Model 4

*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, 19 Dec 2009 04:58:01 -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/19/t12612239867f6ncnewvvinu37.htm/, Retrieved Sat, 19 Dec 2009 12:59:58 +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/19/t12612239867f6ncnewvvinu37.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 «

4132 537 4486 4625 3971 3397 4685 543 4132 4486 4625 3971 3172 594 4685 4132 4486 4625 4280 611 3172 4685 4132 4486 4207 613 4280 3172 4685 4132 4158 611 4207 4280 3172 4685 3933 594 4158 4207 4280 3172 3151 595 3933 4158 4207 4280 3616 591 3151 3933 4158 4207 4221 589 3616 3151 3933 4158 4436 584 4221 3616 3151 3933 4807 573 4436 4221 3616 3151 4849 567 4807 4436 4221 3616 5024 569 4849 4807 4436 4221 3521 621 5024 4849 4807 4436 4650 629 3521 5024 4849 4807 5393 628 4650 3521 5024 4849 5147 612 5393 4650 3521 5024 4845 595 5147 5393 4650 3521 3995 597 4845 5147 5393 4650 4493 593 3995 4845 5147 5393 4680 590 4493 3995 4845 5147 5463 580 4680 4493 3995 4845 4761 574 5463 4680 4493 3995 5307 573 4761 5463 4680 4493 5069 573 5307 4761 5463 4680 3501 620 5069 5307 4761 5463 4952 626 3501 5069 5307 4761 5152 620 4952 3501 5069 5307 5317 588 5152 4952 3501 5069 5189 566 5317 5152 4952 3501 4030 557 5189 5317 5152 4952 4420 561 4030 5189 5317 5152 4571 549 4420 4030 5189 5317 4551 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 5 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = -756.55708054948 + 1.71314936407085X[t] + 0.328377699504215Y1[t] + 0.349916989632899Y2[t] + 0.275562658816889Y3[t] + 0.0704857662751447Y4[t] -152.180602693103M1[t] -237.954081757073M2[t] -1680.21865522304M3[t] -250.234553382229M4[t] + 250.420449060493M5[t] + 67.6731551900197M6[t] -455.587954730776M7[t] -1296.75786254305M8[t] -644.917005983765M9[t] -13.7638107680781M10[t] + 242.583873025313M11[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) -756.55708054948 641.622659 -1.1791 0.244409 0.122205 X 1.71314936407085 1.11706 1.5336 0.131972 0.065986 Y1 0.328377699504215 0.149809 2.192 0.03348 0.01674 Y2 0.349916989632899 0.159075 2.1997 0.032892 0.016446 Y3 0.275562658816889 0.165084 1.6692 0.101864 0.050932 Y4 0.0704857662751447 0.161581 0.4362 0.664714 0.332357 M1 -152.180602693103 193.935323 -0.7847 0.436653 0.218327 M2 -237.954081757073 216.517759 -1.099 0.277485 0.138742 M3 -1680.21865522304 239.643717 -7.0113 0 0 M4 -250.234553382229 382.435382 -0.6543 0.516165 0.258082 M5 250.420449060493 368.20375 0.6801 0.499841 0.249921 M6 67.6731551900197 306.698431 0.2207 0.826341 0.413171 M7 -455.587954730776 228.600306 -1.9929 0.052219 0.02611 M8 -1296.75786254305 253.985082 -5.1056 6e-06 3e-06 M9 -644.917005983765 345.080017 -1.8689 0.068013 0.034006 M10 -13.7638107680781 326.709643 -0.0421 0.966579 0.483289 M11 242.583873025313 258.918847 0.9369 0.353698 0.176849 Multiple Linear Regression - Regression Statistics Multiple R 0.929890278855997 R-squared 0.864695930710883 Adjusted R-squared 0.817633645740756 F-TEST (value) 18.3734370581399 F-TEST (DF numerator) 16 F-TEST (DF denominator) 46 p-value 7.99360577730113e-15 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 306.863173387526 Sum Squared Residuals 4331590.33034728 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 4132 4436.39142849006 -304.391428490064 2 4685 4416.68948713523 268.310512864772 3 3172 3127.31226630106 44.6877336989395 4 4280 4175.74184051477 104.258159485235 5 4207 4641.67541648606 -434.675416486061 6 4158 4441.29060229709 -283.290602297092 7 3933 4045.949967263 -112.949967263002 8 3151 3173.44444887357 -22.4444488735674 9 3616 3464.26199307676 151.738006923243 10 4221 3905.59403315955 315.405966840447 11 4436 4283.40658190522 152.593418094777 12 4807 4377.29581711913 429.704182880869 13 4849 4611.3878874309 237.6121125691 14 5024 4774.54163387015 249.458366129852 15 3521 3610.91162448391 -89.9116244839095 16 4650 4660.00856302659 -10.0085630265941 17 5393 5054.94747090377 338.052529096232 18 5147 5081.9950321317 65.0049678682973 19 4845 4913.98792733363 -68.9879273336342 20 3995 4175.31615917512 -180.316159175124 21 4493 4420.09095310388 72.9090468961155 22 4680 4811.64793192611 -131.647931926107 23 5463 5031.01445131381 431.985548686187 24 4761 5178.02320063416 -417.023200634164 25 5307 5154.22543521137 152.774564788628 26 5069 5231.05085350148 -162.050853501484 27 3501 3843.95045250839 -342.950452508393 28 4952 4787.01317796726 164.986822032744 29 5152 5178.09680204959 -26.0968020495929 30 5317 5065.07595898867 251.924041011334 31 5189 4917.61101782696 271.388982173035 32 4030 4234.11410211956 -204.114102119556 33 4420 4526.99341969654 -106.993419696543 34 4571 4836.46046547233 -265.460465472330 35 4551 4921.33796900649 -370.337969006492 36 4819 4740.52154506693 78.4784549330691 37 5133 4712.74999591589 420.250004084106 38 4532 4808.43917288022 -276.439172880223 39 3339 3447.07097838235 -108.070978382348 40 4380 4397.5487278162 -17.5487278162044 41 4632 4639.71088409858 -7.71088409858154 42 4719 4507.17291875005 211.827081249955 43 4212 4274.30741954654 -62.3074195465354 44 3615 3446.76286635425 168.237133645747 45 3420 3772.03013507626 -352.030135076260 46 4571 3981.25288544692 589.747114553079 47 4407 4321.385057115 85.6149428849957 48 4386 4326.7475274107 59.2524725893004 49 4386 4377.73636595731 8.26363404268934 50 4744 4335.96981532441 408.030184675591 51 3185 3079.57544498022 105.424555019781 52 3890 4131.68769067518 -241.68769067518 53 4520 4389.569426462 130.430573538004 54 3990 4235.46548783249 -245.465487832494 55 3809 3836.14366802986 -27.1436680298636 56 3236 2997.3624234775 238.63757652250 57 3551 3316.62349904656 234.376500953444 58 3264 3772.04468399509 -508.044683995089 59 3579 3878.85594065947 -299.855940659468 60 3537 3687.41190976907 -150.411909769073 61 3038 3552.50888699446 -514.508886994459 62 2888 3375.30903728851 -487.309037288508 63 2198 1807.17923334407 390.82076665593 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 20 0.302571286421191 0.605142572842382 0.697428713578809 21 0.332597326546221 0.665194653092443 0.667402673453779 22 0.353514083037799 0.707028166075598 0.646485916962201 23 0.3796156427715 0.759231285543 0.6203843572285 24 0.576542383356992 0.846915233286015 0.423457616643008 25 0.482322410990654 0.964644821981309 0.517677589009346 26 0.394271452488839 0.788542904977679 0.605728547511161 27 0.462024926765165 0.92404985353033 0.537975073234835 28 0.406246383363235 0.812492766726471 0.593753616636765 29 0.307385256195819 0.614770512391638 0.692614743804181 30 0.371463152421760 0.742926304843519 0.62853684757824 31 0.506960544410539 0.986078911178921 0.493039455589461 32 0.408745343487297 0.817490686974595 0.591254656512703 33 0.347521421004971 0.695042842009942 0.652478578995029 34 0.297417378686492 0.594834757372985 0.702582621313508 35 0.330062177990436 0.660124355980872 0.669937822009564 36 0.264657501060488 0.529315002120975 0.735342498939512 37 0.363080026965838 0.726160053931676 0.636919973034162 38 0.284842780335599 0.569685560671197 0.715157219664401 39 0.238115664409924 0.476231328819848 0.761884335590076 40 0.153695906420090 0.307391812840179 0.84630409357991 41 0.0900280416888288 0.180056083377658 0.909971958311171 42 0.333100729457137 0.666201458914275 0.666899270542863 43 0.571316113826100 0.857367772347799 0.428683886173899 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 0 0 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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