*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: Wed, 30 Dec 2009 13:00:28 -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/Dec/30/t1262203274zod6ynep4z8hxup.htm/, Retrieved Wed, 30 Dec 2009 21:01:26 +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/Dec/30/t1262203274zod6ynep4z8hxup.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:

» Textbox « » Textfile « » CSV «

28029 0 29383 0 36438 0 32034 0 22679 0 24319 0 18004 0 17537 0 20366 0 22782 0 19169 0 13807 0 29743 0 25591 0 29096 0 26482 0 22405 0 27044 0 17970 0 18730 0 19684 0 19785 0 18479 0 10698 0 31956 0 29506 0 34506 0 27165 0 26736 0 23691 0 18157 0 17328 0 18205 0 20995 0 17382 0 9367 0 31124 0 26551 0 30651 0 25859 0 25100 0 25778 0 20418 0 18688 0 20424 0 24776 0 19814 1 12738 1 31566 1 30111 1 30019 1 31934 1 25826 1 26835 1 20205 1 17789 1 20520 1 22518 1 15572 1 11509 1 25447 1 24090 1 27786 1 26195 1 20516 1 22759 1 19028 1 16971 1 20036 1 22485 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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation inschrijvingen[t] = + 11791.4779661017 -419.194915254242dummyvariabele[t] + 17992.4203389831M1[t] + 15886.9203389831M2[t] + 19764.2536723164M3[t] + 16626.4203389831M4[t] + 12225.2536723164M5[t] + 13419.2536723164M6[t] + 7311.92033898305M7[t] + 6188.75367231638M8[t] + 8220.75367231638M9[t] + 10571.7536723164M10[t] + 6459.4M11[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) 11791.4779661017 962.247319 12.2541 0 0 dummyvariabele -419.194915254242 529.165475 -0.7922 0.43154 0.21577 M1 17992.4203389831 1271.466194 14.1509 0 0 M2 15886.9203389831 1271.466194 12.495 0 0 M3 19764.2536723164 1271.466194 15.5445 0 0 M4 16626.4203389831 1271.466194 13.0766 0 0 M5 12225.2536723164 1271.466194 9.6151 0 0 M6 13419.2536723164 1271.466194 10.5542 0 0 M7 7311.92033898305 1271.466194 5.7508 0 0 M8 6188.75367231638 1271.466194 4.8674 9e-06 5e-06 M9 8220.75367231638 1271.466194 6.4656 0 0 M10 10571.7536723164 1271.466194 8.3146 0 0 M11 6459.4 1327.491866 4.8659 9e-06 5e-06 Multiple Linear Regression - Regression Statistics Multiple R 0.945106951835569 R-squared 0.89322715040792 Adjusted R-squared 0.870748655756956 F-TEST (value) 39.7369647869016 F-TEST (DF numerator) 12 F-TEST (DF denominator) 57 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2098.94893594679 Sum Squared Residuals 251118438.235594 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 28029 29783.8983050848 -1754.89830508477 2 29383 27678.3983050847 1704.60169491527 3 36438 31555.7316384181 4882.26836158191 4 32034 28417.8983050847 3616.10169491527 5 22679 24016.7316384181 -1337.73163841812 6 24319 25210.7316384181 -891.731638418078 7 18004 19103.3983050847 -1099.39830508474 8 17537 17980.2316384181 -443.231638418103 9 20366 20012.2316384181 353.768361581912 10 22782 22363.2316384181 418.768361581925 11 19169 18250.8779661017 918.122033898297 12 13807 11791.4779661017 2015.52203389831 13 29743 29783.8983050847 -40.8983050847414 14 25591 27678.3983050847 -2087.39830508475 15 29096 31555.7316384181 -2459.73163841807 16 26482 28417.8983050847 -1935.89830508475 17 22405 24016.7316384181 -1611.73163841807 18 27044 25210.7316384181 1833.26836158192 19 17970 19103.3983050847 -1133.39830508475 20 18730 17980.2316384181 749.768361581926 21 19684 20012.2316384181 -328.231638418077 22 19785 22363.2316384181 -2578.23163841808 23 18479 18250.8779661017 228.122033898308 24 10698 11791.4779661017 -1093.47796610170 25 31956 29783.8983050847 2172.10169491526 26 29506 27678.3983050847 1827.60169491525 27 34506 31555.7316384181 2950.26836158192 28 27165 28417.8983050847 -1252.89830508475 29 26736 24016.7316384181 2719.26836158193 30 23691 25210.7316384181 -1519.73163841808 31 18157 19103.3983050847 -946.398305084747 32 17328 17980.2316384181 -652.231638418074 33 18205 20012.2316384181 -1807.23163841808 34 20995 22363.2316384181 -1368.23163841808 35 17382 18250.8779661017 -868.877966101692 36 9367 11791.4779661017 -2424.47796610170 37 31124 29783.8983050847 1340.10169491526 38 26551 27678.3983050847 -1127.39830508475 39 30651 31555.7316384181 -904.731638418074 40 25859 28417.8983050847 -2558.89830508475 41 25100 24016.7316384181 1083.26836158193 42 25778 25210.7316384181 567.268361581921 43 20418 19103.3983050847 1314.60169491525 44 18688 17980.2316384181 707.768361581926 45 20424 20012.2316384181 411.768361581922 46 24776 22363.2316384181 2412.76836158192 47 19814 17831.6830508475 1982.31694915254 48 12738 11372.2830508475 1365.71694915254 49 31566 29364.7033898305 2201.29661016949 50 30111 27259.2033898305 2851.79661016949 51 30019 31136.5367231638 -1117.53672316384 52 31934 27998.7033898305 3935.29661016949 53 25826 23597.5367231638 2228.46327683617 54 26835 24791.5367231638 2043.46327683616 55 20205 18684.2033898305 1520.79661016949 56 17789 17561.0367231638 227.963276836163 57 20520 19593.0367231638 926.96327683616 58 22518 21944.0367231638 573.963276836157 59 15572 17831.6830508475 -2259.68305084745 60 11509 11372.2830508475 136.71694915254 61 25447 29364.7033898305 -3917.70338983051 62 24090 27259.2033898305 -3169.20338983051 63 27786 31136.5367231638 -3350.53672316384 64 26195 27998.7033898305 -1803.70338983051 65 20516 23597.5367231638 -3081.53672316383 66 22759 24791.5367231638 -2032.53672316384 67 19028 18684.2033898305 343.796610169490 68 16971 17561.0367231638 -590.036723163836 69 20036 19593.0367231638 442.96327683616 70 22485 21944.0367231638 540.963276836157 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.984335520375155 0.0313289592496907 0.0156644796248454 17 0.966785768969157 0.0664284620616863 0.0332142310308432 18 0.952270325630225 0.0954593487395501 0.0477296743697751 19 0.916770033600203 0.166459932799593 0.0832299663997966 20 0.869112430415186 0.261775139169627 0.130887569584814 21 0.802556241943918 0.394887516112164 0.197443758056082 22 0.795705625091643 0.408588749816714 0.204294374908357 23 0.71825176667185 0.5634964666563 0.28174823332815 24 0.6874972688188 0.6250054623624 0.3125027311812 25 0.687222278665048 0.625555442669904 0.312777721334952 26 0.65053981109151 0.69892037781698 0.34946018890849 27 0.68717577243496 0.62564845513008 0.31282422756504 28 0.637067313279523 0.725865373440954 0.362932686720477 29 0.707219223852961 0.585561552294077 0.292780776147039 30 0.66060955842064 0.67878088315872 0.33939044157936 31 0.593255235582573 0.813489528834855 0.406744764417427 32 0.512351279327347 0.975297441345305 0.487648720672652 33 0.475201917610726 0.950403835221452 0.524798082389274 34 0.425811746775084 0.851623493550167 0.574188253224916 35 0.358021580745074 0.716043161490149 0.641978419254926 36 0.385277712879485 0.770555425758971 0.614722287120515 37 0.333240468144585 0.66648093628917 0.666759531855415 38 0.279569466336206 0.559138932672412 0.720430533663794 39 0.251292583297326 0.502585166594651 0.748707416702674 40 0.304114720605794 0.608229441211587 0.695885279394206 41 0.240031595828373 0.480063191656746 0.759968404171627 42 0.178204522310793 0.356409044621587 0.821795477689207 43 0.142837679939637 0.285675359879275 0.857162320060363 44 0.0988306067394091 0.197661213478818 0.90116939326059 45 0.070744177519314 0.141488355038628 0.929255822480686 46 0.06151884914092 0.12303769828184 0.93848115085908 47 0.0601063773170568 0.120212754634114 0.939893622682943 48 0.0372408381279993 0.0744816762559986 0.962759161872 49 0.069248384148242 0.138496768296484 0.930751615851758 50 0.146112760899011 0.292225521798022 0.853887239100989 51 0.139650380242005 0.279300760484010 0.860349619757995 52 0.327938547961317 0.655877095922634 0.672061452038683 53 0.653326782421828 0.693346435156343 0.346673217578172 54 0.958402525925217 0.0831949481495651 0.0415974740747826 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 1 0.0256410256410256 OK 10% type I error level 5 0.128205128205128 NOK

Charts produced by software:

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Parameters (Session):

par1 = 0 ; par2 = 0 ;

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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