Paper -multiple Llineair regression

*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: Sat, 20 Dec 2008 06:50:59 -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/Dec/20/t12297811818o7h3g1ca08qdy4.htm/, Retrieved Sat, 20 Dec 2008 14:53:10 +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/2008/Dec/20/t12297811818o7h3g1ca08qdy4.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}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

2490 0 3266 0 3475 0 3127 0 2955 0 3870 0 2852 0 3142 0 3029 0 3180 0 2560 0 2733 0 2452 0 2553 0 2777 0 2520 0 2318 0 2873 0 2311 0 2395 0 2099 0 2268 0 2316 0 2181 0 2175 0 2627 0 2578 0 3090 0 2634 0 3225 0 2938 0 3174 0 3350 0 2588 0 2061 0 2691 0 2061 0 2918 0 2223 0 2651 0 2379 0 3146 0 2883 0 2768 0 3258 0 2839 0 2470 0 5072 1 1463 1 1600 1 2203 1 2013 1 2169 1 2640 1 2411 1 2528 1 2292 1 1988 1 1774 1 2279 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 Y[t] = + 2733.38297872340 -392.459901800327X[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) 2733.38297872340 79.87358 34.2214 0 0 X -392.459901800327 171.595975 -2.2871 0.025856 0.012928 Multiple Linear Regression - Regression Statistics Multiple R 0.287622934838799 R-squared 0.0827269526452843 Adjusted R-squared 0.0669119001046858 F-TEST (value) 5.23089964025838 F-TEST (DF numerator) 1 F-TEST (DF denominator) 58 p-value 0.0258559181901252 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 547.585673181327 Sum Squared Residuals 17391304.0294599 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 2490 2733.38297872341 -243.382978723406 2 3266 2733.38297872340 532.617021276595 3 3475 2733.38297872340 741.617021276596 4 3127 2733.38297872340 393.617021276596 5 2955 2733.38297872340 221.617021276596 6 3870 2733.38297872340 1136.61702127660 7 2852 2733.38297872340 118.617021276596 8 3142 2733.38297872340 408.617021276596 9 3029 2733.38297872340 295.617021276596 10 3180 2733.38297872340 446.617021276596 11 2560 2733.38297872340 -173.382978723404 12 2733 2733.38297872340 -0.382978723404207 13 2452 2733.38297872340 -281.382978723404 14 2553 2733.38297872340 -180.382978723404 15 2777 2733.38297872340 43.6170212765958 16 2520 2733.38297872340 -213.382978723404 17 2318 2733.38297872340 -415.382978723404 18 2873 2733.38297872340 139.617021276596 19 2311 2733.38297872340 -422.382978723404 20 2395 2733.38297872340 -338.382978723404 21 2099 2733.38297872340 -634.382978723404 22 2268 2733.38297872340 -465.382978723404 23 2316 2733.38297872340 -417.382978723404 24 2181 2733.38297872340 -552.382978723404 25 2175 2733.38297872340 -558.382978723404 26 2627 2733.38297872340 -106.382978723404 27 2578 2733.38297872340 -155.382978723404 28 3090 2733.38297872340 356.617021276596 29 2634 2733.38297872340 -99.3829787234042 30 3225 2733.38297872340 491.617021276596 31 2938 2733.38297872340 204.617021276596 32 3174 2733.38297872340 440.617021276596 33 3350 2733.38297872340 616.617021276596 34 2588 2733.38297872340 -145.382978723404 35 2061 2733.38297872340 -672.382978723404 36 2691 2733.38297872340 -42.3829787234042 37 2061 2733.38297872340 -672.382978723404 38 2918 2733.38297872340 184.617021276596 39 2223 2733.38297872340 -510.382978723404 40 2651 2733.38297872340 -82.3829787234042 41 2379 2733.38297872340 -354.382978723404 42 3146 2733.38297872340 412.617021276596 43 2883 2733.38297872340 149.617021276596 44 2768 2733.38297872340 34.6170212765958 45 3258 2733.38297872340 524.617021276596 46 2839 2733.38297872340 105.617021276596 47 2470 2733.38297872340 -263.382978723404 48 5072 2340.92307692308 2731.07692307692 49 1463 2340.92307692308 -877.923076923077 50 1600 2340.92307692308 -740.923076923077 51 2203 2340.92307692308 -137.923076923077 52 2013 2340.92307692308 -327.923076923077 53 2169 2340.92307692308 -171.923076923077 54 2640 2340.92307692308 299.076923076923 55 2411 2340.92307692308 70.0769230769231 56 2528 2340.92307692308 187.076923076923 57 2292 2340.92307692308 -48.9230769230769 58 1988 2340.92307692308 -352.923076923077 59 1774 2340.92307692308 -566.923076923077 60 2279 2340.92307692308 -61.9230769230769 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.384818955047719 0.769637910095439 0.61518104495228 6 0.564757707280573 0.870484585438854 0.435242292719427 7 0.464624386804904 0.929248773609807 0.535375613195096 8 0.339818276411149 0.679636552822298 0.660181723588851 9 0.239118868781942 0.478237737563885 0.760881131218058 10 0.162453603830859 0.324907207661719 0.83754639616914 11 0.180055475590405 0.360110951180810 0.819944524409595 12 0.142857556178856 0.285715112357712 0.857142443821144 13 0.160519218288330 0.321038436576661 0.83948078171167 14 0.142449563781215 0.28489912756243 0.857550436218785 15 0.100286374130211 0.200572748260423 0.899713625869789 16 0.08699071105571 0.17398142211142 0.91300928894429 17 0.0982878412508634 0.196575682501727 0.901712158749137 18 0.0655505911683563 0.131101182336713 0.934449408831644 19 0.0699891985646993 0.139978397129399 0.9300108014353 20 0.0620975834814904 0.124195166962981 0.93790241651851 21 0.0866639248081238 0.173327849616248 0.913336075191876 22 0.0841843516275437 0.168368703255087 0.915815648372456 23 0.074940447086725 0.14988089417345 0.925059552913275 24 0.078415296042804 0.156830592085608 0.921584703957196 25 0.0808539974607085 0.161707994921417 0.919146002539291 26 0.0557829152939064 0.111565830587813 0.944217084706094 27 0.0380795448746072 0.0761590897492144 0.961920455125393 28 0.0301444566215135 0.0602889132430269 0.969855543378487 29 0.019327626634656 0.038655253269312 0.980672373365344 30 0.0180483197500402 0.0360966395000804 0.98195168024996 31 0.0118610168092281 0.0237220336184563 0.988138983190772 32 0.0100664956898701 0.0201329913797402 0.98993350431013 33 0.0119240871895506 0.0238481743791011 0.98807591281045 34 0.0073971649557081 0.0147943299114162 0.992602835044292 35 0.00957600713754703 0.0191520142750941 0.990423992862453 36 0.00563014350249589 0.0112602870049918 0.994369856497504 37 0.00725677194374348 0.0145135438874870 0.992743228056256 38 0.00442142892513 0.00884285785026 0.99557857107487 39 0.00407773244810586 0.00815546489621172 0.995922267551894 40 0.00229781655712363 0.00459563311424726 0.997702183442876 41 0.00167888274069232 0.00335776548138464 0.998321117259308 42 0.00115379478226192 0.00230758956452384 0.998846205217738 43 0.00059828687444223 0.00119657374888446 0.999401713125558 44 0.000289488766742323 0.000578977533484645 0.999710511233258 45 0.000241638186474069 0.000483276372948137 0.999758361813526 46 0.00011766250560331 0.00023532501120662 0.999882337494397 47 5.49831371375108e-05 0.000109966274275022 0.999945016862863 48 0.5945739799848 0.810852040030401 0.405426020015201 49 0.951017307385617 0.097965385228766 0.048982692614383 50 0.98419562904035 0.0316087419192994 0.0158043709596497 51 0.965943719783677 0.0681125604326451 0.0340562802163226 52 0.94426690556306 0.111466188873878 0.0557330944369391 53 0.889978243923293 0.220043512153414 0.110021756076707 54 0.874407297970306 0.251185404059388 0.125592702029694 55 0.780459314349837 0.439081371300325 0.219540685650163 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 10 0.196078431372549 NOK 5% type I error level 20 0.392156862745098 NOK 10% type I error level 24 0.470588235294118 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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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