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Data X:
6.8 225 0.442 0.672 9.2 6.3 180 0.435 0.797 11.7 6.4 190 0.456 0.761 15.8 6.2 180 0.416 0.651 8.6 6.9 205 0.449 0.9 23.2 6.4 225 0.431 0.78 27.4 6.3 185 0.487 0.771 9.3 6.8 235 0.469 0.75 16 6.9 235 0.435 0.818 4.7 6.7 210 0.48 0.825 12.5 6.9 245 0.516 0.632 20.1 6.9 245 0.493 0.757 9.1 6.3 185 0.374 0.709 8.1 6.1 185 0.424 0.782 8.6 6.2 180 0.441 0.775 20.3 6.8 220 0.503 0.88 25 6.5 194 0.503 0.833 19.2 7.6 225 0.425 0.571 3.3 6.3 210 0.371 0.816 11.2 7.1 240 0.504 0.714 10.5 6.8 225 0.4 0.765 10.1 7.3 263 0.482 0.655 7.2 6.4 210 0.475 0.244 13.6 6.8 235 0.428 0.728 9 7.2 230 0.559 0.721 24.6 6.4 190 0.441 0.757 12.6 6.6 220 0.492 0.747 5.6 6.8 210 0.402 0.739 8.7 6.1 180 0.415 0.713 7.7 6.5 235 0.492 0.742 24.1 6.4 185 0.484 0.861 11.7 6 175 0.387 0.721 7.7 6 192 0.436 0.785 9.6 7.3 263 0.482 0.655 7.2 6.1 180 0.34 0.821 12.3 6.7 240 0.516 0.728 8.9 6.4 210 0.475 0.846 13.6 5.8 160 0.412 0.813 11.2 6.9 230 0.411 0.595 2.8 7 245 0.407 0.573 3.2 7.3 228 0.445 0.726 9.4 5.9 155 0.291 0.707 11.9 6.2 200 0.449 0.804 15.4 6.8 235 0.546 0.784 7.4 7 235 0.48 0.744 18.9 5.9 105 0.359 0.839 7.9 6.1 180 0.528 0.79 12.2 5.7 185 0.352 0.701 11 7.1 245 0.414 0.778 2.8 5.8 180 0.425 0.872 11.8 7.4 240 0.599 0.713 17.1 6.8 225 0.482 0.701 11.6 6.8 215 0.457 0.734 5.8 7 230 0.435 0.764 8.3
Names of X columns:
Height Weight Fieldgoals Freethrows Points

Sample Range: (leave blank to include all observations)
From:
To:

Column Number of Endogenous Series (?)


Fixed Seasonal Effects


Type of Equation


Degree of Predetermination (lagged endogenous variables)


Degree of Seasonal Predetermination


Seasonality


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') }

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	Big Analytics Cloud Computing Center

Multiple Linear Regression - Ordinary Least Squares
Variable	Parameter	S.D.	T-STAT H0: parameter = 0	2-tail p-value	1-tail p-value
(Intercept)	4.14870670628906	14.855006	0.2793	0.781205	0.390603
Height	-3.69049908336127	2.97078	-1.2423	0.220051	0.110026
Weight	0.00945845788151721	0.046297	0.2043	0.838966	0.419483
Fieldgoals	47.9401991647774	15.709131	3.0517	0.003668	0.001834
Freethrows	11.3710192606295	7.868536	1.4451	0.154788	0.077394

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	9.2	10.0123589367483	-0.812358936748346
2	11.7	12.517773887186	-0.817773887185998
3	15.8	12.8406960467427	2.9593039532573
4	8.6	10.3157911993394	-1.71579119933945
5	23.2	12.3823136563589	10.8176863436411
6	27.4	12.1892864594283	15.2107135405717
7	9.3	14.7623100323856	-5.46231003238564
8	16	12.2882683953416	3.71173160465835
9	4.7	11.0624810251259	-6.36248102512589
10	12.5	13.8010254919996	-1.30102549199961
11	20.1	12.925212153811	7.17478784618905
12	9.1	13.2439649805998	-4.14396498059976
13	8.1	8.64006433260676	-0.540064332606763
14	8.6	12.6052585135438	-4.00525851354384
15	20.3	12.9243025667769	7.37569743322306
16	25	15.2545908026032	9.74540919739684
17	19.2	15.5813827174425	3.61861728255749
18	3.3	5.09650333893457	-1.79650333893458
19	11.2	9.94940424303772	1.25059575696228
20	10.5	12.4969612371254	-1.9969612371254
21	10.1	9.05637536306628	1.04362463693372
22	7.2	10.2508314337258	-3.0508314337258
23	13.6	8.06191203075837	5.53808796924163
24	9	10.0725578058519	-1.07255780585193
25	24.6	14.7496348388613	9.85036516113873
26	12.6	12.0761089822285	0.523891017771477
27	5.6	13.9530028667991	-8.35300286679914
28	8.7	8.71473239239671	-0.0147323923967103
29	7.7	11.3419041026698	-3.64190410266982
30	24.1	14.4070745470549	9.69292545294513
31	11.7	15.2728312600118	-3.57283126001183
32	7.7	10.4123042990696	-2.71230429906963
33	9.6	13.6499130748098	-4.04991307480981
34	7.2	10.2508314337258	-3.0508314337258
35	12.3	8.9744592454595	3.3255407545405
36	8.9	14.7076375300961	-5.80763753009605
37	13.6	14.9072656256573	-1.30726562565732
38	11.2	13.2531659986165	-2.05316599861648
39	2.8	7.32888666064328	-4.52888666064328
40	3.2	6.65979040013695	-3.45979040013695
41	9.4	8.95334040628063	0.446659593719373
42	11.9	5.83073166030797	6.06926833969203
43	15.4	13.8267528762838	1.57324712371624
44	7.4	16.3662783858909	-8.96627838589092
45	18.9	12.0092846539182	6.89071534608183
46	7.9	10.1187168518401	-2.21871685184006
47	12.2	17.6347150913581	-5.43471509135815
48	11	9.70871124691339	1.29128875308661
49	2.8	8.95738083438331	-6.15738083438331
50	11.8	14.7364478817661	-2.93644788176607
51	17.1	15.9327594135102	1.16724058648976
52	11.6	12.2597264618977	-0.65972646189774
53	5.8	11.3418805395639	-5.54188053956391
54	8.3	10.0321037873082	-1.73210378730819

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
8	0.346674464959306	0.693348929918612	0.653325535040694
9	0.969673504895931	0.0606529902081386	0.0303264951040693
10	0.942389318935102	0.115221362129795	0.0576106810648977
11	0.964604553136096	0.0707908937278072	0.0353954468639036
12	0.970641444157544	0.0587171116849113	0.0293585558424557
13	0.948552194291449	0.102895611417102	0.0514478057085511
14	0.941052830651116	0.117894338697769	0.0589471693488843
15	0.952979873180514	0.094040253638972	0.047020126819486
16	0.973474302795041	0.0530513944099185	0.0265256972049592
17	0.96339859723598	0.0732028055280407	0.0366014027640203
18	0.946451139553082	0.107097720893836	0.053548860446918
19	0.922584048057446	0.154831903885107	0.0774159519425537
20	0.897298724406581	0.205402551186838	0.102701275593419
21	0.856730843178703	0.286538313642594	0.143269156821297
22	0.818635568456793	0.362728863086414	0.181364431543207
23	0.824505313175872	0.350989373648256	0.175494686824128
24	0.767723788011039	0.464552423977923	0.232276211988961
25	0.900757090646285	0.19848581870743	0.0992429093537148
26	0.863912410917389	0.272175178165221	0.136087589082611
27	0.925550758981867	0.148898482036266	0.0744492410181331
28	0.890077789197883	0.219844421604234	0.109922210802117
29	0.861679328635605	0.27664134272879	0.138320671364395
30	0.971737008861826	0.0565259822763481	0.0282629911381741
31	0.961387112262467	0.0772257754750663	0.0386128877375331
32	0.941960830772221	0.116078338455559	0.0580391692277793
33	0.923401535581714	0.153196928836571	0.0765984644182857
34	0.894314457372777	0.211371085254447	0.105685542627223
35	0.871385497752883	0.257229004494235	0.128614502247117
36	0.856070118817187	0.287859762365625	0.143929881182813
37	0.799030921439965	0.40193815712007	0.200969078560035
38	0.723613024773335	0.55277395045333	0.276386975226665
39	0.703299313295791	0.593401373408418	0.296700686704209
40	0.746249325058182	0.507501349883636	0.253750674941818
41	0.646007856458895	0.707984287082211	0.353992143541105
42	0.58725084670503	0.82549830658994	0.41274915329497
43	0.552039181015052	0.895921637969895	0.447960818984948
44	0.59057656134549	0.81884687730902	0.40942343865451
45	0.852416582232541	0.295166835534918	0.147583417767459
46	0.798975727934986	0.402048544130028	0.201024272065014

Multiple Linear Regression - Regression Statistics
Multiple R	0.471434652205528
R-squared	0.222250631300147
Adjusted R-squared	0.158760886916485
F-TEST (value)	3.50057530484154
F-TEST (DF numerator)	4
F-TEST (DF denominator)	49
p-value	0.013639681676693
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	5.41074474747539
Sum Squared Residuals	1434.5317773943

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	8	0.205128205128205	NOK