Multiple 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, 12 Dec 2009 16:11:16 -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/13/t1260660017f0poxlxnr7vaia6.htm/, Retrieved Sun, 13 Dec 2009 00:20:29 +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/13/t1260660017f0poxlxnr7vaia6.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 «

96.8 0 87.0 0 96.3 0 107.1 0 115.2 0 106.1 0 89.5 0 91.3 0 97.6 0 100.7 0 104.6 0 94.7 0 101.8 0 102.5 0 105.3 0 110.3 0 109.8 0 117.3 0 118.8 0 131.3 0 125.9 0 133.1 0 147.0 0 145.8 0 164.4 0 149.8 0 137.7 0 151.7 0 156.8 0 180.0 0 180.4 0 170.4 0 191.6 0 199.5 0 218.2 0 217.5 0 205.0 0 194.0 0 199.3 0 219.3 0 211.1 0 215.2 0 240.2 0 242.2 0 240.7 0 255.4 0 253.0 0 218.2 0 203.7 0 205.6 0 215.6 0 188.5 0 202.9 0 214.0 0 230.3 0 230.0 0 241.0 0 259.6 1 247.8 1 270.3 1 289.7 1 322.7 1 315.0 1 320.2 1 329.5 1 360.6 1 382.2 1 435.4 1 464.0 1 468.8 1 403.0 1 351.6 1 252.0 1 188.0 1 146.5 1 152.9 1 148.1 1 165.1 1 177.0 1 206.1 1 244.9 1 228.6 1 253.4 1 241.1 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 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 106.454483611626 + 25.9658008658010X[t] -5.10329828901264M1[t] -16.3488971346114M2[t] -23.3230674087817M3[t] -20.5543805400949M4[t] -19.3428365285508M5[t] -9.34557823129251M6[t] -2.89117707689137M7[t] + 7.59179550608124M8[t] + 19.6033395176252M9[t] + 19.476911976912M10[t] + 14.6741702741703M11[t] + 2.13131313131313t + 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) 106.454483611626 29.478979 3.6112 0.000569 0.000285 X 25.9658008658010 26.03679 0.9973 0.322067 0.161033 M1 -5.10329828901264 34.778106 -0.1467 0.88376 0.44188 M2 -16.3488971346114 34.745458 -0.4705 0.639437 0.319718 M3 -23.3230674087817 34.720044 -0.6717 0.503956 0.251978 M4 -20.5543805400949 34.701879 -0.5923 0.555549 0.277775 M5 -19.3428365285508 34.690976 -0.5576 0.578913 0.289457 M6 -9.34557823129251 34.687341 -0.2694 0.788397 0.394198 M7 -2.89117707689137 34.690976 -0.0833 0.933818 0.466909 M8 7.59179550608124 34.701879 0.2188 0.827464 0.413732 M9 19.6033395176252 34.720044 0.5646 0.574143 0.287071 M10 19.476911976912 34.633288 0.5624 0.575657 0.287828 M11 14.6741702741703 34.622364 0.4238 0.672986 0.336493 t 2.13131313131313 0.502195 4.244 6.6e-05 3.3e-05 Multiple Linear Regression - Regression Statistics Multiple R 0.740505739561174 R-squared 0.548348750323041 Adjusted R-squared 0.46447066109732 F-TEST (value) 6.53744923596676 F-TEST (DF numerator) 13 F-TEST (DF denominator) 70 p-value 6.06570922379035e-08 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 64.7656970041792 Sum Squared Residuals 293621.6855906 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 96.8 103.482498453927 -6.68249845392727 2 87 94.3682127396416 -7.36821273964157 3 96.3 89.5253555967842 6.77464440321584 4 107.1 94.4253555967842 12.6746444032158 5 115.2 97.7682127396413 17.4317872603587 6 106.1 109.896784168213 -3.79678416821269 7 89.5 118.482498453927 -28.982498453927 8 91.3 131.096784168213 -39.7967841682127 9 97.6 145.239641311070 -47.6396413110699 10 100.7 147.244526901670 -46.5445269016698 11 104.6 144.573098330241 -39.9730983302412 12 94.7 132.030241187384 -37.3302411873841 13 101.8 129.058256029685 -27.2582560296845 14 102.5 119.943970315399 -17.4439703153987 15 105.3 115.101113172542 -9.80111317254176 16 110.3 120.001113172542 -9.70111317254172 17 109.8 123.343970315399 -13.5439703153989 18 117.3 135.472541743970 -18.1725417439703 19 118.8 144.058256029685 -25.2582560296846 20 131.3 156.672541743970 -25.3725417439703 21 125.9 170.815398886827 -44.9153988868274 22 133.1 172.820284477427 -39.7202844774273 23 147 170.148855905999 -23.1488559059988 24 145.8 157.605998763142 -11.8059987631416 25 164.4 154.634013605442 9.76598639455788 26 149.8 145.519727891156 4.28027210884358 27 137.7 140.676870748299 -2.97687074829934 28 151.7 145.576870748299 6.12312925170068 29 156.8 148.919727891156 7.88027210884356 30 180 161.048299319728 18.9517006802721 31 180.4 169.634013605442 10.7659863945578 32 170.4 182.248299319728 -11.8482993197279 33 191.6 196.391156462585 -4.79115646258505 34 199.5 198.396042053185 1.10395794681510 35 218.2 195.724613481756 22.4753865182436 36 217.5 183.181756338899 34.3182436611008 37 205 180.209771181200 24.7902288188003 38 194 171.095485466914 22.904514533086 39 199.3 166.252628324057 33.0473716759431 40 219.3 171.152628324057 48.1473716759431 41 211.1 174.495485466914 36.6045145330859 42 215.2 186.624056895485 28.5759431045145 43 240.2 195.209771181200 44.9902288188003 44 242.2 207.824056895485 34.3759431045145 45 240.7 221.966914038343 18.7330859616574 46 255.4 223.971799628943 31.4282003710575 47 253 221.300371057514 31.6996289424861 48 218.2 208.757513914657 9.4424860853432 49 203.7 205.785528756957 -2.08552875695728 50 205.6 196.671243042672 8.9287569573284 51 215.6 191.828385899814 23.7716141001855 52 188.5 196.728385899814 -8.22838589981445 53 202.9 200.071243042672 2.82875695732839 54 214 212.199814471243 1.80018552875693 55 230.3 220.785528756957 9.5144712430427 56 230 233.399814471243 -3.39981447124305 57 241 247.5426716141 -6.5426716141002 58 259.6 275.513358070501 -15.9133580705009 59 247.8 272.841929499072 -25.0419294990724 60 270.3 260.299072356215 10.0009276437848 61 289.7 257.327087198516 32.3729128014843 62 322.7 248.21280148423 74.48719851577 63 315 243.369944341373 71.630055658627 64 320.2 248.269944341373 71.930055658627 65 329.5 251.61280148423 77.88719851577 66 360.6 263.741372912802 96.8586270871985 67 382.2 272.327087198516 109.872912801484 68 435.4 284.941372912802 150.458627087198 69 464 299.084230055659 164.915769944341 70 468.8 301.089115646259 167.710884353742 71 403 298.41768707483 104.58231292517 72 351.6 285.874829931973 65.7251700680272 73 252 282.902844774273 -30.9028447742733 74 188 273.788559059988 -85.7885590599876 75 146.5 268.945701917131 -122.445701917131 76 152.9 273.845701917130 -120.945701917130 77 148.1 277.188559059988 -129.088559059988 78 165.1 289.317130488559 -124.217130488559 79 177 297.902844774273 -120.902844774273 80 206.1 310.517130488559 -104.417130488559 81 244.9 324.659987631416 -79.7599876314162 82 228.6 326.664873222016 -98.0648732220161 83 253.4 323.993444650588 -70.5934446505875 84 241.1 311.45058750773 -70.3505875077304 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.000947862732703297 0.00189572546540659 0.999052137267297 18 8.46882013730509e-05 0.000169376402746102 0.999915311798627 19 6.96739554422517e-05 0.000139347910884503 0.999930326044558 20 6.99210838898216e-05 0.000139842167779643 0.99993007891611 21 1.68541541393958e-05 3.37083082787915e-05 0.99998314584586 22 4.7921151991973e-06 9.5842303983946e-06 0.9999952078848 23 2.44695753206073e-06 4.89391506412146e-06 0.999997553042468 24 1.91929947807331e-06 3.83859895614661e-06 0.999998080700522 25 1.50416846641238e-06 3.00833693282476e-06 0.999998495831534 26 4.28191431788229e-07 8.56382863576458e-07 0.999999571808568 27 9.1631075452779e-08 1.83262150905558e-07 0.999999908368925 28 1.80312908351082e-08 3.60625816702164e-08 0.99999998196871 29 3.49201164116366e-09 6.98402328232732e-09 0.999999996507988 30 2.16804399870083e-09 4.33608799740166e-09 0.999999997831956 31 2.22729850471351e-09 4.45459700942701e-09 0.999999997772701 32 8.52536473282281e-10 1.70507294656456e-09 0.999999999147464 33 1.29793898985294e-09 2.59587797970589e-09 0.999999998702061 34 1.50769576315348e-09 3.01539152630696e-09 0.999999998492304 35 2.46959829668889e-09 4.93919659337778e-09 0.999999997530402 36 3.83668623705395e-09 7.6733724741079e-09 0.999999996163314 37 1.06461803487717e-09 2.12923606975434e-09 0.999999998935382 38 2.83787147662344e-10 5.67574295324688e-10 0.999999999716213 39 7.30123923235793e-11 1.46024784647159e-10 0.999999999926988 40 2.26441432390822e-11 4.52882864781644e-11 0.999999999977356 41 5.1269152717163e-12 1.02538305434326e-11 0.999999999994873 42 1.19392652257862e-12 2.38785304515724e-12 0.999999999998806 43 7.9113913577429e-13 1.58227827154858e-12 0.999999999999209 44 5.61899572452188e-13 1.12379914490438e-12 0.999999999999438 45 3.45480042583199e-13 6.90960085166397e-13 0.999999999999654 46 1.6453220644415e-13 3.290644128883e-13 0.999999999999835 47 3.88541460232303e-14 7.77082920464606e-14 0.999999999999961 48 1.65296448662065e-14 3.3059289732413e-14 0.999999999999983 49 3.77423859211557e-14 7.54847718423113e-14 0.999999999999962 50 2.28643492727117e-14 4.57286985454235e-14 0.999999999999977 51 8.66444596632846e-15 1.73288919326569e-14 0.999999999999991 52 4.72421041808255e-14 9.4484208361651e-14 0.999999999999953 53 4.80509904655557e-14 9.61019809311114e-14 0.999999999999952 54 2.88485443235013e-14 5.76970886470026e-14 0.999999999999971 55 9.41439987767628e-15 1.88287997553526e-14 0.99999999999999 56 2.66829600235489e-15 5.33659200470978e-15 0.999999999999997 57 5.93425824482947e-16 1.18685164896589e-15 1 58 1.91289627262613e-14 3.82579254525226e-14 0.99999999999998 59 6.08236509242856e-11 1.21647301848571e-10 0.999999999939176 60 0.000203260480254132 0.000406520960508264 0.999796739519746 61 0.0327243131308355 0.065448626261671 0.967275686869165 62 0.0732416985654277 0.146483397130855 0.926758301434572 63 0.0594217208359866 0.118843441671973 0.940578279164013 64 0.045430177124541 0.090860354249082 0.95456982287546 65 0.0287282593946798 0.0574565187893596 0.97127174060532 66 0.0197803899432742 0.0395607798865485 0.980219610056726 67 0.0143993182891717 0.0287986365783434 0.985600681710828 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 44 0.862745098039216 NOK 5% type I error level 46 0.901960784313726 NOK 10% type I error level 49 0.96078431372549 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/13/t1260660017f0poxlxnr7vaia6/10b0ia1260659471.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/13/t1260660017f0poxlxnr7vaia6/10b0ia1260659471.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/13/t1260660017f0poxlxnr7vaia6/1h7ux1260659471.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/13/t1260660017f0poxlxnr7vaia6/1h7ux1260659471.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/13/t1260660017f0poxlxnr7vaia6/2ebvu1260659471.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/13/t1260660017f0poxlxnr7vaia6/2ebvu1260659471.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/13/t1260660017f0poxlxnr7vaia6/3nihu1260659471.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/13/t1260660017f0poxlxnr7vaia6/3nihu1260659471.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/13/t1260660017f0poxlxnr7vaia6/46nkm1260659471.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/13/t1260660017f0poxlxnr7vaia6/46nkm1260659471.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/13/t1260660017f0poxlxnr7vaia6/5k2uu1260659471.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/13/t1260660017f0poxlxnr7vaia6/5k2uu1260659471.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/13/t1260660017f0poxlxnr7vaia6/663mu1260659471.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/13/t1260660017f0poxlxnr7vaia6/663mu1260659471.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/13/t1260660017f0poxlxnr7vaia6/78mnu1260659471.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/13/t1260660017f0poxlxnr7vaia6/78mnu1260659471.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/13/t1260660017f0poxlxnr7vaia6/878t01260659471.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/13/t1260660017f0poxlxnr7vaia6/878t01260659471.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/13/t1260660017f0poxlxnr7vaia6/9z6jv1260659471.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/13/t1260660017f0poxlxnr7vaia6/9z6jv1260659471.ps (open in new window)

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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