*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: Thu, 09 Dec 2010 19:15:59 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/09/t12919220555kkx2lvbvkvzbjg.htm/, Retrieved Thu, 09 Dec 2010 20:14:15 +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/2010/Dec/09/t12919220555kkx2lvbvkvzbjg.htm/}, year = {2010}, } @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 = {2010}, 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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8587 0 9743 9084 9081 9700 9731 0 8587 9743 9084 9081 9563 0 9731 8587 9743 9084 9998 0 9563 9731 8587 9743 9437 0 9998 9563 9731 8587 10038 0 9437 9998 9563 9731 9918 0 10038 9437 9998 9563 9252 0 9918 10038 9437 9998 9737 0 9252 9918 10038 9437 9035 0 9737 9252 9918 10038 9133 0 9035 9737 9252 9918 9487 0 9133 9035 9737 9252 8700 0 9487 9133 9035 9737 9627 0 8700 9487 9133 9035 8947 0 9627 8700 9487 9133 9283 0 8947 9627 8700 9487 8829 0 9283 8947 9627 8700 9947 0 8829 9283 8947 9627 9628 0 9947 8829 9283 8947 9318 0 9628 9947 8829 9283 9605 0 9318 9628 9947 8829 8640 0 9605 9318 9628 9947 9214 0 8640 9605 9318 9628 9567 0 9214 8640 9605 9318 8547 0 9567 9214 8640 9605 9185 0 8547 9567 9214 8640 9470 0 9185 8547 9567 9214 9123 0 9470 9185 8547 9567 9278 0 9123 9470 9185 8547 10170 0 9278 9123 9470 9185 9434 0 10170 9278 9123 9470 9655 0 9434 10170 9278 9123 9429 0 9655 9434 10170 9278 8739 0 9429 9655 9434 10170 9552 0 8739 9429 9655 9434 9687 1 9552 8739 9429 9655 9019 1 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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation births[t] = + 4290.89132456752 + 131.651523693341difference[t] + 0.108196703969025Y1[t] + 0.154343076203814Y2[t] + 0.237959866862384Y3[t] + 0.0510733953878393Y4[t] -770.958525039385M1[t] + 176.625479263266M2[t] -253.792403401782M3[t] + 9.40421424853412M4[t] -185.287572708533M5[t] + 403.52059922142M6[t] + 199.734827907282M7[t] -101.130816660665M8[t] -119.148713516400M9[t] -847.616376220034M10[t] -304.047680579611M11[t] + 3.22629603458473t + 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) 4290.89132456752 1655.215049 2.5923 0.012292 0.006146 difference 131.651523693341 139.159386 0.946 0.348417 0.174209 Y1 0.108196703969025 0.14475 0.7475 0.458083 0.229041 Y2 0.154343076203814 0.136943 1.1271 0.264794 0.132397 Y3 0.237959866862384 0.137245 1.7338 0.088762 0.044381 Y4 0.0510733953878393 0.146009 0.3498 0.727877 0.363939 M1 -770.958525039385 209.514566 -3.6797 0.000547 0.000274 M2 176.625479263266 236.030242 0.7483 0.457577 0.228788 M3 -253.792403401782 174.216279 -1.4568 0.15108 0.07554 M4 9.40421424853412 240.16382 0.0392 0.968912 0.484456 M5 -185.287572708533 219.4378 -0.8444 0.402256 0.201128 M6 403.52059922142 191.718751 2.1048 0.040071 0.020035 M7 199.734827907282 210.27704 0.9499 0.346492 0.173246 M8 -101.130816660665 238.135869 -0.4247 0.672791 0.336396 M9 -119.148713516400 218.23283 -0.546 0.587377 0.293689 M10 -847.616376220034 196.396946 -4.3158 7e-05 3.5e-05 M11 -304.047680579611 222.053505 -1.3693 0.176694 0.088347 t 3.22629603458473 3.551075 0.9085 0.367706 0.183853 Multiple Linear Regression - Regression Statistics Multiple R 0.885845071872243 R-squared 0.784721491360339 Adjusted R-squared 0.715669894249504 F-TEST (value) 11.3642772099939 F-TEST (DF numerator) 17 F-TEST (DF denominator) 53 p-value 3.73157060806761e-12 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 271.470354791428 Sum Squared Residuals 3905896.13712095 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 8587 8635.69757280774 -48.6975728077437 2 9731 9532.2440184306 198.755981569396 3 9563 9207.37763749757 355.622362502429 4 9998 9390.7677455605 607.232254439491 5 9437 9433.62342668454 3.37657331546353 6 10038 10050.5494885619 -12.5494885619189 7 9918 9923.36197827739 -5.36197827738936 8 9252 9594.22065575015 -342.220655750149 9 9737 9603.21058611289 133.789413887114 10 9035 8829.79205872168 205.207941278322 11 9133 9210.8792773924 -77.8792773923923 12 9487 9501.80334560043 -14.8033456004296 13 8700 8645.22114149435 54.7788585056529 14 9627 9552.98462817436 74.0153718256399 15 8947 9193.86637076807 -246.866370768074 16 9283 9360.59712414157 -77.597124141572 17 8829 9280.92646834529 -451.926468345289 18 9947 9761.23123437048 185.768765629523 19 9628 9656.7885239338 -28.7885239337919 20 9318 9406.31686732497 -88.3168673249673 21 9605 9551.60065661047 53.3993433895307 22 8640 8790.75624887185 -150.756248871851 23 9214 9187.37791223118 26.6220877688152 24 9567 9460.2774576062 106.722542393806 25 8547 8604.35838379756 -57.3583837975583 26 9185 9586.59428901608 -401.594289016078 27 9470 9184.318223745 285.681776254997 28 9123 9355.35792505138 -232.357925051385 29 9278 9270.05948633234 7.94051366765665 30 10170 9925.71078428258 244.289215717422 31 9434 9777.56978963927 -343.569789639273 32 9655 9557.1330021226 97.8669978773998 33 9429 9672.83294631896 -243.832946318959 34 8739 8827.66795106919 -88.6679510691908 35 9552 9279.92479335465 272.075206645353 36 9687 9657.82578187818 29.1742181218188 37 9019 8854.4461333702 164.553866629796 38 9672 9912.03807968516 -240.038079685155 39 9206 9526.04501831905 -320.045018319052 40 9069 9690.77201402876 -621.772014028764 41 9788 9533.8304660936 254.169533906392 42 10312 10104.9749920023 207.02500799766 43 10105 10015.6825573822 89.3174426177814 44 9863 9940.61835216399 -77.6183521639874 45 9656 10029.1068737279 -373.106873727889 46 9295 9221.62253163864 73.3774683613571 47 9946 9629.25101578066 316.748984219336 48 9701 9889.62574204475 -188.625742044747 49 9049 9099.38695839362 -50.3869583936155 50 10190 10078.3133316655 111.686668334486 51 9706 9648.89111159502 57.1088884049797 52 9765 9871.38945544317 -106.389455443170 53 9893 9849.81787546932 43.1821245306768 54 9994 10407.9099316141 -413.909931614052 55 10433 10227.3543459666 205.645654033375 56 10073 10026.2741944585 46.7258055414821 57 10112 10070.8597318247 41.1402681752623 58 9266 9403.89732366386 -137.897323663865 59 9820 9801.93295225783 18.0670477421700 60 10097 10029.4676728704 67.5323271295508 61 9115 9177.88981013653 -62.8898101365311 62 10411 10153.8256530283 257.174346971711 63 9678 9809.50163807528 -131.501638075280 64 10408 9977.1157357746 430.884264225401 65 10153 10009.7422770749 143.257722925100 66 10368 10578.6235691686 -210.623569168634 67 10581 10498.2428048007 82.7571951992975 68 10597 10233.4369281798 363.563071820222 69 10680 10291.3892054051 388.610794594942 70 9738 9639.26388603477 98.736113965228 71 9556 10111.6340489833 -555.634048983283 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.822122455598207 0.355755088803586 0.177877544401793 22 0.726239083632223 0.547521832735554 0.273760916367777 23 0.734083475606155 0.531833048787691 0.265916524393845 24 0.697426669369347 0.605146661261306 0.302573330630653 25 0.6212075131184 0.757584973763201 0.378792486881600 26 0.567476913246912 0.865046173506177 0.432523086753088 27 0.77767102672314 0.444657946553721 0.222328973276860 28 0.737703853684781 0.524592292630437 0.262296146315219 29 0.674084407667949 0.651831184664101 0.325915592332051 30 0.851940121044033 0.296119757911935 0.148059878955967 31 0.813235523535133 0.373528952929733 0.186764476464867 32 0.803790093947487 0.392419812105027 0.196209906052513 33 0.729203596280934 0.541592807438133 0.270796403719066 34 0.7155454023228 0.568909195354399 0.284454597677199 35 0.698693243288173 0.602613513423654 0.301306756711827 36 0.611577624308671 0.776844751382659 0.388422375691329 37 0.558245627152926 0.883508745694147 0.441754372847074 38 0.495608556092782 0.991217112185565 0.504391443907218 39 0.43767433348393 0.87534866696786 0.56232566651607 40 0.693203304440348 0.613593391119304 0.306796695559652 41 0.739854124654332 0.520291750691336 0.260145875345668 42 0.70781319933602 0.58437360132796 0.29218680066398 43 0.674127004739975 0.651745990520049 0.325872995260025 44 0.613829990890536 0.772340018218927 0.386170009109464 45 0.535793591148136 0.928412817703727 0.464206408851864 46 0.440996186435053 0.881992372870106 0.559003813564947 47 0.714764429436041 0.570471141127917 0.285235570563959 48 0.586626461343611 0.826747077312779 0.413373538656389 49 0.822608135569515 0.354783728860970 0.177391864430485 50 0.696464716105798 0.607070567788404 0.303535283894202 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 = 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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