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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 04:49:55 -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/t1258717857fljc0skms2mbege.htm/, Retrieved Fri, 20 Nov 2009 12:51:09 +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/t1258717857fljc0skms2mbege.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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1,58 0,55 1,59 0,55 1,6 0,55 1,6 0,55 1,6 0,55 1,6 0,56 1,61 0,56 1,61 0,56 1,62 0,56 1,63 0,56 1,63 0,55 1,63 0,56 1,63 0,55 1,63 0,55 1,64 0,56 1,64 0,55 1,64 0,55 1,65 0,55 1,65 0,55 1,65 0,53 1,65 0,53 1,65 0,53 1,66 0,53 1,67 0,54 1,68 0,54 1,68 0,54 1,68 0,55 1,68 0,55 1,69 0,54 1,7 0,55 1,7 0,56 1,71 0,58 1,73 0,59 1,73 0,6 1,73 0,6 1,74 0,6 1,74 0,59 1,74 0,6 1,75 0,6 1,78 0,62 1,82 0,65 1,83 0,68 1,84 0,73 1,85 0,78 1,86 0,78 1,86 0,82 1,87 0,82 1,87 0,81 1,87 0,83 1,87 0,85 1,87 0,86 1,87 0,85 1,87 0,85 1,88 0,82 1,88 0,8 1,87 0,81 1,87 0,8 1,87 0,8 1,87 0,8 1,87 0,8 1,87 0,79

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 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 1.39450175395646 + 0.340169624901634X[t] -0.00181850174385351M1[t] -0.00116977140470005M2[t] -0.000997065664072645M3[t] + 0.00121665782596459M4[t] + 0.00606970281639524M5[t] + 0.00892274780682585M6[t] + 0.00641511429764998M7[t] + 0.000546802288867615M8[t] + 0.00476052577890482M9[t] -0.000427446980074374M10[t] + 0.00046661575976609M11[t] + 0.00378627650996281t + 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) 1.39450175395646 0.016644 83.7832 0 0 X 0.340169624901634 0.032204 10.5629 0 0 M1 -0.00181850174385351 0.009256 -0.1965 0.845088 0.422544 M2 -0.00116977140470005 0.009721 -0.1203 0.904728 0.452364 M3 -0.000997065664072645 0.009709 -0.1027 0.918639 0.459319 M4 0.00121665782596459 0.009691 0.1255 0.900624 0.450312 M5 0.00606970281639524 0.00968 0.6271 0.53365 0.266825 M6 0.00892274780682585 0.00967 0.9227 0.360862 0.180431 M7 0.00641511429764998 0.009664 0.6638 0.510057 0.255029 M8 0.000546802288867615 0.009665 0.0566 0.955123 0.477561 M9 0.00476052577890482 0.009654 0.4931 0.624228 0.312114 M10 -0.000427446980074374 0.009655 -0.0443 0.964875 0.482438 M11 0.00046661575976609 0.009647 0.0484 0.961626 0.480813 t 0.00378627650996281 0.000217 17.433 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.991688932549206 R-squared 0.983446938940583 Adjusted R-squared 0.978868432690106 F-TEST (value) 214.796460928308 F-TEST (DF numerator) 13 F-TEST (DF denominator) 47 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.0152504234527843 Sum Squared Residuals 0.0109310445279940 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 1.58 1.58356282241847 -0.00356282241847002 2 1.59 1.58799782926758 0.00200217073241852 3 1.6 1.59195681151817 0.00804318848182836 4 1.6 1.59795681151817 0.00204318848182837 5 1.6 1.60659613301857 -0.00659613301856506 6 1.6 1.61663715076798 -0.0166371507679749 7 1.61 1.61791579376876 -0.00791579376876178 8 1.61 1.61583375826994 -0.00583375826994225 9 1.62 1.62383375826994 -0.00383375826994223 10 1.63 1.62243206202093 0.00756793797907393 11 1.63 1.62371070502171 0.006289294978287 12 1.63 1.63043206202093 -0.000432062020926052 13 1.63 1.62899814053802 0.00100185946198101 14 1.63 1.63343314738714 -0.00343314738713537 15 1.64 1.64079382588674 -0.000793825886741844 16 1.64 1.64339212963773 -0.0033921296377255 17 1.64 1.65203145113812 -0.0120314511381190 18 1.65 1.65867077263851 -0.00867077263851238 19 1.65 1.6599494156393 -0.00994941563929933 20 1.65 1.65106398764245 -0.00106398764244708 21 1.65 1.65906398764245 -0.0090639876424471 22 1.65 1.65766229139343 -0.00766229139343073 23 1.66 1.66234263064323 -0.00234263064323399 24 1.67 1.66906398764245 0.000936012357552973 25 1.68 1.67103176240856 0.0089682375914437 26 1.68 1.67546676925767 0.00453323074232744 27 1.68 1.68282744775728 -0.00282744775727914 28 1.68 1.68882744775728 -0.00882744775727915 29 1.69 1.69406507300866 -0.00406507300865628 30 1.7 1.70410609075807 -0.00410609075806603 31 1.7 1.70878643000787 -0.00878643000786932 32 1.71 1.71350778700708 -0.0035077870070824 33 1.73 1.7249094832561 0.00509051674390125 34 1.73 1.7269094832561 0.00309051674390130 35 1.73 1.73158982250590 -0.00158982250590198 36 1.74 1.73490948325610 0.0050905167439013 37 1.74 1.73347556177319 0.00652443822680838 38 1.74 1.74131226487132 -0.00131226487132422 39 1.75 1.74527124712191 0.00472875287808552 40 1.78 1.75807463961995 0.0219253603800528 41 1.82 1.77691904986739 0.0430809501326104 42 1.83 1.79376346011483 0.0362365398851679 43 1.84 1.8120505843607 0.0279494156392993 44 1.85 1.82697703010696 0.0230229698930372 45 1.86 1.83497703010696 0.0250229698930372 46 1.86 1.84718211885401 0.0128178811459882 47 1.87 1.85186245810382 0.018137541896185 48 1.87 1.85178042260500 0.0182195773950046 49 1.87 1.86055158986914 0.00944841013086265 50 1.87 1.87178998921629 -0.00178998921628635 51 1.87 1.87915066771589 -0.0091506677158929 52 1.87 1.88174897146688 -0.0117489714668766 53 1.87 1.89038829296727 -0.0203882929672701 54 1.88 1.88682252572061 -0.00682252572061463 55 1.88 1.88129777622337 -0.00129777622336891 56 1.87 1.88261743697357 -0.0126174369735655 57 1.87 1.88721574072455 -0.0172157407245491 58 1.87 1.88581404447553 -0.0158140444755328 59 1.87 1.89049438372534 -0.020494383725336 60 1.87 1.89381404447553 -0.0238140444755328 61 1.87 1.89238012299263 -0.0223801229926257 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.0107572451556727 0.0215144903113454 0.989242754844327 18 0.00232876214262528 0.00465752428525056 0.997671237857375 19 0.00111595958248040 0.00223191916496081 0.99888404041752 20 0.000344716013824551 0.000689432027649102 0.999655283986175 21 0.000351945495430277 0.000703890990860554 0.99964805450457 22 0.000857114192365567 0.00171422838473113 0.999142885807634 23 0.000319941549088036 0.000639883098176072 0.999680058450912 24 0.000118062792663675 0.000236125585327349 0.999881937207336 25 0.000200407713899102 0.000400815427798204 0.9997995922861 26 8.08745333451187e-05 0.000161749066690237 0.999919125466655 27 3.47444651721434e-05 6.94889303442868e-05 0.999965255534828 28 2.18048072190983e-05 4.36096144381967e-05 0.999978195192781 29 1.54315079395946e-05 3.08630158791891e-05 0.99998456849206 30 2.27202331958586e-05 4.54404663917173e-05 0.999977279766804 31 3.12256941957e-05 6.24513883914e-05 0.999968774305804 32 2.67514855442952e-05 5.35029710885903e-05 0.999973248514456 33 3.22906662037787e-05 6.45813324075575e-05 0.999967709333796 34 2.42471905199030e-05 4.84943810398061e-05 0.99997575280948 35 8.57138946197005e-05 0.000171427789239401 0.99991428610538 36 0.000232696389757752 0.000465392779515505 0.999767303610242 37 0.00140192166101792 0.00280384332203584 0.998598078338982 38 0.0131415453567058 0.0262830907134115 0.986858454643294 39 0.130373177180816 0.260746354361632 0.869626822819184 40 0.575573062400501 0.848853875198998 0.424426937599499 41 0.938723276945066 0.122553446109868 0.061276723054934 42 0.91909588973759 0.161808220524820 0.0809041102624099 43 0.924529336222913 0.150941327554174 0.0754706637770872 44 0.9162073045724 0.167585390855200 0.0837926954276002 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 20 0.714285714285714 NOK 5% type I error level 22 0.785714285714286 NOK 10% type I error level 22 0.785714285714286 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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