workshop 10 - multiple regression 1 (jonas poels)

*Unverified author*

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

Title produced by software: Multiple Regression

Date of computation: Fri, 24 Dec 2010 19:58:59 +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/24/t1293220624mkzw7ndlst6eoty.htm/, Retrieved Fri, 24 Dec 2010 20:57:06 +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/24/t1293220624mkzw7ndlst6eoty.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 «

1 162556 162556 1081 1081 213118 213118 230380558 6282929 1 29790 29790 309 309 81767 81767 25266003 4324047 1 87550 87550 458 458 153198 153198 70164684 4108272 0 84738 0 588 0 -26007 0 -15292116 -1212617 1 54660 54660 299 299 126942 126942 37955658 1485329 1 42634 42634 156 156 157214 157214 24525384 1779876 0 40949 0 481 0 129352 0 62218312 1367203 1 42312 42312 323 323 234817 234817 75845891 2519076 1 37704 37704 452 452 60448 60448 27322496 912684 1 16275 16275 109 109 47818 47818 5212162 1443586 0 25830 0 115 0 245546 0 28237790 1220017 0 12679 0 110 0 48020 0 5282200 984885 1 18014 18014 239 239 -1710 -1710 -408690 1457425 0 43556 0 247 0 32648 0 8064056 -572920 1 24524 24524 497 497 95350 95350 47388950 929144 0 6532 0 103 0 151352 0 15589256 1151176 0 7123 0 109 0 288170 0 31410530 790090 1 20813 20813 502 502 114337 114337 57397174 774497 1 37597 37597 248 248 37884 37884 9395232 990576 0 17821 0 373 0 122844 0 45820812 454195 1 12988 12988 119 119 82340 82340 9798460 876607 1 2 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 'RServer@AstonUniversity' @ vre.aston.ac.uk R Framework error message The field 'Names of X columns' contains a hard return which cannot be interpreted. Please, resubmit your request without hard returns in the 'Names of X columns'. Multiple Linear Regression - Estimated Regression Equation Costs[t] = + 2063.55395662252 -11913.6029498857Group[t] + 1.21878029308951GrCosts[t] + 75.2638113483493Trades[t] -32.7684671272523GrTrades[t] + 0.0202124527097466Dividends[t] + 0.060607189985472GrDiv[t] -0.000411636898666929TrDiv[t] -0.00112908749933964`Wealth `[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) 2063.55395662252 2549.629995 0.8094 0.420423 0.210211 Group -11913.6029498857 3855.329102 -3.0902 0.002654 0.001327 GrCosts 1.21878029308951 0.110586 11.0211 0 0 Trades 75.2638113483493 9.706848 7.7537 0 0 GrTrades -32.7684671272523 13.448677 -2.4366 0.016774 0.008387 Dividends 0.0202124527097466 0.02208 0.9154 0.362386 0.181193 GrDiv 0.060607189985472 0.032476 1.8662 0.065236 0.032618 TrDiv -0.000411636898666929 8.6e-05 -4.8091 6e-06 3e-06 `Wealth ` -0.00112908749933964 0.001909 -0.5914 0.555752 0.277876 Multiple Linear Regression - Regression Statistics Multiple R 0.939496178111833 R-squared 0.88265306868674 Adjusted R-squared 0.872336854944916 F-TEST (value) 85.5597887729104 F-TEST (DF numerator) 8 F-TEST (DF denominator) 91 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 7800.64963583693 Sum Squared Residuals 5537362261.43854 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 162556 149504.473043705 13051.5269562947 2 29790 30914.2104955658 -1124.21049556582 3 87550 95177.4694648157 -7627.46946481567 4 84738 53456.9596723112 31281.0403276888 5 54660 62432.9810798445 -7772.98107984454 6 42634 49341.494277142 -6707.494277142 7 40949 13724.9235897586 27224.0764102414 8 42312 40357.5804207611 1954.41957923888 9 37704 47918.6769144332 -10214.6769144332 10 16275 14706.7733634168 1568.22663658321 11 25830 2680.75693026026 23149.2430697397 12 12679 8026.8054161374 4652.1945838626 13 18014 20645.9164216757 -2631.9164216757 14 43556 18641.0253233378 24914.9746766622 15 24524 28309.5326387696 -3785.53263876963 16 6532 5158.03024452344 1373.96975547656 17 7123 2270.11799392248 4852.88200607752 18 20813 21588.4939540605 -775.493954060504 19 37597 44587.1792552386 -6990.17925523864 20 17821 13245.5712873899 4575.42871261006 21 12988 12667.9311035726 320.068896427372 22 22330 23821.2178382579 -1491.21783825786 23 13326 5342.6874969088 7983.3125030912 24 16189 12187.3534401805 4001.64655981947 25 7146 6374.22074866502 771.779251334977 26 15824 5878.05608377211 9945.9439162279 27 26088 30445.4298746508 -4357.42987465081 28 11326 10792.4247205906 533.575279409369 29 8568 4124.14680318708 4443.85319681292 30 14416 22305.0368142044 -7889.03681420438 31 3369 707.917426304573 2661.08257369543 32 11819 12343.0737782113 -524.073778211257 33 6620 4354.1867459551 2265.8132540449 34 4519 3258.99652699554 1260.00347300446 35 2220 6157.11627354434 -3937.11627354434 36 18562 8842.77090267056 9719.22909732944 37 10327 6648.82093459847 3678.17906540153 38 5336 4648.07101532682 687.928984673183 39 2365 4861.66208537516 -2496.66208537516 40 4069 9571.39390667975 -5502.39390667975 41 7710 22584.8491287363 -14874.8491287363 42 13718 5760.38139204542 7957.61860795458 43 4525 11675.6207455067 -7150.62074550672 44 6869 6795.0348666189 73.9651333811031 45 4628 5933.88704869268 -1305.88704869268 46 3653 2463.53754886439 1189.46245113561 47 1265 6842.03762833243 -5577.03762833243 48 7489 5331.09336568941 2157.90663431059 49 4901 6104.6647571238 -1203.6647571238 50 2284 4814.40679896873 -2530.40679896873 51 3160 1884.67997436369 1275.32002563631 52 4150 3574.57463674487 575.425363255133 53 7285 9651.18971391746 -2366.18971391746 54 1134 -131.082437427084 1265.08243742708 55 4658 4640.91380683534 17.0861931646626 56 2384 7676.68662854082 -5292.68662854082 57 3748 2996.63561171155 751.364388288451 58 5371 5906.09226145593 -535.092261455934 59 1285 7330.443965701 -6045.44396570101 60 9327 8781.45113559163 545.548864408371 61 5565 4172.90111783994 1392.09888216006 62 1528 4936.27182289551 -3408.27182289551 63 3122 1256.3490846445 1865.6509153555 64 7317 6067.89598479592 1249.10401520408 65 2675 6874.896636173 -4199.896636173 66 13253 39359.7287167857 -26106.7287167857 67 880 6539.10608850677 -5659.10608850677 68 2053 368.660535640832 1684.33946435917 69 1424 6206.71932932822 -4782.71932932822 70 4036 2776.71052122278 1259.28947877722 71 3045 -2397.17620744868 5442.17620744868 72 5119 5325.74883139904 -206.748831399038 73 1431 4918.20313066186 -3487.20313066186 74 554 3764.39347075699 -3210.39347075699 75 1975 4951.82890970487 -2976.82890970487 76 1286 -2150.28512464692 3436.28512464692 77 1012 5282.27049459243 -4270.27049459243 78 810 5181.83741258342 -4371.83741258342 79 1280 8514.99469414336 -7234.99469414336 80 666 -1016.9444447844 1682.9444447844 81 1380 4209.89449037406 -2829.89449037406 82 4608 2956.6648892901 1651.3351107099 83 876 5464.98604109407 -4588.98604109407 84 814 3589.74454858877 -2775.74454858877 85 514 4163.9777535983 -3649.9777535983 86 5692 3031.40555645839 2660.59444354161 87 3642 6647.80418907509 -3005.80418907509 88 540 4180.89931389035 -3640.89931389035 89 2099 5821.39841642578 -3722.39841642578 90 567 4052.19413729219 -3485.19413729219 91 2001 5420.07938520468 -3419.07938520468 92 2949 366.121270525859 2582.87872947414 93 2253 7724.82926879222 -5471.82926879222 94 6533 7221.04504686802 -688.045046868016 95 1889 5108.85467225391 -3219.85467225391 96 3055 -921.890221808906 3976.89022180891 97 272 4049.70126787434 -3777.70126787434 98 1414 -172.640963348586 1586.64096334859 99 2564 4678.71519026039 -2114.71519026039 100 1383 -2482.48014223957 3865.48014223957 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 12 0.98241204984111 0.0351759003177802 0.0175879501588901 13 0.965057709147785 0.0698845817044306 0.0349422908522153 14 0.99971720086258 0.000565598274840451 0.000282799137420225 15 0.99940493790224 0.00119012419552069 0.000595062097760345 16 0.999922446083969 0.000155107832062933 7.75539160314665e-05 17 0.999914179463303 0.000171641073393857 8.58205366969287e-05 18 0.999799478555206 0.000401042889587712 0.000200521444793856 19 0.999585053916507 0.000829892166985819 0.000414946083492909 20 0.999999719249619 5.6150076254598e-07 2.8075038127299e-07 21 0.999999548539352 9.02921295840664e-07 4.51460647920332e-07 22 0.999999001305987 1.99738802660943e-06 9.98694013304717e-07 23 0.9999993977602 1.20447959990695e-06 6.02239799953475e-07 24 0.999999993615094 1.2769811624307e-08 6.38490581215352e-09 25 0.999999993746895 1.2506209796564e-08 6.25310489828199e-09 26 0.9999999996666 6.66799267528029e-10 3.33399633764015e-10 27 0.999999999096422 1.80715607952222e-09 9.0357803976111e-10 28 0.999999999853628 2.92744284649653e-10 1.46372142324827e-10 29 0.99999999968436 6.31281282277885e-10 3.15640641138942e-10 30 0.999999999999882 2.35200744212465e-13 1.17600372106232e-13 31 0.999999999999763 4.73739588936667e-13 2.36869794468333e-13 32 0.999999999999265 1.4691980856564e-12 7.345990428282e-13 33 0.99999999999828 3.43821406530425e-12 1.71910703265213e-12 34 0.999999999995219 9.5624644134736e-12 4.7812322067368e-12 35 0.999999999989436 2.1127815100711e-11 1.05639075503555e-11 36 1 5.80765490780112e-17 2.90382745390056e-17 37 1 6.60083000940192e-18 3.30041500470096e-18 38 1 2.43805808570005e-17 1.21902904285003e-17 39 1 9.42759912250955e-17 4.71379956125477e-17 40 1 6.58916765459297e-17 3.29458382729648e-17 41 1 7.63839522685792e-21 3.81919761342896e-21 42 1 3.57015999171375e-31 1.78507999585688e-31 43 1 6.75069254455245e-31 3.37534627227623e-31 44 1 3.83763709048089e-33 1.91881854524045e-33 45 1 2.08598694182392e-33 1.04299347091196e-33 46 1 1.78077354868277e-32 8.90386774341384e-33 47 1 1.41650329324055e-31 7.08251646620273e-32 48 1 9.9230141448835e-31 4.96150707244175e-31 49 1 2.60495806788769e-31 1.30247903394384e-31 50 1 6.64811773374206e-31 3.32405886687103e-31 51 1 4.19162749170413e-30 2.09581374585207e-30 52 1 3.55832418458022e-29 1.77916209229011e-29 53 1 3.48072221767871e-28 1.74036110883936e-28 54 1 1.72235911353529e-27 8.61179556767646e-28 55 1 1.46610168543675e-26 7.33050842718373e-27 56 1 6.23191928200466e-26 3.11595964100233e-26 57 1 4.59222146869966e-25 2.29611073434983e-25 58 1 1.30836629603465e-26 6.54183148017327e-27 59 1 5.4217187807301e-26 2.71085939036505e-26 60 1 5.73604037120601e-25 2.86802018560301e-25 61 1 4.68535608009569e-24 2.34267804004784e-24 62 1 3.84218951450393e-23 1.92109475725196e-23 63 1 3.60712656543017e-22 1.80356328271509e-22 64 1 3.41911880535572e-21 1.70955940267786e-21 65 1 2.72428309280215e-20 1.36214154640107e-20 66 1 2.03684595665024e-20 1.01842297832512e-20 67 1 1.66904183396575e-19 8.34520916982875e-20 68 1 1.64616407018362e-18 8.2308203509181e-19 69 1 1.1451658846384e-17 5.725829423192e-18 70 1 1.09672187527083e-16 5.48360937635413e-17 71 1 8.86030366870848e-16 4.43015183435424e-16 72 1 7.14545874199412e-18 3.57272937099706e-18 73 1 7.36930482823956e-17 3.68465241411978e-17 74 1 8.6807136728478e-16 4.3403568364239e-16 75 0.999999999999997 5.69382922614801e-15 2.84691461307401e-15 76 0.99999999999997 6.01780629757276e-14 3.00890314878638e-14 77 0.99999999999967 6.61319064075196e-13 3.30659532037598e-13 78 0.999999999996274 7.45158882032533e-12 3.72579441016267e-12 79 0.999999999994678 1.06435021046553e-11 5.32175105232763e-12 80 0.999999999931042 1.37915019080559e-10 6.89575095402797e-11 81 0.999999999213688 1.57262348979926e-09 7.86311744899632e-10 82 0.99999999081811 1.83637787587096e-08 9.1818893793548e-09 83 0.999999984852095 3.02958102605301e-08 1.51479051302651e-08 84 0.999999798423468 4.03153064678299e-07 2.0157653233915e-07 85 0.999997969268589 4.06146282290381e-06 2.03073141145191e-06 86 0.99997739295162 4.52140967590271e-05 2.26070483795136e-05 87 0.999809106867594 0.00038178626481119 0.000190893132405595 88 0.99881509179963 0.00236981640073875 0.00118490820036937 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 75 0.974025974025974 NOK 5% type I error level 76 0.987012987012987 NOK 10% type I error level 77 1 NOK

Charts produced by software:

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Parameters (Session):

par1 = 4 ; par2 = none ; par3 = 2 ; par4 = yes ;

Parameters (R input):

par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ; par4 = yes ;

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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