*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: Fri, 10 Dec 2010 17:15:43 +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/10/t1292001242gqz5yez4hdvnuz1.htm/, Retrieved Fri, 10 Dec 2010 18:16:12 +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/10/t1292001242gqz5yez4hdvnuz1.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:

» Textbox « » Textfile « » CSV «

9081 0 9700 9084 0 9081 9743 0 9084 8587 0 9743 9731 0 8587 9563 0 9731 9998 0 9563 9437 0 9998 10038 0 9437 9918 0 10038 9252 0 9918 9737 0 9252 9035 0 9737 9133 0 9035 9487 0 9133 8700 0 9487 9627 0 8700 8947 0 9627 9283 0 8947 8829 0 9283 9947 0 8829 9628 0 9947 9318 0 9628 9605 0 9318 8640 0 9605 9214 0 8640 9567 0 9214 8547 0 9567 9185 0 8547 9470 0 9185 9123 0 9470 9278 0 9123 10170 0 9278 9434 0 10170 9655 0 9434 9429 0 9655 8739 0 9429 9552 0 8739 9687 1 9552 9019 1 9687 9672 1 9019 9206 1 9672 9069 1 9206 9788 1 9069 10312 1 9788 10105 1 10312 9863 1 10105 9656 1 9863 9295 1 9656 9946 1 9295 9701 1 9946 9049 1 9701 10190 1 9049 9706 1 10190 9765 1 9706 9893 1 9765 9994 1 9893 10433 1 9994 10073 1 10433 10112 1 10073 9266 1 10112 9820 1 9266 10097 1 9820 9115 1 10097 10411 1 9115 9678 1 10411 10408 1 9678 10153 1 10408 10368 1 10153 10581 1 10368 10597 1 10581 10680 1 10597 9738 1 10680 9556 1 9738

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 8 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation geboortes[t] = + 7081.7941033014 + 199.675838880545x[t] + 0.256058903274213lag[t] -734.101623515508M1[t] -192.216032923728M2[t] -31.7260810906930M3[t] -978.949523039809M4[t] + 207.941772420758M5[t] -418.172883089656M6[t] -147.288559126564M7[t] -242.175514609627M8[t] + 340.128057574066M9[t] + 66.8844528782934M10[t] -129.762106052565M11[t] + 4.30039216255456t + 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) 7081.7941033014 1203.095097 5.8863 0 0 x 199.675838880545 138.369988 1.4431 0.154293 0.077146 lag 0.256058903274213 0.126882 2.0181 0.048137 0.024069 M1 -734.101623515508 155.946063 -4.7074 1.6e-05 8e-06 M2 -192.216032923728 175.080661 -1.0979 0.276721 0.138361 M3 -31.7260810906930 167.455871 -0.1895 0.850383 0.425192 M4 -978.949523039809 163.047635 -6.0041 0 0 M5 207.941772420758 199.972477 1.0399 0.302651 0.151326 M6 -418.172883089656 162.226857 -2.5777 0.012464 0.006232 M7 -147.288559126564 167.357157 -0.8801 0.382384 0.191192 M8 -242.175514609627 162.848266 -1.4871 0.142307 0.071154 M9 340.128057574066 163.568861 2.0794 0.041934 0.020967 M10 66.8844528782934 167.376058 0.3996 0.69089 0.345445 M11 -129.762106052565 163.666672 -0.7928 0.431046 0.215523 t 4.30039216255456 3.219944 1.3355 0.186826 0.093413 Multiple Linear Regression - Regression Statistics Multiple R 0.868784961568442 R-squared 0.754787309447479 Adjusted R-squared 0.696601247282474 F-TEST (value) 12.9719606614216 F-TEST (DF numerator) 14 F-TEST (DF denominator) 59 p-value 3.44391182238724e-13 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 278.921965516086 Sum Squared Residuals 4590050.30799406 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 9081 8835.76423370831 245.235766291688 2 9084 9223.44975533591 -139.449755335911 3 9743 9389.00827604132 353.991723958678 4 8587 8614.82804351247 -27.8280435124679 5 9731 9510.0156389506 220.984361049400 6 9563 9181.13276094844 381.867239051561 7 9998 9413.29958132402 584.700418675982 8 9437 9434.09864092779 2.90135907220801 9 10038 9877.0535605372 160.946439462793 10 9918 9762.0017488718 155.998251128209 11 9252 9538.92851371058 -286.928513710581 12 9737 9502.45578234507 234.544217654926 13 9035 8896.84311908011 138.156880919886 14 9133 9263.27575173595 -130.275751735951 15 9487 9453.15986825241 33.8401317475861 16 8700 8600.88167022492 99.1183297750762 17 9627 9590.55500097124 36.4449990287599 18 8947 9206.10734095858 -259.107340958575 19 9283 9307.17200285776 -24.1720028577577 20 8829 9302.62123103738 -473.621231037385 21 9947 9772.97445329714 174.025546702861 22 9628 9790.3050946245 -162.305094624492 23 9318 9516.27613771171 -198.276137711714 24 9605 9570.96037591183 34.0396240881725 25 8640 8914.64804979857 -274.648049798573 26 9214 9213.7371908933 0.262809106708605 27 9567 9525.50534536828 41.4946546317201 28 8547 8672.97108843752 -125.971088437516 29 9185 9602.98269472094 -417.98269472094 30 9470 9144.53401166203 325.465988337972 31 9123 9492.69551522083 -369.695515220826 32 9278 9313.25651246417 -35.2565124641652 33 10170 9939.54960681792 230.450393182084 34 9434 9899.0109360053 -465.010936005296 35 9655 9518.20541642717 136.794583572829 36 9429 9708.8569322659 -279.856932265892 37 8739 8921.18638877297 -182.186388772966 38 9552 9290.6917282681 261.308271731907 39 9687 9863.33379950616 -176.333799506164 40 9019 8954.97870166162 64.0212983383794 41 9672 9975.12304189757 -303.123041897568 42 9206 9520.51524238777 -314.515242387769 43 9069 9676.37650958763 -607.376509587633 44 9788 9550.70987651856 237.290123481443 45 10312 10321.4201923190 -9.4201923189644 46 10105 10186.6518451014 -81.6518451014338 47 9863 9941.30148535537 -78.3014853553676 48 9656 10013.3977289781 -357.397728978128 49 9295 9230.59230464741 64.4076953525882 50 9946 9684.34102331976 261.658976680245 51 9701 10015.8257133469 -314.825713346858 52 9049 9010.16823225811 38.8317677418854 53 10190 10034.4095149465 155.590485053550 54 9706 9704.75846023447 1.24153976553359 55 9765 9856.0106671754 -91.0106671753944 56 9893 9780.53157914806 112.468420851936 57 9994 10399.9110831134 -405.911083113412 58 10433 10156.8298198109 276.170180189111 59 10073 10076.8935115800 -3.89351157996427 60 10112 10118.7748046164 -6.77480461636733 61 9266 9398.95987049111 -132.959870491108 62 9820 9728.52002107546 91.4799789245422 63 10097 10035.1669974850 61.8330025150379 64 9115 9163.17226390536 -48.1722639053576 65 10411 10102.9141085132 308.085891486798 66 9678 9812.95218380872 -134.952183808722 67 10408 9900.44572383437 507.554276165629 68 10153 9996.78215990404 156.217840095962 69 10368 10518.0911039154 -150.091103915362 70 10581 10304.2005555861 276.799444413901 71 10597 10166.3949352152 430.605064784797 72 10680 10304.5543758827 375.445624117290 73 9738 9596.00603350152 141.993966498484 74 9556 9900.98452937154 -344.984529371541 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 18 0.601048456298771 0.797903087402458 0.398951543701229 19 0.576799787266883 0.846400425466234 0.423200212733117 20 0.440821481427016 0.881642962854031 0.559178518572984 21 0.488904204779561 0.977808409559122 0.511095795220439 22 0.379550908392861 0.759101816785722 0.620449091607139 23 0.371049105313413 0.742098210626826 0.628950894686587 24 0.280236123846838 0.560472247693677 0.719763876153162 25 0.215175296162837 0.430350592325675 0.784824703837163 26 0.322214217779428 0.644428435558855 0.677785782220572 27 0.25808547625228 0.51617095250456 0.74191452374772 28 0.189285808382600 0.378571616765199 0.8107141916174 29 0.208923913388092 0.417847826776183 0.791076086611908 30 0.359307735700465 0.71861547140093 0.640692264299535 31 0.35260865281698 0.70521730563396 0.64739134718302 32 0.355519889703715 0.71103977940743 0.644480110296285 33 0.449329612416087 0.898659224832175 0.550670387583913 34 0.421891024381516 0.843782048763032 0.578108975618484 35 0.487844342441342 0.975688684882683 0.512155657558658 36 0.424459654612999 0.848919309225998 0.575540345387001 37 0.393236649574048 0.786473299148095 0.606763350425952 38 0.478779446656557 0.957558893313114 0.521220553343443 39 0.403439277915177 0.806878555830354 0.596560722084823 40 0.385267352580371 0.770534705160741 0.614732647419629 41 0.3309876282447 0.6619752564894 0.6690123717553 42 0.295076101604146 0.590152203208293 0.704923898395853 43 0.550774737717972 0.898450524564055 0.449225262282028 44 0.551112054652807 0.897775890694386 0.448887945347193 45 0.61502176066163 0.76995647867674 0.38497823933837 46 0.547805499680026 0.904389000639948 0.452194500319974 47 0.483776583639437 0.967553167278874 0.516223416360563 48 0.531308002244404 0.937383995511192 0.468691997755596 49 0.448105516358929 0.896211032717859 0.551894483641071 50 0.77718150729254 0.44563698541492 0.22281849270746 51 0.681409519135837 0.637180961728325 0.318590480864163 52 0.60841167251015 0.7831766549797 0.39158832748985 53 0.549621776016914 0.900756447966172 0.450378223983086 54 0.581268573085861 0.837462853828278 0.418731426914139 55 0.458015905572301 0.916031811144602 0.541984094427699 56 0.313709318150287 0.627418636300574 0.686290681849713 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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