Paper - Multiple Regression Model 3

*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: Sun, 12 Dec 2010 20:06:08 +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/12/t1292184421wqon04xjbehy69j.htm/, Retrieved Sun, 12 Dec 2010 21:07:01 +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/12/t1292184421wqon04xjbehy69j.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:

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25.94 23688100 39.18 3940.35 0,0274 144.7 28.66 13741000 35.78 4696.69 0,0322 140.8 33.95 14143500 42.54 4572.83 0,0376 137.1 31.01 16763800 27.92 3860.66 0,0307 137.7 21.00 16634600 25.05 3400.91 0,0319 144.7 26.19 13693300 32.03 3966.11 0,0373 139.2 25.41 10545800 27.95 3766.99 0,0366 143.0 30.47 9409900 27.95 4206.35 0,0341 140.8 12.88 39182200 24.15 3672.82 0,0345 142.5 9.78 37005800 27.57 3369.63 0,0345 135.8 8.25 15818500 22.97 2597.93 0,0345 132.6 7.44 16952000 17.37 2470.52 0,0339 128.6 10.81 24563400 24.45 2772.73 0,0373 115.7 9.12 14163200 23.62 2151.83 0,0353 109.2 11.03 18184800 21.90 1840.26 0,0292 116.9 12.74 20810300 27.12 2116.24 0,0327 109.9 9.98 12843000 27.70 2110.49 0,0362 116.1 11.62 13866700 29.23 2160.54 0,0325 118.9 9.40 15119200 26.50 2027.13 0,0272 116.3 9.27 8301600 22.84 1805.43 0,0272 114.0 7.76 14039600 20.49 1498.80 0,0265 97.0 8.78 12139700 23.28 1690.20 0,0213 85.3 10.65 9649000 25.71 1930.58 0,019 84.9 10.95 8513600 26.52 1950.40 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 7 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation Apple[t] = -135.237765758431 -6.92930786369107e-07Volume[t] + 4.08575435495335Microsoft[t] + 0.0273638855674244NASDAQ[t] + 28.4463862390989Inflatie[t] -0.491355185021774Consumentenvertrouwen[t] + 1.68889394426909t + 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) -135.237765758431 19.256258 -7.0231 0 0 Volume -6.92930786369107e-07 0 -2.5807 0.011035 0.005517 Microsoft 4.08575435495335 0.918239 4.4496 1.9e-05 1e-05 NASDAQ 0.0273638855674244 0.006593 4.1506 6.1e-05 3.1e-05 Inflatie 28.4463862390989 207.329257 0.1372 0.891094 0.445547 Consumentenvertrouwen -0.491355185021774 0.164581 -2.9855 0.003417 0.001708 t 1.68889394426909 0.127815 13.2136 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.940901818676937 R-squared 0.885296232389568 Adjusted R-squared 0.879700926652474 F-TEST (value) 158.221243661534 F-TEST (DF numerator) 6 F-TEST (DF denominator) 123 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 26.5822933572503 Sum Squared Residuals 86914.0533761022 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 25.94 47.6203922582219 -21.6803922582219 2 28.66 65.0596023063397 -36.3996023063397 3 33.95 92.6716248524704 -58.7216248524703 4 31.01 12.8322720271830 18.177727972817 5 21 -13.1013193909541 34.1013193909541 6 26.19 37.4663893988560 -11.2763893988560 7 25.41 17.3306461573766 8.07935384262342 8 30.47 32.8391023862361 -2.36910238623609 9 12.88 -17.0513925961639 29.9313925961639 10 9.78 -4.88550092004212 14.6655009200421 11 8.25 -26.854118458832 35.104118458832 12 7.44 -50.368965700453 57.808965700453 13 10.81 -10.3222648531589 21.1322648531589 14 9.12 -18.6712488777555 27.7912488777555 15 11.03 -39.2792665814369 50.3092665814369 16 12.74 -6.99109089803629 19.7310908980363 17 9.98 -0.515854110966513 10.4958541109665 18 11.62 6.60340707587911 5.01659292412089 19 9.4 -6.25356251836246 15.6535625183625 20 9.27 -19.7308610888205 29.0008610888205 21 7.76 -31.6769892874143 39.4369892874143 22 8.78 -6.43395933788622 15.2139593378862 23 10.65 13.6180465968853 -2.96804659688531 24 10.95 15.0797997489084 -4.12979974890839 25 12.36 5.81749144249887 6.54250855750113 26 10.85 -5.66087562573002 16.51087562573 27 11.84 -1.15798936854931 12.9979893685493 28 12.14 -16.6646963911402 28.8046963911402 29 11.65 -19.7739102026169 31.4239102026169 30 8.86 -18.0894929648164 26.9494929648164 31 7.63 -24.9728231740389 32.6028231740389 32 7.38 -16.8624105803951 24.2424105803951 33 7.25 -28.3430994061799 35.5930994061799 34 8.03 0.0813156832701045 7.9486843167299 35 7.75 11.8036589582432 -4.05365895824315 36 7.16 2.13147506489139 5.02852493510861 37 7.18 -4.48013160977126 11.6601316097713 38 7.51 6.72765033793577 0.782349662064226 39 7.07 12.4367820767873 -5.36678207678731 40 7.11 7.43757418992007 -0.327574189920074 41 8.98 4.76930324082595 4.21069675917405 42 9.53 16.3744418612400 -6.84444186123995 43 10.54 28.0772063495220 -17.5372063495220 44 11.31 30.725446620261 -19.415446620261 45 10.36 37.0825160155296 -26.7225160155296 46 11.44 34.2420336358629 -22.8020336358629 47 10.45 31.1169909500695 -20.6669909500695 48 10.69 40.1315113696156 -29.4415113696156 49 11.28 38.4751533232602 -27.1951533232602 50 11.96 42.2826132927211 -30.3226132927211 51 13.52 31.8326786360434 -18.3126786360434 52 12.89 35.259629669038 -22.369629669038 53 14.03 43.5944494302591 -29.5644494302591 54 16.27 46.5402216760989 -30.2702216760989 55 16.17 40.5111138273433 -24.3411138273433 56 17.25 42.8363813486232 -25.5863813486232 57 19.38 48.1198247068595 -28.7398247068595 58 26.2 44.6840143182479 -18.4840143182479 59 33.53 54.4380034285798 -20.9080034285798 60 32.2 56.4250522720303 -24.2250522720303 61 38.45 36.4877963477307 1.96220365226932 62 44.86 39.5037788418986 5.35622115810142 63 41.67 48.3685744697666 -6.6985744697666 64 36.06 48.5475104570991 -12.4875104570991 65 39.76 61.4135448736617 -21.6535448736617 66 36.81 60.0564435648387 -23.2464435648387 67 42.65 69.5905745002651 -26.9405745002651 68 46.89 79.0849905910029 -32.1949905910029 69 53.61 79.1482637161787 -25.5382637161787 70 57.59 72.9876114102866 -15.3976114102866 71 67.82 85.266221488155 -17.4462214881551 72 71.89 78.1972981016392 -6.30729810163916 73 75.51 76.7302789767895 -1.22027897678947 74 68.49 77.316888337418 -8.82688833741798 75 62.72 79.699332293952 -16.9793322939520 76 70.39 67.035904080195 3.35409591980497 77 59.77 70.3599421976234 -10.5899421976234 78 57.27 71.8560952064922 -14.5860952064922 79 67.96 71.7868382480608 -3.82683824806083 80 67.85 88.6540848664657 -20.8040848664657 81 76.98 92.7301803877898 -15.7501803877898 82 81.08 108.391300703363 -27.3113007033626 83 91.66 114.188458660763 -22.5284586607625 84 84.84 110.296851449950 -25.4568514499504 85 85.73 104.350734924320 -18.6207349243204 86 84.61 110.188713489727 -25.578713489727 87 92.91 112.949089868605 -20.0390898686052 88 99.8 127.392729892974 -27.5927298929741 89 121.19 129.860861072444 -8.67086107244447 90 122.04 120.647073035436 1.39292696456383 91 131.76 113.995006808733 17.7649931912669 92 138.48 122.652715714628 15.8272842853720 93 153.47 132.353805169118 21.1161948308820 94 189.95 170.919476171579 19.0305238284211 95 182.22 152.876048468654 29.3439515313457 96 198.08 170.810531630444 27.2694683695564 97 135.36 134.159085828334 1.20091417166599 98 125.02 128.555635844006 -3.53563584400596 99 143.5 143.176077769243 0.323922230757482 100 173.95 153.217611323405 20.7323886765953 101 188.75 164.409378285476 24.3406217145242 102 167.44 159.117437515450 8.3225624845495 103 158.95 155.041658304202 3.90834169579771 104 169.53 167.832378853101 1.69762114689925 105 113.66 143.950282105205 -30.2902821052049 106 107.59 113.235329365615 -5.64532936561481 107 92.67 113.642695383806 -20.9726953838057 108 85.35 123.989944613498 -38.6399446134984 109 90.13 130.974377181877 -40.8443771818768 110 89.31 120.472177510882 -31.1621775108823 111 105.12 135.059086054011 -29.9390860540109 112 125.83 145.887785291799 -20.0577852917987 113 135.81 147.379933953111 -11.5699339531111 114 142.43 162.308990108187 -19.8789901081872 115 163.39 169.648983012293 -6.2589830122933 116 168.21 176.682207970864 -8.47220797086446 117 185.35 183.898051146686 1.45194885331349 118 188.5 191.131141299836 -2.63114129983579 119 199.91 206.809169694330 -6.89916969433031 120 210.73 212.746708030587 -2.01670803058705 121 192.06 192.292042209460 -0.232042209459598 122 204.62 210.468276881728 -5.84827688172815 123 235 217.324249565806 17.6757504341937 124 261.09 221.423290221788 39.6667097782118 125 256.88 188.259887644323 68.6201123556772 126 251.53 182.313226223778 69.2167737762222 127 257.25 201.540823705851 55.7091762941487 128 243.1 197.051470719490 46.0485292805096 129 283.75 208.591082585556 75.1589174144439 130 300.98 222.189981187953 78.7900188120467 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.00542820920296272 0.0108564184059254 0.994571790797037 11 0.00173826838534356 0.00347653677068712 0.998261731614656 12 0.000310966513671861 0.000621933027343721 0.999689033486328 13 5.4898665114721e-05 0.000109797330229442 0.999945101334885 14 8.24731423065337e-06 1.64946284613067e-05 0.99999175268577 15 3.48021178413945e-06 6.9604235682789e-06 0.999996519788216 16 6.5098218503746e-07 1.30196437007492e-06 0.999999349017815 17 9.44775734450921e-08 1.88955146890184e-07 0.999999905522427 18 1.33959871420700e-08 2.67919742841401e-08 0.999999986604013 19 2.68598861490292e-09 5.37197722980584e-09 0.999999997314011 20 4.52707659987368e-10 9.05415319974736e-10 0.999999999547292 21 7.29223845531052e-11 1.45844769106210e-10 0.999999999927078 22 1.52945456502641e-11 3.05890913005282e-11 0.999999999984705 23 2.5994690514974e-12 5.1989381029948e-12 0.9999999999974 24 3.58468810580145e-13 7.16937621160289e-13 0.999999999999642 25 5.6868540859591e-14 1.13737081719182e-13 0.999999999999943 26 8.89300753640398e-15 1.77860150728080e-14 0.999999999999991 27 1.13982823153340e-15 2.27965646306679e-15 0.999999999999999 28 3.41838829187996e-16 6.83677658375993e-16 1 29 7.05618858216625e-17 1.41123771643325e-16 1 30 1.23281426045513e-17 2.46562852091026e-17 1 31 3.20614197983149e-18 6.41228395966298e-18 1 32 6.34801118139012e-19 1.26960223627802e-18 1 33 3.12590861838408e-19 6.25181723676815e-19 1 34 6.79359058775805e-20 1.35871811755161e-19 1 35 9.6644946698919e-21 1.93289893397838e-20 1 36 1.96741108510884e-21 3.93482217021768e-21 1 37 9.0852630009779e-22 1.81705260019558e-21 1 38 2.45209175571813e-22 4.90418351143626e-22 1 39 5.38007641860861e-23 1.07601528372172e-22 1 40 2.13677250264975e-23 4.27354500529951e-23 1 41 1.62113508714327e-23 3.24227017428654e-23 1 42 6.17574174941764e-24 1.23514834988353e-23 1 43 1.31780886717577e-24 2.63561773435153e-24 1 44 2.5077538906245e-25 5.015507781249e-25 1 45 4.50475081311511e-26 9.00950162623021e-26 1 46 6.33173149410331e-27 1.26634629882066e-26 1 47 1.52929662834931e-27 3.05859325669862e-27 1 48 2.91803770836957e-28 5.83607541673915e-28 1 49 3.58681374337469e-29 7.17362748674938e-29 1 50 4.45968245142462e-30 8.91936490284924e-30 1 51 2.65650716930689e-30 5.31301433861377e-30 1 52 1.15346424331286e-30 2.30692848662572e-30 1 53 2.67399041750040e-31 5.34798083500081e-31 1 54 2.22885435623873e-31 4.45770871247746e-31 1 55 2.56583727019362e-31 5.13167454038723e-31 1 56 2.51295391454472e-31 5.02590782908944e-31 1 57 3.7759965148776e-31 7.5519930297552e-31 1 58 7.3825146432475e-27 1.4765029286495e-26 1 59 2.59571621585752e-23 5.19143243171505e-23 1 60 1.18582991443131e-22 2.37165982886261e-22 1 61 1.27393107947317e-20 2.54786215894634e-20 1 62 9.48216155809739e-18 1.89643231161948e-17 1 63 6.38675315362945e-16 1.27735063072589e-15 1 64 4.63613489168704e-15 9.27226978337409e-15 0.999999999999995 65 1.88246492116587e-14 3.76492984233173e-14 0.999999999999981 66 2.97865426943172e-14 5.95730853886344e-14 0.99999999999997 67 4.53733488998584e-14 9.07466977997167e-14 0.999999999999955 68 1.09555451892583e-13 2.19110903785166e-13 0.99999999999989 69 1.40551626500403e-12 2.81103253000805e-12 0.999999999998594 70 3.76502071308424e-11 7.53004142616848e-11 0.99999999996235 71 8.08448944751627e-09 1.61689788950325e-08 0.99999999191551 72 1.96126509668405e-06 3.9225301933681e-06 0.999998038734903 73 3.33798002086457e-05 6.67596004172915e-05 0.999966620199791 74 0.000114160183033920 0.000228320366067840 0.999885839816966 75 9.3454411533818e-05 0.000186908823067636 0.999906545588466 76 0.000130536111980881 0.000261072223961762 0.99986946388802 77 0.000105872613312396 0.000211745226624792 0.999894127386688 78 7.16496974121193e-05 0.000143299394824239 0.999928350302588 79 0.000424439011807441 0.000848878023614881 0.999575560988193 80 0.00102502218840398 0.00205004437680796 0.998974977811596 81 0.00494254395774701 0.00988508791549402 0.995057456042253 82 0.0111037109232175 0.0222074218464349 0.988896289076783 83 0.0269791058662739 0.0539582117325478 0.973020894133726 84 0.0248973312985634 0.0497946625971267 0.975102668701437 85 0.0204164740230014 0.0408329480460028 0.979583525976999 86 0.0167011064420808 0.0334022128841617 0.98329889355792 87 0.0181271004610845 0.0362542009221691 0.981872899538915 88 0.0251405052453991 0.0502810104907982 0.9748594947546 89 0.0652137565129539 0.130427513025908 0.934786243487046 90 0.155804784148102 0.311609568296204 0.844195215851898 91 0.247278172808953 0.494556345617906 0.752721827191047 92 0.42457139954446 0.84914279908892 0.57542860045554 93 0.799786802098355 0.400426395803289 0.200213197901645 94 0.942403743428067 0.115192513143867 0.0575962565719334 95 0.972654423606945 0.0546911527861096 0.0273455763930548 96 0.999560550546958 0.000878898906084294 0.000439449453042147 97 0.9991879128419 0.00162417431620199 0.000812087158100996 98 0.999106570319584 0.00178685936083232 0.000893429680416161 99 0.998673660123286 0.00265267975342777 0.00132633987671389 100 0.999167105308505 0.00166578938299072 0.00083289469149536 101 0.99946606589413 0.00106786821174116 0.000533934105870582 102 0.99989001470333 0.000219970593341799 0.000109985296670900 103 0.99978718264433 0.000425634711339854 0.000212817355669927 104 0.999983169440637 3.3661118726436e-05 1.6830559363218e-05 105 0.999966595655998 6.68086880032113e-05 3.34043440016057e-05 106 0.999928888471802 0.000142223056396742 7.1111528198371e-05 107 0.999883478510613 0.000233042978773738 0.000116521489386869 108 0.999786528581103 0.000426942837794588 0.000213471418897294 109 0.99947738810039 0.00104522379922008 0.000522611899610041 110 0.99888519625076 0.00222960749847968 0.00111480374923984 111 0.99794548374888 0.00410903250223814 0.00205451625111907 112 0.997429343944786 0.00514131211042753 0.00257065605521377 113 0.995474768517976 0.00905046296404786 0.00452523148202393 114 0.990194022446231 0.0196119551075371 0.00980597755376856 115 0.9815161820634 0.0369676358732004 0.0184838179366002 116 0.965884046020487 0.0682319079590259 0.0341159539795130 117 0.985420662684092 0.0291586746318168 0.0145793373159084 118 0.996388649834545 0.00722270033091091 0.00361135016545546 119 0.988382942619211 0.0232341147615778 0.0116170573807889 120 0.996670791284125 0.00665841743175016 0.00332920871587508 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 91 0.81981981981982 NOK 5% type I error level 101 0.90990990990991 NOK 10% type I error level 105 0.945945945945946 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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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Software written by Ed van Stee & Patrick Wessa

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