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Data X:
140824 1794 71 159 130 278691 186099 110459 1351 70 149 143 197623 113854 105079 2024 78 178 118 233139 99776 112098 2724 106 164 146 221690 106194 43929 1306 53 100 73 177540 100792 76173 631 28 129 89 70849 47552 187326 5171 130 156 146 566234 250931 22807 381 19 67 22 33186 6853 144408 2135 61 148 132 226511 115466 66485 1919 45 132 92 245577 110896 79089 2183 113 169 147 313453 169351 81625 2262 123 230 203 248379 94853 68788 1999 78 122 113 200620 72591 103297 3005 81 191 171 367785 101345 69446 2246 87 162 87 266325 113713 114948 5053 183 237 208 394271 165354 167949 2362 76 156 153 335567 164263 125081 3490 168 157 97 407650 135213 125818 1476 57 123 95 182016 111669 136588 2397 88 203 197 267365 134163 112431 2545 72 187 160 279428 140303 103037 3071 105 152 148 484574 150773 82317 1534 43 89 84 196721 111848 118906 1774 56 227 227 197899 102509 83515 3756 130 165 154 255978 96785 104581 3019 132 162 151 255126 116136 103129 2985 131 174 142 281816 158376 83243 2010 89 154 148 278027 153990 37110 1636 55 129 110 173134 64057 113344 3126 76 174 149 382760 230054 139165 2522 83 195 179 302413 184531 86652 2099 81 186 149 251255 114198 112302 2429 96 197 187 355456 198299 69652 1117 45 157 153 109546 33750 119442 3550 102 168 163 427915 189723 69867 2764 56 159 127 273950 100826 101629 3743 124 161 151 427825 188355 70168 2021 87 153 100 247287 104470 31081 947 33 55 46 115658 58391 103925 3681 205 166 156 386534 164808 92622 3380 83 151 128 340132 134097 79011 1842 71 148 111 194127 80238 93487 1909 79 129 119 213258 133252 64520 1819 65 181 148 182398 54518 93473 2598 84 93 65 157164 121850 114360 5557 153 150 134 457592 79367 33032 918 42 82 66 78800 56968 96125 2386 81 229 201 213831 106314 151911 4144 122 193 177 368086 191889 89256 2430 62 176 156 203104 104864 95676 2158 77 179 158 244371 160792 5950 496 24 12 7 24188 15049 149695 2688 331 181 175 399093 191179 32551 744 17 67 61 65029 25109 31701 1161 64 52 41 101097 45824 100087 3214 61 148 133 297973 129711 169707 2793 88 230 228 352671 210012 150491 3962 203 148 140 367083 194679 120192 2758 148 160 155 371178 197680 95893 2316 88 155 141 269973 81180 151715 4066 149 198 181 389761 197765 176225 3293 121 104 75 315924 214738 59900 3094 121 169 97 285807 96252 104767 2755 90 163 142 282351 124527 114799 1606 73 151 136 250558 153242 72128 1989 70 116 87 254710 145707 143592 2137 138 153 140 215915 113963 89626 2889 154 195 169 247349 134904 131072 2536 86 149 129 260919 114268 126817 1729 71 106 92 182308 94333 81351 2673 72 179 160 256761 102204 22618 893 32 88 67 73566 23824 88977 2338 88 185 179 263796 111563 92059 1958 56 133 90 207899 91313 81897 2217 67 164 144 228779 89770 108146 2355 89 169 144 363571 100125 126372 3099 98 153 144 382785 165278 249771 1974 109 166 134 220401 181712 71154 2472 67 164 146 225097 80906 71571 2117 68 146 121 215445 75881 55918 1968 49 141 112 188786 83963 160141 4218 130 183 145 481148 175721 38692 1370 70 99 99 145943 68580 102812 2440 107 134 96 292287 136323 56622 870 25 28 27 80953 55792 15986 2081 57 101 77 164260 25157 123534 1573 61 139 137 179344 100922 108535 4034 220 159 151 413462 118845 93879 3042 125 222 126 358697 170492 144551 3098 106 171 159 180679 81716 56750 2604 102 154 101 298696 115750 127654 2386 82 154 144 288706 105590 65594 1896 66 129 102 197956 92795 59938 3146 77 140 135 282361 82390 146975 2589 87 156 147 329202 135599 165904 1960 43 156 155 220636 127667 169265 2017 63 138 138 277071 163073 183500 2261 87 153 113 305984 211381 165986 4184 161 251 248 416032 189944 184923 4021 116 126 116 412530 226168 140358 2841 141 198 176 297080 117495 149959 2488 68 168 140 318235 195894 57224 2172 194 138 59 200486 80684 43750 602 14 71 64 43287 19630 48029 2196 84 90 40 189520 88634 104978 2474 153 167 98 255152 139292 100046 2834 56 172 139 288617 128602 101047 2761 93 162 135 314167 135848 197426 1339 85 129 97 170268 178377 160902 3258 99 179 142 164399 106330 147172 2088 76 163 155 350667 178303 109432 2331 90 164 115 303273 116938 1168 398 11 0 0 23623 5841 83248 2213 74 155 103 195849 106020 25162 530 25 32 30 61857 24610 45724 1825 52 189 130 184709 74151 110529 3154 121 140 102 428191 232241 855 387 16 0 0 21054 6622 101382 2137 52 111 77 252805 127097 14116 492 22 25 9 31961 13155 89506 3792 122 159 150 351541 160501 135356 2161 71 183 163 246359 91502 116066 1789 95 184 148 187003 24469 144244 1857 55 119 94 172442 88229 8773 568 34 27 21 38214 13983 102153 2353 48 163 151 241539 80716 117440 2818 83 198 187 358276 157384 104128 1445 64 205 171 209821 122975 134238 3846 86 191 170 441447 191469 134047 2554 99 187 145 348017 231257 279488 3501 131 210 198 439634 258287 79756 1457 40 166 152 208962 122531 66089 1213 44 145 112 105332 61394 102070 3039 355 187 173 311111 86480 146760 4475 190 186 177 459327 195791 154771 1821 58 164 153 159057 18284 165933 4359 136 172 161 411980 147581 64593 2008 80 147 115 173486 72558 92280 1980 51 167 147 284582 147341 67150 2563 99 158 124 283913 114651 128692 1991 120 144 57 234203 100187 124089 4096 123 169 144 386740 130332 125386 2339 92 145 126 246963 134218 37238 2035 63 79 78 173260 10901 140015 3237 107 194 153 346730 145758 150047 1974 58 212 196 176654 75767 154451 2703 89 148 130 259048 134969 156349 2736 111 171 159 312540 169216 0 2 0 0 0 1 0 6023 207 10 0 0 14688 7953 0 5 1 0 0 98 0 0 8 2 0 0 455 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 84601 2399 91 141 94 283222 105406 68946 3448 163 204 129 409280 174586 0 0 0 0 0 0 0 0 4 4 0 0 203 0 1644 151 5 0 0 7199 4245 6179 474 20 15 13 46660 21509 3926 141 5 4 4 17547 7670 52789 1145 46 172 89 121550 15673 0 29 2 0 0 969 0 100350 2060 73 125 71 242228 75882
Names of X columns:
Pviews Logins SubmittedFM Submitted FM+120 TotTimeRFC TotCompTime
Sample Range:
(leave blank to include all observations)
From:
To:
Column Number of Endogenous Series
(?)
Fixed Seasonal Effects
Do not include Seasonal Dummies
Do not include Seasonal Dummies
Include Seasonal Dummies
Type of Equation
Linear Trend
No Linear Trend
Linear Trend
First Differences
Seasonal Differences (s)
First and Seasonal Differences (s)
Degree of Predetermination (lagged endogenous variables)
Degree of Seasonal Predetermination
Seasonality
12
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2
3
4
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11
12
Chart options
R Code
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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