*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 15:17:57 +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/t1291648573i6m23osrkpohufi.htm/, Retrieved Mon, 06 Dec 2010 16:16:24 +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/t1291648573i6m23osrkpohufi.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 2.77 3411.13 14153.22 9327.78 8241 -6.2 3 1 2.76 3288.18 15418.03 9753.63 8444 -7.1 2 1.2 2.76 3280.37 16666.97 10443.5 8490 -1.4 2 1.2 2.46 3173.95 16505.21 10853.87 8388 -0.1 2 0.8 2.46 3165.26 17135.96 10704.02 8099 -0.9 -8 0.7 2.47 3092.71 18033.25 11052.23 7984 0 0 0.7 2.71 3053.05 17671 10935.47 7786 0.1 -2 0.9 2.8 3181.96 17544.22 10714.03 8086 2.6 3 1.2 2.89 2999.93 17677.9 10394.48 9315 6 5 1.3 3.36 3249.57 18470.97 10817.9 9113 6.4 8 1.5 3.31 3210.52 18409.96 11251.2 9023 8.6 8 1.9 3.5 3030.29 18941.6 11281.26 9026 6.4 9 1.8 3.51 2803.47 19685.53 10539.68 9787 7.7 11 1.9 3.71 2767.63 19834.71 10483.39 9536 9.2 13 2.2 3.71 2882.6 19598.93 10947.43 9490 8.6 12 2.1 3.71 2863.36 17039.97 10580.27 9736 7.4 13 2.2 4.21 2897.06 16969.28 10582.92 9694 8.6 15 2.7 4.21 3012.61 16973.38 10654.41 9647 6.2 13 2.8 4.21 3142.95 16329.89 11014.51 9753 6 16 2.9 4.5 3032.93 16153.34 10967.87 10070 6.6 10 3.4 4.51 3045.78 15311.7 10433.56 10137 5.1 14 3 4.51 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 9 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation BEL_20[t] = -1829.91346353290 + 0.0932493209745398Nikkei[t] + 0.340625474153254DJ_Indust[t] -0.0461339961375057Goudprijs[t] -3.13234058387437Conjunct_Seizoenzuiver[t] -3.40204073251154Cons_vertrouw[t] -40.6029474729970Alg_consumptie_index_BE[t] + 46.1458989103431Gem_rente_kasbon_1j[t] + 166.234384975720M1[t] + 211.441636202194M2[t] + 145.674425778467M3[t] + 104.382150990713M4[t] + 55.5711165024448M5[t] -4.54850954972528M6[t] -9.27999423012134M7[t] -1.80540573459105M8[t] + 65.0922035015173M9[t] + 102.426980918673M10[t] + 78.1752424408722M11[t] + 7.05246043891046t + 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) -1829.91346353290 396.703255 -4.6128 1.1e-05 5e-06 Nikkei 0.0932493209745398 0.020151 4.6275 1e-05 5e-06 DJ_Indust 0.340625474153254 0.043937 7.7526 0 0 Goudprijs -0.0461339961375057 0.021183 -2.1779 0.031512 0.015756 Conjunct_Seizoenzuiver -3.13234058387437 8.45438 -0.3705 0.71171 0.355855 Cons_vertrouw -3.40204073251154 7.501817 -0.4535 0.651069 0.325535 Alg_consumptie_index_BE -40.6029474729970 31.022759 -1.3088 0.193277 0.096639 Gem_rente_kasbon_1j 46.1458989103431 47.00212 0.9818 0.328323 0.164161 M1 166.234384975720 125.376334 1.3259 0.187576 0.093788 M2 211.441636202194 125.977555 1.6784 0.096056 0.048028 M3 145.674425778467 125.946402 1.1566 0.249881 0.124941 M4 104.382150990713 126.440595 0.8255 0.410818 0.205409 M5 55.5711165024448 123.926442 0.4484 0.654716 0.327358 M6 -4.54850954972528 124.324802 -0.0366 0.97088 0.48544 M7 -9.27999423012134 124.738355 -0.0744 0.940828 0.470414 M8 -1.80540573459105 124.942163 -0.0144 0.988497 0.494248 M9 65.0922035015173 124.563236 0.5226 0.60231 0.301155 M10 102.426980918673 124.367276 0.8236 0.411926 0.205963 M11 78.1752424408722 123.525367 0.6329 0.52811 0.264055 t 7.05246043891046 2.795793 2.5225 0.013056 0.006528 Multiple Linear Regression - Regression Statistics Multiple R 0.934941793727624 R-squared 0.874116157658626 Adjusted R-squared 0.852760862975715 F-TEST (value) 40.932057863762 F-TEST (DF numerator) 19 F-TEST (DF denominator) 112 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 288.923167774606 Sum Squared Residuals 9349378.85021425 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 3484.74 2534.02114712633 950.718852873674 2 3411.13 2608.47459422049 802.655405779515 3 3288.18 2801.49323261313 486.686767386874 4 3280.37 3084.88324623281 195.486753767186 5 3173.95 3184.69794168707 -10.7479416870737 6 3165.26 3193.785816389 -28.5258163889966 7 3092.71 3384.73266462838 -292.022664628377 8 3053.05 3337.36663672685 -284.316636726849 9 3181.96 3277.35744518876 -95.3974451887568 10 2999.93 3168.8389390444 -168.908939044399 11 3249.57 3357.25266260533 -107.682662605332 12 3210.52 3417.82120965294 -207.301209652936 13 3030.29 3658.79478612352 -628.50478612352 14 2803.47 3487.00921576899 -683.539215768993 15 2767.63 3410.92774799485 -643.297747994851 16 2882.6 3524.22935742517 -641.629357425168 17 2863.36 3126.80591151088 -263.445911510876 18 2897.06 3039.12287284004 -142.062872840037 19 3012.61 3078.60718789925 -65.9971878992468 20 3142.95 3150.64062278773 -7.6906227877324 21 3032.93 3176.30910125195 -143.379101251949 22 3045.78 2964.45493270193 81.3250672980713 23 3110.52 2979.24232169379 131.277678306210 24 3013.24 2902.5991972917 110.640802708298 25 2987.1 3051.6343875118 -64.5343875117993 26 2995.55 3109.55371282317 -114.003712823174 27 2833.18 2754.88446768889 78.2955323111083 28 2848.96 2839.49838530974 9.4616146902643 29 2794.83 2933.93648470224 -139.106484702244 30 2845.26 2850.05605188813 -4.79605188812484 31 2915.02 2686.73642490625 228.283575093747 32 2892.63 2626.10126646834 266.528733531663 33 2604.42 2121.19596131122 483.224038688777 34 2641.65 2299.05784858478 342.592151415219 35 2659.81 2480.17418366772 179.635816332280 36 2638.53 2453.56456329165 184.965436708353 37 2720.25 2517.19035019666 203.05964980334 38 2745.88 2514.41301750447 231.466982495533 39 2735.7 2797.79835498630 -62.0983549863025 40 2811.7 2679.8979854921 131.802014507899 41 2799.43 2644.01113865752 155.418861342482 42 2555.28 2348.67071174700 206.609288253004 43 2304.98 2010.83414680724 294.145853192756 44 2214.95 1991.2180815781 223.731918421901 45 2065.81 1830.89276859119 234.917231408806 46 1940.49 1791.83042103848 148.659578961518 47 2042 1982.58354969615 59.416450303854 48 1995.37 1857.72597228793 137.644027712072 49 1946.81 1993.81250060264 -47.0025006026429 50 1765.9 1838.89297939166 -72.9929793916587 51 1635.25 1814.84101277089 -179.591012770887 52 1833.42 1890.77697325789 -57.3569732578883 53 1910.43 1958.42336958905 -47.9933695890542 54 1959.67 2117.66138002378 -157.991380023775 55 1969.6 2216.31774557692 -246.717745576917 56 2061.41 2254.13152166134 -192.721521661344 57 2093.48 2416.70330871334 -323.223308713343 58 2120.88 2597.23667872717 -476.356678727169 59 2174.56 2495.02958803531 -320.469588035314 60 2196.72 2563.62674243379 -366.906742433792 61 2350.44 2934.02667244014 -583.586672440137 62 2440.25 2990.70106878267 -550.451068782671 63 2408.64 2903.76169847032 -495.121698470325 64 2472.81 2900.43142873969 -427.621428739685 65 2407.6 2669.06550322987 -261.465503229871 66 2454.62 2746.57851880803 -291.958518808029 67 2448.05 2665.6779765628 -217.627976562798 68 2497.84 2600.56767631484 -102.727676314841 69 2645.64 2748.01841625171 -102.378416251705 70 2756.76 2689.56356005696 67.1964399430367 71 2849.27 2826.22269804069 23.0473019593099 72 2921.44 2878.74503547568 42.6949645243168 73 2981.85 3042.11576961814 -60.2657696181366 74 3080.58 3153.26314225632 -72.6831422563204 75 3106.22 3079.27143318082 26.948566819183 76 3119.31 2896.81616927087 222.493830729126 77 3061.26 2889.47106478781 171.788935212188 78 3097.31 2852.49225484560 244.817745154395 79 3161.69 2895.27782162376 266.412178376245 80 3257.16 2947.30052442882 309.859475571180 81 3277.01 3061.78557865143 215.224421348566 82 3295.32 3049.03014569472 246.289854305285 83 3363.99 3233.94162174953 130.048378250467 84 3494.17 3273.1038096405 221.066190359502 85 3667.03 3469.59436554623 197.435634453773 86 3813.06 3551.59897984671 261.461020153290 87 3917.96 3613.58137426977 304.378625730234 88 3895.51 3635.03947158522 260.470528414775 89 3801.06 3511.31668029212 289.743319707881 90 3570.12 3296.57809190852 273.541908091477 91 3701.61 3292.539780215 409.070219784997 92 3862.27 3456.6463434808 405.623656519201 93 3970.1 3693.417149394 276.682850606002 94 4138.52 3929.60727773035 208.912722269645 95 4199.75 3911.98732717343 287.762672826574 96 4290.89 4009.28330579892 281.606694201080 97 4443.91 4249.84639433541 194.063605664587 98 4502.64 4347.72760198227 154.912398017730 99 4356.98 4140.16728673163 216.812713268371 100 4591.27 4275.46543564731 315.804564352688 101 4696.96 4501.35724635082 195.602753649178 102 4621.4 4531.61533166643 89.7846683335693 103 4562.84 4612.75642372264 -49.9164237226385 104 4202.52 4356.34248836437 -153.822488364367 105 4296.49 4465.59284961735 -169.102849617354 106 4435.23 4636.2088858338 -200.978885833801 107 4105.18 4216.15173970512 -110.971739705118 108 4116.68 4196.54296930608 -79.8629693060819 109 3844.49 3823.10345843720 21.3865415627959 110 3720.98 3759.29648754651 -38.3164875465073 111 3674.4 3497.55663226248 176.843367737517 112 3857.62 3806.1896936347 51.4303063652964 113 3801.06 3855.63915298752 -54.5791529875167 114 3504.37 3560.90942307378 -56.5394230737847 115 3032.6 3209.19378241135 -176.59378241135 116 3047.03 3346.12310492481 -299.093104924814 117 2962.34 3186.03912753891 -223.699127538906 118 2197.82 2318.32840662910 -120.508406629096 119 2014.45 2178.30728940516 -163.857289405160 120 1862.83 2103.58222525945 -240.752225259453 121 1905.41 2088.18016806193 -182.770168061932 122 1810.99 1729.49919987674 81.490800123258 123 1670.07 1579.92675903092 90.1432409690804 124 1864.44 1924.78185340449 -60.3418534044938 125 2052.02 2087.23550620509 -35.2155062050931 126 2029.6 2162.4795468097 -132.879546809699 127 2070.83 2219.86604564642 -149.036045646417 128 2293.41 2458.78173326400 -165.371733263996 129 2443.27 2596.13829349014 -152.868293490137 130 2513.17 2641.39290395831 -128.222903958309 131 2466.92 2575.12701822777 -108.207018227771 132 2502.66 2586.45496956136 -83.7949695613586 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 23 0.171201136977058 0.342402273954116 0.828798863022942 24 0.0779723137856717 0.155944627571343 0.922027686214328 25 0.0444801723490121 0.0889603446980242 0.955519827650988 26 0.0196782365506479 0.0393564731012958 0.980321763449352 27 0.00803252779852416 0.0160650555970483 0.991967472201476 28 0.00319344116587403 0.00638688233174806 0.996806558834126 29 0.00180028522530496 0.00360057045060993 0.998199714774695 30 0.000742583506381132 0.00148516701276226 0.999257416493619 31 0.000284796591511973 0.000569593183023947 0.999715203408488 32 9.23169701472007e-05 0.000184633940294401 0.999907683029853 33 8.74074571100918e-05 0.000174814914220184 0.99991259254289 34 3.22256377037297e-05 6.44512754074594e-05 0.999967774362296 35 1.47821129305409e-05 2.95642258610819e-05 0.99998521788707 36 7.36243329036599e-06 1.47248665807320e-05 0.99999263756671 37 2.64384878591697e-06 5.28769757183394e-06 0.999997356151214 38 1.81169348658725e-06 3.6233869731745e-06 0.999998188306513 39 1.46464270762981e-06 2.92928541525961e-06 0.999998535357292 40 1.80146198055577e-05 3.60292396111153e-05 0.999981985380194 41 0.000147090551491254 0.000294181102982508 0.999852909448509 42 7.57608683876598e-05 0.000151521736775320 0.999924239131612 43 3.99819601600853e-05 7.99639203201706e-05 0.99996001803984 44 3.80725861247481e-05 7.61451722494961e-05 0.999961927413875 45 4.44751874736872e-05 8.89503749473744e-05 0.999955524812526 46 6.02384948960904e-05 0.000120476989792181 0.999939761505104 47 0.000135499183546814 0.000270998367093628 0.999864500816453 48 0.000168906657031833 0.000337813314063667 0.999831093342968 49 0.000306030347062808 0.000612060694125617 0.999693969652937 50 0.000195783922554726 0.000391567845109452 0.999804216077445 51 0.000101148436240234 0.000202296872480468 0.99989885156376 52 8.75825791807284e-05 0.000175165158361457 0.99991241742082 53 0.000189898165397236 0.000379796330794471 0.999810101834603 54 0.000263425845778141 0.000526851691556282 0.999736574154222 55 0.000317992238531903 0.000635984477063806 0.999682007761468 56 0.000685833956803706 0.00137166791360741 0.999314166043196 57 0.000548665644336396 0.00109733128867279 0.999451334355664 58 0.00191857977758245 0.00383715955516489 0.998081420222418 59 0.00162703793271758 0.00325407586543516 0.998372962067282 60 0.00132786142134343 0.00265572284268687 0.998672138578657 61 0.00148704451386995 0.00297408902773989 0.99851295548613 62 0.00187621651522464 0.00375243303044927 0.998123783484775 63 0.0117777326197297 0.0235554652394595 0.98822226738027 64 0.121887956230068 0.243775912460135 0.878112043769932 65 0.424843139380452 0.849686278760904 0.575156860619548 66 0.64608928787568 0.70782142424864 0.35391071212432 67 0.823085101594466 0.353829796811069 0.176914898405534 68 0.904106371950703 0.191787256098595 0.0958936280492974 69 0.973552616927925 0.0528947661441493 0.0264473830720746 70 0.992145936801713 0.0157081263965740 0.00785406319828702 71 0.99826654308608 0.00346691382784194 0.00173345691392097 72 0.999804809523008 0.000390380953984355 0.000195190476992177 73 0.999985123793035 2.97524139291884e-05 1.48762069645942e-05 74 0.9999985364302 2.92713960125355e-06 1.46356980062678e-06 75 0.999999942972909 1.14054183072453e-07 5.70270915362265e-08 76 0.99999998901819 2.19636210976787e-08 1.09818105488393e-08 77 0.999999998214833 3.57033419681764e-09 1.78516709840882e-09 78 0.999999998985349 2.02930261770487e-09 1.01465130885243e-09 79 0.99999999875694 2.48612222058396e-09 1.24306111029198e-09 80 0.999999999335786 1.32842806664082e-09 6.64214033320408e-10 81 0.999999999403403 1.19319302796948e-09 5.96596513984742e-10 82 0.999999999394566 1.21086798880362e-09 6.0543399440181e-10 83 0.999999998624918 2.75016349222907e-09 1.37508174611454e-09 84 0.999999996645332 6.70933669451476e-09 3.35466834725738e-09 85 0.99999999403352 1.19329606682527e-08 5.96648033412636e-09 86 0.99999999145118 1.70976397591806e-08 8.5488198795903e-09 87 0.99999999471408 1.05718405349796e-08 5.28592026748981e-09 88 0.999999998965526 2.06894714538849e-09 1.03447357269425e-09 89 0.999999999878849 2.42302823955694e-10 1.21151411977847e-10 90 0.999999999980058 3.98849026661947e-11 1.99424513330974e-11 91 0.999999999941596 1.16807648829504e-10 5.8403824414752e-11 92 0.999999999794076 4.11848942936719e-10 2.05924471468359e-10 93 0.999999999089523 1.8209540439428e-09 9.104770219714e-10 94 0.999999998125887 3.74822513059431e-09 1.87411256529715e-09 95 0.999999991999762 1.60004754459736e-08 8.00023772298682e-09 96 0.999999972649137 5.47017251086111e-08 2.73508625543055e-08 97 0.999999901907827 1.96184346855913e-07 9.80921734279566e-08 98 0.999999580410647 8.39178706135815e-07 4.19589353067908e-07 99 0.999998575962715 2.84807456906469e-06 1.42403728453235e-06 100 0.999994961820986 1.00763580274477e-05 5.03817901372386e-06 101 0.999984194283636 3.16114327278508e-05 1.58057163639254e-05 102 0.999957488633105 8.50227337893005e-05 4.25113668946502e-05 103 0.999924640802347 0.000150718395305150 7.53591976525749e-05 104 0.999732248793858 0.000535502412284193 0.000267751206142096 105 0.999285354962 0.00142929007600078 0.000714645038000389 106 0.998804877559575 0.00239024488084963 0.00119512244042482 107 0.996452819278296 0.00709436144340855 0.00354718072170427 108 0.98652602538967 0.0269479492206603 0.0134739746103301 109 0.964613104188494 0.0707737916230125 0.0353868958115063 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 72 0.827586206896552 NOK 5% type I error level 77 0.885057471264368 NOK 10% type I error level 80 0.919540229885057 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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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