683.72727 0.92582159 1.1 11214.14286 1.036865325 1.4 13950.23077 0.944443576 1.3 11179.13333 0.944901812 1.5 11801.875 0.989151445 1.6 11188.82353 1.054361624 1.7 16456.27273 1.033478919 1.1 11110.0625 1.001368875 1.6 16530.69231 1.019812646 1.3 10038.41176 0.993902155 1.7 11681.25 0.961444482 1.6 11148.88235 0.957449711 1.7 8631 0.93308639 1.9 9386.444444 1.045170549 1.8 9764.736842 0.953166261 1.9 12043.75 0.966782226 1.6 12948.06667 0.972992606 1.5 10987.125 1.013607482 1.6 11648.3125 0.984839518 1.6 10633.35294 0.973220775 1.7 10219.3 0.957284573 2 9037.6 0.972067159 2 10296.31579 0.986878944 1.9 11705.41176 0.954654488 1.7 10681.94444 0.978986976 1.8 9362.947368 1.003056035 1.9 113 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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Invoer/inflatie[t] = + 54.4678682869157 + 19736.9890382847`Uitvoer/inflatie`[t] -4260.49052841623Inflatie[t] -2600.41110213936M1[t] + 511.415961808663M2[t] + 397.466380062199M3[t] -191.940314138286M4[t] -1531.96966104220M5[t] -844.712461834646M6[t] -671.981889680457M7[t] + 400.300576732874M8[t] -172.657737688075M9[t] -272.504655250035M10[t] + 297.501985184866M11[t] -26.4309477551256t + 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) 54.4678682869157 6051.67942 0.009 0.992859 0.496429 `Uitvoer/inflatie` 19736.9890382847 6944.096051 2.8423 0.00671 0.003355 Inflatie -4260.49052841623 623.664301 -6.8314 0 0 M1 -2600.41110213936 935.528045 -2.7796 0.007915 0.003958 M2 511.415961808663 707.678516 0.7227 0.473624 0.236812 M3 397.466380062199 714.549904 0.5562 0.580798 0.290399 M4 -191.940314138286 776.844708 -0.2471 0.805973 0.402986 M5 -1531.96966104220 952.047675 -1.6091 0.114582 0.057291 M6 -844.712461834646 859.821057 -0.9824 0.331142 0.165571 M7 -671.981889680457 732.053175 -0.9179 0.363544 0.181772 M8 400.300576732874 742.537861 0.5391 0.592477 0.296238 M9 -172.657737688075 712.221312 -0.2424 0.809555 0.404778 M10 -272.504655250035 701.299285 -0.3886 0.699426 0.349713 M11 297.501985184866 704.679953 0.4222 0.674904 0.337452 t -26.4309477551256 16.55801 -1.5963 0.11743 0.058715 Multiple Linear Regression - Regression Statistics Multiple R 0.923156921377264 R-squared 0.852218701486747 Adjusted R-squared 0.806242297504847 F-TEST (value) 18.5360016808238 F-TEST (DF numerator) 14 F-TEST (DF denominator) 45 p-value 3.50830475781549e-14 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1088.85489387133 Sum Squared Residuals 53352224.0958391 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 10284.5 11956.8697125110 -1672.36971251104 2 12792 13389.6089591449 -597.608959144895 3 12823.61538 13244.3340116276 -420.718631627615 4 13845.66667 13468.4743527129 377.192317287128 5 15335.63636 13635.5114277194 1700.12493228065 6 11188.5 12419.5050571235 -1231.0050571235 7 13633.25 13555.6329638609 77.6170361390786 8 12298.46667 12892.0941991091 -593.627529109136 9 15353.63636 13643.6196038034 1710.01675619661 10 12696.15385 12908.1480398015 -211.994189801517 11 12213.93333 13125.4422452141 -911.508915214052 12 13683.72727 13323.6874872049 360.039782795114 13 11214.14286 11610.3672592507 -396.224399250729 14 13950.23077 13297.6853813731 652.545388626859 15 11179.13333 12314.2509450973 -1135.11761509725 16 11801.875 12145.7187717691 -343.843771769142 17 11188.82353 11640.2620123761 -451.438482376064 18 16456.27273 14445.2208612035 2011.0518687965 19 11110.0625 11827.5196349476 -717.457134947606 20 16530.69231 14515.5428181823 2015.14949181768 21 10038.41176 11700.5622677962 -1662.15050779617 22 11681.25 11359.7167191115 321.533280888521 23 11148.88235 11398.3986075122 -249.516257512174 24 8631 9741.50896937573 -1110.50896937573 25 9386.444444 9752.91978987123 -366.475345871229 26 9764.736842 10596.3792294913 -831.642387491307 27 12043.75 12002.8840104653 40.8659895347464 28 12948.06667 11935.6696233349 1012.39704666515 29 10987.125 10944.7756382375 42.3493617625198 30 11648.3125 11037.8088995681 610.50360043186 31 10633.35294 10528.7404678959 104.612472104067 32 10219.3 9981.91218384338 237.387816156622 33 9037.6 9674.2866595068 -636.686659506803 34 10296.31579 10266.3978852138 29.9179047862289 35 11705.41176 11026.0579487401 679.353811259897 36 10681.94444 10756.3260118887 -74.381571888684 37 9362.947368 8178.4856627974 1184.46170520259 38 11306.35294 11465.1550593118 -158.802119311781 39 10984.45 10466.9304607794 517.519539220574 40 10062.61905 10041.4829669374 21.1360830626299 41 8118.583333 8725.0204340908 -606.437101090796 42 8867.48 8377.01076779927 490.469232200726 43 8346.72 7054.4650954625 1292.25490453750 44 8529.307692 8691.89757786712 -162.589885867121 45 10697.18182 9556.36697469448 1140.81484530552 46 8591.84 7777.75818495923 814.081815040767 47 8695.607143 7287.63736130783 1407.96978169217 48 8125.571429 6909.55430156025 1216.01712743975 49 7009.758621 5759.15086856959 1250.60775243041 50 7883.466667 6947.95858967888 935.508077321123 51 7527.645161 6530.19444303045 997.45071796955 52 6763.758621 7830.64029624576 -1066.88167524576 53 6682.333333 7366.9320435763 -684.598710576306 54 7855.681818 9736.70146230559 -1881.01964430559 55 6738.88 7495.90727783304 -757.027277833038 56 7895.434783 9391.75467599805 -1496.31989299805 57 6361.884615 6913.87904919916 -551.994434199156 58 6935.956522 7889.495332914 -953.538810914 59 8344.454545 9270.75296522584 -926.298420225837 60 9107.944444 9499.11081297045 -391.16636897045 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 18 0.0396557973045622 0.0793115946091243 0.960344202695438 19 0.0149734650655189 0.0299469301310378 0.985026534934481 20 0.00791729210478549 0.0158345842095710 0.992082707895215 21 0.0277724367935391 0.0555448735870782 0.97222756320646 22 0.0381554598937814 0.0763109197875627 0.961844540106219 23 0.0192592755484715 0.038518551096943 0.980740724451528 24 0.160672905171715 0.321345810343430 0.839327094828285 25 0.160048732925869 0.320097465851738 0.83995126707413 26 0.238079351340466 0.476158702680932 0.761920648659534 27 0.192011246509730 0.384022493019461 0.80798875349027 28 0.244146067746356 0.488292135492711 0.755853932253644 29 0.430489681506037 0.860979363012074 0.569510318493963 30 0.359962258982155 0.71992451796431 0.640037741017845 31 0.268688113028761 0.537376226057521 0.73131188697124 32 0.208310106952111 0.416620213904222 0.791689893047889 33 0.448381637275994 0.896763274551987 0.551618362724006 34 0.385900410605091 0.771800821210182 0.614099589394909 35 0.290994610320489 0.581989220640977 0.709005389679511 36 0.464500039424954 0.929000078849908 0.535499960575046 37 0.465150217498443 0.930300434996886 0.534849782501557 38 0.590776865912517 0.818446268174966 0.409223134087483 39 0.690864591206261 0.618270817587478 0.309135408793739 40 0.563964121567726 0.872071756864549 0.436035878432274 41 0.942904312117155 0.114191375765689 0.0570956878828446 42 0.919998620121816 0.160002759756368 0.0800013798781842 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 3 0.12 NOK 10% type I error level 6 0.24 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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