*Unverified author*

R Software Module: rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Thu, 27 Nov 2008 15:47:32 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Nov/27/t1227826082ggg6kr62xtztxqc.htm/, Retrieved Thu, 27 Nov 2008 22:48:12 +0000

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/2008/Nov/27/t1227826082ggg6kr62xtztxqc.htm/}, year = {2008}, } @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 = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

Feedback Forum:

2008-11-27 13:41:43 [a2386b643d711541400692649981f2dc]  [reply]  test Post a new message

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

2120.88 0 2174.56 0 2196.72 0 2350.44 0 2440.25 0 2408.64 0 2472.81 0 2407.6 0 2454.62 0 2448.05 0 2497.84 0 2645.64 0 2756.76 0 2849.27 0 2921.44 0 2981.85 0 3080.58 0 3106.22 0 3119.31 0 3061.26 0 3097.31 0 3161.69 0 3257.16 0 3277.01 0 3295.32 0 3363.99 0 3494.17 0 3667.03 0 3813.06 0 3917.96 0 3895.51 0 3801.06 0 3570.12 0 3701.61 0 3862.27 0 3970.1 0 4138.52 0 4199.75 0 4290.89 0 4443.91 0 4502.64 1 4356.98 1 4591.27 1 4696.96 1 4621.4 1 4562.84 1 4202.52 1 4296.49 1 4435.23 1 4105.18 1 4116.68 1 3844.49 1 3720.98 1 3674.4 1 3857.62 1 3801.06 1 3504.37 1 3032.6 1 3047.03 1 2962.34 1 2197.82 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 4 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Bel20[t] = + 3128.62668 + 754.2233dummy[t] -222.612779999999M1[t] + 59.0786599999997M2[t] + 124.508659999999M3[t] + 178.072659999999M4[t] + 81.1859999999996M5[t] + 62.523999999999M6[t] + 156.987999999999M7[t] + 123.271999999999M8[t] + 19.247999999999M9[t] -48.9580000000007M10[t] -56.9520000000007M11[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) 3128.62668 331.203189 9.4462 0 0 dummy 754.2233 196.995911 3.8286 0.000373 0.000187 M1 -222.612779999999 435.772291 -0.5108 0.6118 0.3059 M2 59.0786599999997 456.645416 0.1294 0.897601 0.448801 M3 124.508659999999 456.645416 0.2727 0.786285 0.393142 M4 178.072659999999 456.645416 0.39 0.698292 0.349146 M5 81.1859999999996 454.942568 0.1785 0.859118 0.429559 M6 62.523999999999 454.942568 0.1374 0.891264 0.445632 M7 156.987999999999 454.942568 0.3451 0.731548 0.365774 M8 123.271999999999 454.942568 0.271 0.787582 0.393791 M9 19.247999999999 454.942568 0.0423 0.966428 0.483214 M10 -48.9580000000007 454.942568 -0.1076 0.914751 0.457375 M11 -56.9520000000007 454.942568 -0.1252 0.9009 0.45045 Multiple Linear Regression - Regression Statistics Multiple R 0.501826061360067 R-squared 0.251829395860158 Adjusted R-squared 0.0647867448251975 F-TEST (value) 1.34637417972165 F-TEST (DF numerator) 12 F-TEST (DF denominator) 48 p-value 0.224943719556308 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 719.327359990521 Sum Squared Residuals 24836728.8398848 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 2120.88 2906.01389999999 -785.133899999994 2 2174.56 3187.70534 -1013.14534 3 2196.72 3253.13534 -1056.41534 4 2350.44 3306.69934 -956.25934 5 2440.25 3209.81268 -769.56268 6 2408.64 3191.15068 -782.51068 7 2472.81 3285.61468 -812.80468 8 2407.6 3251.89868 -844.29868 9 2454.62 3147.87468 -693.25468 10 2448.05 3079.66868 -631.61868 11 2497.84 3071.67468 -573.83468 12 2645.64 3128.62668 -482.986680000001 13 2756.76 2906.0139 -149.253900000001 14 2849.27 3187.70534 -338.43534 15 2921.44 3253.13534 -331.695340000000 16 2981.85 3306.69934 -324.849339999999 17 3080.58 3209.81268 -129.232680000000 18 3106.22 3191.15068 -84.9306799999997 19 3119.31 3285.61468 -166.30468 20 3061.26 3251.89868 -190.638680000000 21 3097.31 3147.87468 -50.56468 22 3161.69 3079.66868 82.02132 23 3257.16 3071.67468 185.485320000000 24 3277.01 3128.62668 148.383319999999 25 3295.32 2906.0139 389.306099999999 26 3363.99 3187.70534 176.284660000000 27 3494.17 3253.13534 241.034660000001 28 3667.03 3306.69934 360.330660000001 29 3813.06 3209.81268 603.24732 30 3917.96 3191.15068 726.80932 31 3895.51 3285.61468 609.89532 32 3801.06 3251.89868 549.16132 33 3570.12 3147.87468 422.24532 34 3701.61 3079.66868 621.94132 35 3862.27 3071.67468 790.59532 36 3970.1 3128.62668 841.47332 37 4138.52 2906.0139 1232.5061 38 4199.75 3187.70534 1012.04466 39 4290.89 3253.13534 1037.75466 40 4443.91 3306.69934 1137.21066 41 4502.64 3964.03598 538.60402 42 4356.98 3945.37398 411.60602 43 4591.27 4039.83798 551.432020000001 44 4696.96 4006.12198 690.83802 45 4621.4 3902.09798 719.30202 46 4562.84 3833.89198 728.94802 47 4202.52 3825.89798 376.62202 48 4296.49 3882.84998 413.640019999999 49 4435.23 3660.2372 774.992799999999 50 4105.18 3941.92864 163.251360000000 51 4116.68 4007.35864 109.321360000001 52 3844.49 4060.92264 -216.432639999999 53 3720.98 3964.03598 -243.05598 54 3674.4 3945.37398 -270.973979999999 55 3857.62 4039.83798 -182.217980000000 56 3801.06 4006.12198 -205.061980000000 57 3504.37 3902.09798 -397.72798 58 3032.6 3833.89198 -801.29198 59 3047.03 3825.89798 -778.86798 60 2962.34 3882.84998 -920.50998 61 2197.82 3660.2372 -1462.41720000000 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.498623477171816 0.997246954343632 0.501376522828184 17 0.429303783711053 0.858607567422105 0.570696216288947 18 0.389373838118544 0.778747676237088 0.610626161881456 19 0.35360770585194 0.70721541170388 0.64639229414806 20 0.333414794298033 0.666829588596066 0.666585205701967 21 0.303876460542854 0.607752921085707 0.696123539457146 22 0.281798871127802 0.563597742255604 0.718201128872198 23 0.262473634969214 0.524947269938428 0.737526365030786 24 0.225560089637207 0.451120179274413 0.774439910362793 25 0.2389660090384 0.4779320180768 0.7610339909616 26 0.26719470229005 0.5343894045801 0.73280529770995 27 0.303204836198905 0.606409672397811 0.696795163801095 28 0.330455067333363 0.660910134666726 0.669544932666637 29 0.350161518148152 0.700323036296303 0.649838481851848 30 0.37238241437759 0.74476482875518 0.62761758562241 31 0.381485464047436 0.762970928094872 0.618514535952564 32 0.389499853656541 0.778999707313083 0.610500146343459 33 0.373620607515139 0.747241215030278 0.626379392484861 34 0.341366991324381 0.682733982648761 0.65863300867562 35 0.303687270763974 0.607374541527949 0.696312729236026 36 0.264478646740643 0.528957293481285 0.735521353259357 37 0.27964832126807 0.55929664253614 0.72035167873193 38 0.270147102977911 0.540294205955822 0.729852897022089 39 0.252087597212705 0.504175194425409 0.747912402787295 40 0.222669966826022 0.445339933652044 0.777330033173978 41 0.164966200136140 0.329932400272281 0.83503379986386 42 0.112334043295546 0.224668086591092 0.887665956704454 43 0.0721992702998972 0.144398540599794 0.927800729700103 44 0.0459819143469597 0.0919638286939194 0.95401808565304 45 0.0303397071428098 0.0606794142856197 0.96966029285719 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 0 0 OK 10% type I error level 2 0.0666666666666667 OK

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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