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Data X:
1 1910 61 17 56 84 4 21 51 2 2598 74 19 73 47 3 15 48 3 2144 57 18 62 63 3 17 46 4 1331 50 15 42 28 3 20 42 5 1431 48 15 59 22 2 12 38 6 7334 2 12 27 18 6 4 38 7 1133 41 15 59 20 5 9 36 8 1195 31 20 78 27 5 11 35 9 1522 61 14 56 37 5 12 35 10 1551 12 12 47 23 6 7 35 11 2108 46 13 51 67 5 14 34 12 1335 31 17 47 28 4 11 34 13 1065 33 12 48 28 5 9 31 14 842 49 10 35 45 3 14 31 15 1539 15 13 47 15 5 4 31 16 1508 59 15 55 36 5 11 31 17 1598 28 12 42 12 2 10 30 18 1219 55 16 55 30 6 9 30 19 1443 35 13 47 28 9 8 30 20 1546 44 15 54 27 2 14 30 21 914 41 15 60 43 5 13 30 22 1370 26 13 51 10 3 10 28 23 1318 28 12 47 22 4 9 27 24 1313 40 15 52 27 4 11 27 25 1743 28 12 38 21 11 7 27 26 1102 67 12 12 24 5 10 26 27 1275 56 12 48 52 3 15 26 28 1253 54 12 48 24 5 7 26 29 1487 25 8 32 19 5 10 26 30 1098 19 9 27 12 0 4 26 31 1176 36 12 47 21 3 10 25 32 903 42 16 58 71 4 13 25 33 1290 19 14 47 19 4 5 25 34 1050 57 13 46 24 5 10 25 35 930 28 15 60 12 2 10 25 36 821 32 15 56 29 5 11 24 37 826 10 12 41 13 3 7 24 38 1402 28 12 45 22 11 6 24 39 1495 41 12 48 27 5 8 24 40 1064 48 15 60 36 5 10 24 41 1469 57 12 48 27 3 9 24 42 1493 35 13 42 21 5 8 24 43 1239 30 12 47 28 4 11 24 44 1317 39 12 41 17 3 5 23 45 708 17 15 49 15 8 5 23 46 872 33 12 39 26 3 10 23 47 853 55 12 39 19 3 8 23 48 1174 30 12 42 34 11 9 23 49 982 22 13 50 21 4 7 23 50 1202 42 12 41 32 6 8 23 51 873 49 15 52 14 14 5 23 52 1000 13 9 36 17 6 5 22 53 1131 15 13 45 16 3 7 22 54 793 24 12 46 18 5 10 22 55 1106 3 13 55 8 8 2 22 56 1205 35 13 49 30 8 5 22 57 1671 37 13 48 31 3 13 22 58 1374 28 13 39 19 3 10 21 59 775 19 12 48 10 3 5 21 60 804 38 15 45 24 5 10 21 61 1224 29 14 52 28 6 8 21 62 1233 38 15 51 27 3 7 20 63 1170 35 14 41 16 3 10 20 64 913 23 9 32 17 3 5 20 65 613 27 14 52 30 3 9 20 66 1204 32 16 54 20 4 6 19 67 933 7 9 27 10 5 6 18 68 861 57 12 41 30 3 9 18 69 932 39 12 45 34 5 11 18 70 705 18 13 52 13 13 6 18
Names of X columns:
Rang Pageviews Blogs PR LFM KCS SPR CH Hours

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
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 - Ordinary Least Squares
Variable	Parameter	S.D.	T-STAT H0: parameter = 0	2-tail p-value	1-tail p-value
(Intercept)	95.7151231150161	7.193954	13.3049	0	0
Pageviews	0.000811260866225306	0.001739	0.4665	0.642529	0.321265
Blogs	-0.0967248435916392	0.093794	-1.0312	0.306497	0.153248
PR	1.54079952985965	0.874556	1.7618	0.083112	0.041556
LFM	-0.123726061471697	0.183882	-0.6729	0.50358	0.25179
KCS	0.142466830241949	0.120535	1.1819	0.241813	0.120906
SPR	0.0742760351352662	0.465626	0.1595	0.873787	0.436894
CH	0.284731988242068	0.573976	0.4961	0.621628	0.310814
`Hours\r`	-2.96193342808933	0.248093	-11.9388	0	0

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	1	-22.1855667229931	23.1855667229931
2	2	-20.0747265982923	22.0747265982923
3	3	-10.2057294276376	13.2057294276376
4	4	-4.62049734826695	8.62049734826695
5	5	2.19153617035387	2.80846382964613
6	6	8.21596816004922	-2.21596816004922
7	7	7.63441967373456	-0.634419673734564
8	8	18.5338339809601	-10.5338339809601
9	9	11.0839474403475	-2.08394744034752
10	10	10.535007305522	-0.535007305522019
11	11	19.8934520511609	-8.89345205116092
12	12	20.8906440414713	-8.89064404147126
13	13	21.0410425525564	-8.04104255255635
14	14	21.5364176063876	-7.53641760638759
15	15	21.5554242447723	-6.55542424477232
16	16	24.3510999606083	-8.35109996060832
17	17	23.4437932080972	-6.44379320809723
18	18	27.6562889797842	-9.65628897978419
19	19	25.7930806445259	-6.79308064452591
20	20	28.2676264041034	-8.26762640410337
21	21	29.5202930996286	-8.52029309962864
22	22	29.5927496252256	-7.59274962522556
23	23	32.7722985269116	-9.77229852691162
24	24	36.8931105093952	-12.8931105093952
25	25	34.0386203875234	-9.03862038752342
26	26	36.761084543193	-10.761084543193
27	27	38.7754468572913	-11.7754468572913
28	28	32.832673722977	-4.83267372297702
29	29	31.7858099074563	-2.7858099074563
30	30	31.1329684124403	-1.13296841244025
31	31	37.875156714218	-6.87515671421804
32	32	49.9273583913975	-17.9273583913975
33	33	41.0592442871859	-8.05924428718592
34	34	37.982194281977	-3.98219428197695
35	35	40.1068675729938	-5.10686757299381
36	36	46.0178746459458	-10.0178746459458
37	37	41.8164205346795	-4.81642053467953
38	38	41.6394331281066	-3.6394331281066
39	39	40.9224211544414	-1.92242115444143
40	40	44.8850451165371	-4.88504511653711
41	41	39.4899107924249	1.51008920757512
42	42	42.929502611497	-0.929502611496954
43	43	42.8248244735004	0.175175526499625
44	44	42.3720659284116	1.6279340715884
45	45	47.7249912328943	-2.72499123289427
46	46	45.5447174408225	0.455282559177543
47	47	41.8346251371703	5.16537486282967
48	48	47.157925503558	0.842074496442033
49	49	45.3854881884856	3.61451181151443
50	50	45.202622921782	4.79737707821799
51	51	44.6956654770435	6.30433452295647
52	52	43.8107354184755	8.18926458152452
53	53	48.9773935117974	4.02260648820258
54	54	47.4558198508378	6.54418014916219
55	55	46.6885350910549	8.31146490894511
56	56	48.404477520758	7.595522479242
57	57	50.7617440192096	6.23825598079044
58	58	52.9029931879704	5.09700681202958
59	59	47.9273760249334	11.0726239750666
60	60	54.673454970675	5.326545029325
61	61	53.5525055462718	7.44749445372823
62	62	56.6657153972739	5.33428460272608
63	63	55.8883024103987	7.11169758960128
64	64	48.9688502838572	15.0311497161429
65	65	56.5590458156009	8.44095418439909
66	66	60.1463689024367	5.85363109756333
67	67	56.511186409004	10.488813590996
68	68	58.0617476753236	9.93825232467636
69	69	60.6533735033108	8.34662649668918
70	70	59.3539010064507	10.6460989935493

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
12	0.0477871498075366	0.0955742996150733	0.952212850192463
13	0.0205657660452348	0.0411315320904697	0.979434233954765
14	0.00841396235655387	0.0168279247131077	0.991586037643446
15	0.00584943391846088	0.0116988678369218	0.994150566081539
16	0.00779275532114907	0.0155855106422981	0.992207244678851
17	0.0343902719703859	0.0687805439407718	0.965609728029614
18	0.0282098741971383	0.0564197483942767	0.971790125802862
19	0.0540229554279916	0.108045910855983	0.945977044572008
20	0.211695398169557	0.423390796339114	0.788304601830443
21	0.508256114916811	0.983487770166379	0.491743885083189
22	0.600158135251138	0.799683729497724	0.399841864748862
23	0.603908656801206	0.792182686397589	0.396091343198794
24	0.561668443840747	0.876663112318505	0.438331556159253
25	0.568746849011592	0.862506301976816	0.431253150988408
26	0.505105849626225	0.989788300747551	0.494894150373775
27	0.459261607159482	0.918523214318965	0.540738392840518
28	0.567216154173966	0.865567691652069	0.432783845826034
29	0.655524598273492	0.688950803453017	0.344475401726508
30	0.773824853491072	0.452350293017856	0.226175146508928
31	0.836710137356167	0.326579725287666	0.163289862643833
32	0.82212432718974	0.35575134562052	0.17787567281026
33	0.888482376049775	0.22303524790045	0.111517623950225
34	0.915640539771366	0.168718920457268	0.084359460228634
35	0.939450554613354	0.121098890773293	0.0605494453866463
36	0.976730768060057	0.0465384638798867	0.0232692319399434
37	0.991465181373654	0.0170696372526915	0.00853481862634574
38	0.997886945163494	0.00422610967301156	0.00211305483650578
39	0.999082813263119	0.00183437347376172	0.000917186736880859
40	0.999713382961996	0.0005732340760091	0.00028661703800455
41	0.999822874233395	0.0003542515332095	0.00017712576660475
42	0.999852035132562	0.000295929734876263	0.000147964867438132
43	0.999900940043499	0.000198119913001364	9.90599565006822e-05
44	0.999977355078343	4.52898433142684e-05	2.26449216571342e-05
45	0.999991736075228	1.6527849543831e-05	8.26392477191552e-06
46	0.999994993172259	1.00136554828518e-05	5.00682774142588e-06
47	0.999995355176082	9.28964783589031e-06	4.64482391794516e-06
48	0.999994869625329	1.02607493417073e-05	5.13037467085365e-06
49	0.999995571327786	8.85734442733593e-06	4.42867221366796e-06
50	0.999989979372124	2.00412557524363e-05	1.00206278762181e-05
51	0.999968100049962	6.37999000751851e-05	3.18999500375926e-05
52	0.999962990203306	7.40195933879336e-05	3.70097966939668e-05
53	0.999961919381369	7.61612372612087e-05	3.80806186306043e-05
54	0.999962965912989	7.40681740213596e-05	3.70340870106798e-05
55	0.999893777355041	0.000212445289917676	0.000106222644958838
56	0.999628490533398	0.000743018933204461	0.00037150946660223
57	0.998019172925257	0.0039616541494852	0.0019808270747426
58	0.990802471123484	0.0183950577530328	0.00919752887651639

Multiple Linear Regression - Regression Statistics
Multiple R	0.910480067958451
R-squared	0.828973954149626
Adjusted R-squared	0.8065443087922
F-TEST (value)	36.9588524891752
F-TEST (DF numerator)	8
F-TEST (DF denominator)	61
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	8.95113952383889
Sum Squared Residuals	4887.49682528907

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	20	0.425531914893617	NOK
5% type I error level	27	0.574468085106383	NOK
10% type I error level	30	0.638297872340426	NOK