*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: Mon, 06 Dec 2010 16:36:51 +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/06/t1291653299ewp1iaegagmrh5a.htm/, Retrieved Mon, 06 Dec 2010 17:35:09 +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/06/t1291653299ewp1iaegagmrh5a.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:

» Textbox « » Textfile « » CSV «

3484.74 13830.14 9349.44 7977 -5.6 6 1 3.17 3411.13 14153.22 9327.78 8241 -6.2 3 1 3.17 3288.18 15418.03 9753.63 8444 -7.1 2 1.2 3.36 3280.37 16666.97 10443.5 8490 -1.4 2 1.2 3.11 3173.95 16505.21 10853.87 8388 -0.1 2 0.8 3.11 3165.26 17135.96 10704.02 8099 -0.9 -8 0.7 3.57 3092.71 18033.25 11052.23 7984 0 0 0.7 4.04 3053.05 17671 10935.47 7786 0.1 -2 0.9 4.21 3181.96 17544.22 10714.03 8086 2.6 3 1.2 4.36 2999.93 17677.9 10394.48 9315 6 5 1.3 4.75 3249.57 18470.97 10817.9 9113 6.4 8 1.5 4.43 3210.52 18409.96 11251.2 9023 8.6 8 1.9 4.7 3030.29 18941.6 11281.26 9026 6.4 9 1.8 4.81 2803.47 19685.53 10539.68 9787 7.7 11 1.9 5.01 2767.63 19834.71 10483.39 9536 9.2 13 2.2 5 2882.6 19598.93 10947.43 9490 8.6 12 2.1 4.81 2863.36 17039.97 10580.27 9736 7.4 13 2.2 5.11 2897.06 16969.28 10582.92 9694 8.6 15 2.7 5.1 3012.61 16973.38 10654.41 9647 6.2 13 2.8 5.11 3142.95 16329.89 11014.51 9753 6 16 2.9 5.21 3032.93 16153.34 10967.87 10070 6.6 10 3.4 5.21 3045.78 15311.7 10433.56 10137 5.1 14 3 5.21 3 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 10 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation BEL_20[t] = -1619.34491058766 + 0.097090018535330Nikkei[t] + 0.377623204905491DJ_Indust[t] + 0.0224418967318068Goudprijs[t] -11.9978133248867Conjunct_Seizoenzuiver[t] + 13.1960386198306Cons_vertrouw[t] + 35.1584463072643Alg_consumptie_index_BE[t] -281.151660194821Gem_rente_kasbon_5j[t] + 101.669511969855M1[t] + 111.675876231966M2[t] + 66.9582047439335M3[t] + 27.0773094453436M4[t] + 9.19557078440676M5[t] -8.26816866526923M6[t] + 43.5191316121944M7[t] + 54.7982173057046M8[t] + 90.3544111508069M9[t] + 154.637115270349M10[t] + 85.9311944465136M11[t] + 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) -1619.34491058766 360.842489 -4.4877 1.7e-05 9e-06 Nikkei 0.097090018535330 0.015819 6.1374 0 0 DJ_Indust 0.377623204905491 0.035999 10.4898 0 0 Goudprijs 0.0224418967318068 0.008695 2.5811 0.011128 0.005564 Conjunct_Seizoenzuiver -11.9978133248867 7.307075 -1.6419 0.103382 0.051691 Cons_vertrouw 13.1960386198306 6.991986 1.8873 0.061684 0.030842 Alg_consumptie_index_BE 35.1584463072643 24.31066 1.4462 0.150885 0.075442 Gem_rente_kasbon_5j -281.151660194821 56.829501 -4.9473 3e-06 1e-06 M1 101.669511969855 116.822167 0.8703 0.385985 0.192993 M2 111.675876231966 117.85931 0.9475 0.345388 0.172694 M3 66.9582047439335 117.419158 0.5702 0.569641 0.28482 M4 27.0773094453436 117.575576 0.2303 0.818277 0.409139 M5 9.19557078440676 115.390203 0.0797 0.936624 0.468312 M6 -8.26816866526923 114.916944 -0.0719 0.94277 0.471385 M7 43.5191316121944 114.74208 0.3793 0.705193 0.352597 M8 54.7982173057046 114.627044 0.4781 0.633533 0.316767 M9 90.3544111508069 114.685489 0.7878 0.432437 0.216218 M10 154.637115270349 115.096969 1.3435 0.18179 0.090895 M11 85.9311944465136 114.558184 0.7501 0.454748 0.227374 Multiple Linear Regression - Regression Statistics Multiple R 0.94372311410716 R-squared 0.890613316100117 Adjusted R-squared 0.873188888576242 F-TEST (value) 51.1129169024226 F-TEST (DF numerator) 18 F-TEST (DF denominator) 113 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 268.132458734677 Sum Squared Residuals 8124136.74326266 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 3484.74 2824.94932725762 659.79067274238 2 3411.13 2831.67944896253 579.450551037465 3 3288.18 3026.34361786074 261.836382139262 4 3280.37 3371.16595702633 -90.7959570263253 5 3173.95 3460.59456225228 -286.644562252277 6 3165.26 3186.09006272444 -20.8300627244404 7 3092.71 3416.53562046413 -323.825620464133 8 3053.05 3275.75311444174 -222.70311444174 9 3181.96 3226.47236691210 -44.5123669120959 10 2999.93 3090.11186975507 -90.1818697550748 11 3249.57 3385.55429526564 -135.984295265644 12 3210.52 3367.06124372353 -156.541243723530 13 3030.29 3536.91507305959 -506.625073059586 14 2803.47 3314.27051443885 -510.800514438848 15 2767.63 3278.90181337856 -511.27181337856 16 2882.6 3434.23459844578 -551.634598445783 17 2863.36 2981.53971781858 -118.179717818577 18 2897.06 2989.65626779428 -92.5962677942793 19 3012.61 3070.89015368888 -58.2801536888809 20 3142.95 3175.44209763084 -32.4920976308441 21 3032.93 3114.56308713044 -81.6330871304413 22 3045.78 2953.58419646163 92.1958035383672 23 3110.52 2966.14395016107 144.376049838927 24 3013.24 2968.46511074246 44.7748892575436 25 2987.1 3029.90319403906 -42.8031940390629 26 2995.55 2990.54142188693 5.00857811306545 27 2833.18 2664.59635271701 168.583647282989 28 2848.96 2794.88723600528 54.0727639947217 29 2794.83 2939.84732636752 -145.017326367522 30 2845.26 2946.22098484891 -100.960984848915 31 2915.02 2797.29075293645 117.729247063550 32 2892.63 2660.34624676337 232.283753236633 33 2604.42 2132.61689243756 471.803107562441 34 2641.65 2271.92859150958 369.721408490422 35 2659.81 2407.31788325785 252.492116742151 36 2638.53 2399.32144294878 239.208557051219 37 2720.25 2548.91463235998 171.335367640016 38 2745.88 2492.10523568421 253.774764315794 39 2735.7 2709.69673962339 26.0032603766056 40 2811.7 2472.99135095788 338.708649042122 41 2799.43 2449.88175063835 349.548249361649 42 2555.28 2156.51035095622 398.769649043779 43 2304.98 1878.2034968129 426.776503187098 44 2214.95 1929.12242698476 285.827573015238 45 2065.81 1795.90033131494 269.909668685061 46 1940.49 1776.75680346372 163.733196536281 47 2042 1891.28608291027 150.713917089728 48 1995.37 1743.94856603094 251.421433969057 49 1946.81 1921.68390785491 25.1260921450883 50 1765.9 1753.67211643368 12.2278835663206 51 1635.25 1679.23165110453 -43.9816511045273 52 1833.42 1771.17849040016 62.2415095998413 53 1910.43 2017.38506129133 -106.955061291331 54 1959.67 2369.02970769841 -409.359707698409 55 1969.6 2376.18941793250 -406.589417932497 56 2061.41 2345.81140615421 -284.401406154209 57 2093.48 2584.35994753175 -490.879947531753 58 2120.88 2515.97294061163 -395.092940611629 59 2174.56 2525.63302147816 -351.073021478160 60 2196.72 2567.71439975515 -370.994399755147 61 2350.44 2882.44325306799 -532.003253067986 62 2440.25 2897.72556474247 -457.475564742468 63 2408.64 2826.54859490051 -417.908594900511 64 2472.81 2915.55822575873 -442.748225758727 65 2407.6 2624.86826017711 -217.268260177112 66 2454.62 2827.44797155566 -372.827971555662 67 2448.05 2650.93711425795 -202.887114257947 68 2497.84 2663.55323750216 -165.713237502159 69 2645.64 2760.68167711004 -115.041677110037 70 2756.76 2710.38474250976 46.3752574902388 71 2849.27 2808.55571393923 40.7142860607731 72 2921.44 2864.60926941584 56.8307305841598 73 2981.85 2953.88030397927 27.9696960207345 74 3080.58 3168.90350949230 -88.323509492304 75 3106.22 3176.90368584923 -70.6836858492261 76 3119.31 2936.13144867646 183.178551323542 77 3061.26 2856.49322090725 204.766779092751 78 3097.31 2965.06967595899 132.240324041010 79 3161.69 3110.11319464421 51.5768053557948 80 3257.16 3158.00157654276 99.1584234572418 81 3277.01 3185.12892124683 91.8810787531733 82 3295.32 3254.47344789792 40.8465521020795 83 3363.99 3369.74779724366 -5.75779724366406 84 3494.17 3491.93053071749 2.23946928250979 85 3667.03 3685.70754337421 -18.6775433742065 86 3813.06 3741.42921322358 71.6307867764211 87 3917.96 3673.72249825942 244.237501740584 88 3895.51 3708.68404932705 186.825950672954 89 3801.06 3598.57749367387 202.482506326132 90 3570.12 3313.32176750317 256.798232496835 91 3701.61 3356.59519517905 345.014804820952 92 3862.27 3514.41553114797 347.854468852029 93 3970.1 3676.07256246039 294.027437539608 94 4138.52 3988.45623625326 150.063763746744 95 4199.75 3998.73254195989 201.017458040108 96 4290.89 3910.76716303597 380.122836964035 97 4443.91 4185.42827991608 258.481720083922 98 4502.64 4262.80160010089 239.838399899109 99 4356.98 3998.90291842320 358.077081576795 100 4591.27 4203.17891811961 388.091081880395 101 4696.96 4420.0950882854 276.864911714602 102 4621.4 4336.48201019186 284.917989808139 103 4562.84 4398.03746831465 164.802531685346 104 4202.52 4120.1316944217 82.3883055783028 105 4296.49 4305.34034454639 -8.85034454639469 106 4435.23 4638.5329817899 -203.302981789899 107 4105.18 4150.08985488328 -44.9098548832834 108 4116.68 4240.72854501824 -124.048545018241 109 3844.49 3817.23190931791 27.2580906820945 110 3720.98 3872.06691585994 -151.086915859942 111 3674.4 3766.79191888594 -92.3919188859348 112 3857.62 3950.20310536987 -92.5831053698668 113 3801.06 3956.74444591671 -155.684445916706 114 3504.37 3528.70311771171 -24.333117711709 115 3032.6 3100.94100226371 -68.3410022637077 116 3047.03 3157.2452875544 -110.215287554398 117 2962.34 3153.97241587285 -191.632415872854 118 2197.82 2162.61237058675 35.2076294132463 119 2014.45 1896.19368260242 118.256317397579 120 1862.83 1857.37789164693 5.45210835307332 121 1905.41 1975.26257577339 -69.8525757733936 122 1810.99 1765.23445917461 45.7555408253865 123 1670.07 1592.57020899748 77.4997910025243 124 1864.44 1899.79661991287 -35.3566199128735 125 2052.02 2055.93307267161 -3.91307267160933 126 2029.6 2081.41808305635 -51.8180830563478 127 2070.83 2116.80658350557 -45.9765835055748 128 2293.41 2525.39738085609 -231.987380856094 129 2443.27 2638.34145343671 -195.071453436706 130 2513.17 2722.73581916078 -209.565819160776 131 2466.92 2836.76517629852 -369.845176298515 132 2502.66 2831.12583696468 -328.465836964683 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 22 0.0545682816817718 0.109136563363544 0.945431718318228 23 0.0603585562786019 0.120717112557204 0.939641443721398 24 0.116817775494850 0.233635550989701 0.88318222450515 25 0.0682951066519698 0.136590213303940 0.93170489334803 26 0.0484346028710521 0.0968692057421042 0.951565397128948 27 0.0239107039007436 0.0478214078014871 0.976089296099256 28 0.0321787988874815 0.0643575977749631 0.967821201112518 29 0.0351437952238826 0.0702875904477651 0.964856204776117 30 0.0216220160199059 0.0432440320398118 0.978377983980094 31 0.0115459397125865 0.023091879425173 0.988454060287413 32 0.00650009185348118 0.0130001837069624 0.993499908146519 33 0.00996663191904888 0.0199332638380978 0.99003336808095 34 0.00690028291906368 0.0138005658381274 0.993099717080936 35 0.00386541070337018 0.00773082140674035 0.99613458929663 36 0.00207445372836406 0.00414890745672812 0.997925546271636 37 0.00110637473477159 0.00221274946954318 0.998893625265228 38 0.00249077079047962 0.00498154158095925 0.99750922920952 39 0.00445124183939195 0.0089024836787839 0.995548758160608 40 0.0181031915995776 0.0362063831991552 0.981896808400422 41 0.0150081513710780 0.0300163027421561 0.984991848628922 42 0.0170157699297252 0.0340315398594503 0.982984230070275 43 0.0272887498827037 0.0545774997654075 0.972711250117296 44 0.0539235983644967 0.107847196728993 0.946076401635503 45 0.108917189670311 0.217834379340623 0.891082810329689 46 0.324582121162863 0.649164242325726 0.675417878837137 47 0.511228729345633 0.977542541308734 0.488771270654367 48 0.544241752940389 0.911516494119221 0.455758247059611 49 0.512953272342962 0.974093455314076 0.487046727657038 50 0.458804100521952 0.917608201043903 0.541195899478048 51 0.40489238695706 0.80978477391412 0.59510761304294 52 0.553447765741959 0.893104468516082 0.446552234258041 53 0.645364213755895 0.709271572488211 0.354635786244105 54 0.819990638068178 0.360018723863645 0.180009361931822 55 0.834594007766029 0.330811984467942 0.165405992233971 56 0.806931874716124 0.386136250567751 0.193068125283876 57 0.825645828158399 0.348708343683202 0.174354171841601 58 0.86856016435226 0.262879671295479 0.131439835647740 59 0.848632482900715 0.30273503419857 0.151367517099285 60 0.82393623213127 0.352127535737461 0.176063767868731 61 0.85510607190866 0.289787856182680 0.144893928091340 62 0.869927346537851 0.260145306924299 0.130072653462149 63 0.937484966911952 0.125030066176095 0.0625150330880476 64 0.994615026044495 0.0107699479110093 0.00538497395550463 65 0.998719057992453 0.00256188401509327 0.00128094200754664 66 0.999640652436452 0.000718695127097004 0.000359347563548502 67 0.999951873670318 9.62526593631777e-05 4.81263296815888e-05 68 0.999977336201047 4.53275979066333e-05 2.26637989533167e-05 69 0.999987186236277 2.56275274460655e-05 1.28137637230328e-05 70 0.999992308566895 1.53828662102570e-05 7.69143310512852e-06 71 0.99999425601817 1.14879636609501e-05 5.74398183047504e-06 72 0.999994444238163 1.11115236739173e-05 5.55576183695865e-06 73 0.999997302988666 5.3940226676377e-06 2.69701133381885e-06 74 0.999999041947625 1.91610475042714e-06 9.58052375213569e-07 75 0.99999990086932 1.98261362079871e-07 9.91306810399357e-08 76 0.999999953442636 9.31147276026831e-08 4.65573638013415e-08 77 0.999999990405507 1.91889869745944e-08 9.59449348729721e-09 78 0.99999999328991 1.34201782143454e-08 6.71008910717268e-09 79 0.999999989638075 2.07238497873747e-08 1.03619248936873e-08 80 0.999999991063407 1.78731856735111e-08 8.93659283675553e-09 81 0.99999998619668 2.76066403345250e-08 1.38033201672625e-08 82 0.999999972194669 5.56106621715987e-08 2.78053310857993e-08 83 0.999999963360269 7.32794625114006e-08 3.66397312557003e-08 84 0.999999939170575 1.21658850164832e-07 6.08294250824162e-08 85 0.999999941197996 1.17604007257742e-07 5.88020036288711e-08 86 0.999999971502233 5.69955344438824e-08 2.84977672219412e-08 87 0.99999999251632 1.49673589763533e-08 7.48367948817664e-09 88 0.999999998982198 2.03560455669455e-09 1.01780227834727e-09 89 0.99999999947134 1.05732020661709e-09 5.28660103308545e-10 90 0.999999999817286 3.65428758537997e-10 1.82714379268999e-10 91 0.999999999354749 1.29050230571643e-09 6.45251152858214e-10 92 0.999999999452017 1.09596565757279e-09 5.47982828786394e-10 93 0.999999997833977 4.33204625386485e-09 2.16602312693242e-09 94 0.999999994484268 1.10314635139605e-08 5.51573175698023e-09 95 0.999999978859906 4.22801877642693e-08 2.11400938821346e-08 96 0.999999942656755 1.14686490986503e-07 5.73432454932513e-08 97 0.999999775600657 4.48798686708328e-07 2.24399343354164e-07 98 0.99999969284137 6.14317259871989e-07 3.07158629935994e-07 99 0.999999806461154 3.87077692299481e-07 1.93538846149740e-07 100 0.99999918240609 1.63518782144992e-06 8.17593910724959e-07 101 0.999996761368098 6.47726380356991e-06 3.23863190178495e-06 102 0.999990161772387 1.96764552260977e-05 9.83822761304886e-06 103 0.999965206454302 6.95870913961568e-05 3.47935456980784e-05 104 0.999878830841586 0.00024233831682857 0.000121169158414285 105 0.99956508648047 0.000869827039059782 0.000434913519529891 106 0.999004154322534 0.00199169135493203 0.000995845677466013 107 0.997177660335526 0.00564467932894811 0.00282233966447406 108 0.991346272693665 0.0173074546126695 0.00865372730633476 109 0.993063062068661 0.0138738758626779 0.00693693793133896 110 0.984626325325907 0.0307473493481855 0.0153736746740927 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 48 0.539325842696629 NOK 5% type I error level 61 0.685393258426966 NOK 10% type I error level 65 0.730337078651685 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No 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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