*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 16:40:41 +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/t1291653519tbux3xxgebm0lzt.htm/, Retrieved Mon, 06 Dec 2010 17:38:50 +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/t1291653519tbux3xxgebm0lzt.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 15 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation BEL_20[t] = -1599.03720837273 + 0.101061464791887Nikkei[t] + 0.369872254147376DJ_Indust[t] + 0.0144742968554702Goudprijs[t] -13.0075815890662Conjunct_Seizoenzuiver[t] + 14.0577880911957Cons_vertrouw[t] + 33.7278234341511Alg_consumptie_index_BE[t] -269.764154997347Gem_rente_kasbon_5j[t] + 99.4975226309243M1[t] + 111.784180391219M2[t] + 64.7722526051577M3[t] + 23.7198433389575M4[t] + 8.23471602593218M5[t] -12.6633778006483M6[t] + 36.2211969330588M7[t] + 46.5102316274506M8[t] + 84.1335508449912M9[t] + 149.910334438272M10[t] + 86.0422081747543M11[t] + 1.14348517765727t + 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) -1599.03720837273 365.422654 -4.3759 2.7e-05 1.4e-05 Nikkei 0.101061464791887 0.018511 5.4596 0 0 DJ_Indust 0.369872254147376 0.040625 9.1045 0 0 Goudprijs 0.0144742968554702 0.020991 0.6895 0.491914 0.245957 Conjunct_Seizoenzuiver -13.0075815890662 7.722738 -1.6843 0.094904 0.047452 Cons_vertrouw 14.0577880911957 7.315156 1.9217 0.05718 0.02859 Alg_consumptie_index_BE 33.7278234341511 24.639609 1.3688 0.173787 0.086893 Gem_rente_kasbon_5j -269.764154997347 63.228974 -4.2665 4.2e-05 2.1e-05 M1 99.4975226309243 117.36685 0.8477 0.398386 0.199193 M2 111.784180391219 118.292641 0.945 0.346703 0.173352 M3 64.7722526051577 117.966928 0.5491 0.58405 0.292025 M4 23.7198433389575 118.281489 0.2005 0.841424 0.420712 M5 8.23471602593218 115.837061 0.0711 0.943454 0.471727 M6 -12.6633778006483 115.818998 -0.1093 0.91313 0.456565 M7 36.2211969330588 116.483753 0.311 0.756413 0.378206 M8 46.5102316274506 116.749653 0.3984 0.691112 0.345556 M9 84.1335508449912 116.068017 0.7249 0.470047 0.235024 M10 149.910334438272 116.073767 1.2915 0.199186 0.099593 M11 86.0422081747543 114.979409 0.7483 0.455831 0.227916 t 1.14348517765727 2.739961 0.4173 0.677231 0.338616 Multiple Linear Regression - Regression Statistics Multiple R 0.943813094641892 R-squared 0.890783157617505 Adjusted R-squared 0.872255300427617 F-TEST (value) 48.0780453178196 F-TEST (DF numerator) 19 F-TEST (DF denominator) 112 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 269.117649405580 Sum Squared Residuals 8111522.63281751 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 3484.74 2808.62255748293 676.117442517073 2 3411.13 2816.14460449073 594.985395509268 3 3288.18 3011.68750543237 276.492494567625 4 3280.37 3347.12570049667 -66.75570049667 5 3173.95 3436.34346903232 -262.393469032320 6 3165.26 3163.08884094277 2.17115905723315 7 3092.71 3404.89334452617 -312.183344526174 8 3053.05 3265.13347760171 -212.083477601714 9 3181.96 3220.9491968528 -38.9891968527991 10 2999.93 3083.03015493371 -83.1001549337123 11 3249.57 3384.18225754057 -134.612257540572 12 3210.52 3364.11886361002 -153.598863610019 13 3030.29 3539.27759960481 -508.987599604814 14 2803.47 3325.24114318235 -521.771143182348 15 2767.63 3291.41608457393 -523.78608457393 16 2882.6 3440.27775944428 -557.677759444277 17 2863.36 2987.19267340104 -123.832673401042 18 2897.06 2992.7343023541 -95.6743023541023 19 3012.61 3072.71635019271 -60.1063501927108 20 3142.95 3175.01334970606 -32.0633497060587 21 3032.93 3107.98789687846 -75.0578968784617 22 3045.78 2955.44552357251 90.334476427491 23 3110.52 2969.77080150319 140.749198496806 24 3013.24 2969.85328337957 43.3867166204268 25 2987.1 3029.97120326318 -42.8712032631799 26 2995.55 2988.34564398673 7.20435601326654 27 2833.18 2663.28164303577 169.898356964234 28 2848.96 2795.60817755712 53.3518224428814 29 2794.83 2940.41724116218 -145.587241162180 30 2845.26 2938.26566647897 -93.0056664789676 31 2915.02 2789.94204359655 125.077956403453 32 2892.63 2650.4283830932 242.201616906799 33 2604.42 2124.96132957595 479.458670424053 34 2641.65 2259.55215326141 382.097846738591 35 2659.81 2391.89166008817 267.918339911832 36 2638.53 2394.81886575890 243.711134241104 37 2720.25 2543.56670488732 176.683295112677 38 2745.88 2488.13647858727 257.743521412726 39 2735.7 2707.26648155643 28.4335184435654 40 2811.7 2470.28859715743 341.411402842567 41 2799.43 2451.71990910627 347.710090893729 42 2555.28 2156.96171915732 398.318280842685 43 2304.98 1884.31788708140 420.662112918596 44 2214.95 1929.01329304077 285.93670695923 45 2065.81 1796.82707486377 268.982925136225 46 1940.49 1780.9854445357 159.504555464300 47 2042 1896.11900096138 145.880999038625 48 1995.37 1744.93884517396 250.431154826039 49 1946.81 1916.52569765169 30.2843023483113 50 1765.9 1748.8691241306 17.0308758694006 51 1635.25 1674.88519054437 -39.635190544373 52 1833.42 1776.96787284007 56.4521271599324 53 1910.43 2018.95454320583 -108.524543205828 54 1959.67 2366.29066720967 -406.620667209671 55 1969.6 2372.83446355801 -403.234463558007 56 2061.41 2341.92555286725 -280.515552867254 57 2093.48 2583.21889902119 -489.738899021194 58 2120.88 2512.05612354128 -391.176123541277 59 2174.56 2527.51597035947 -352.955970359474 60 2196.72 2568.03298054503 -371.312980545027 61 2350.44 2886.24202052657 -535.802020526574 62 2440.25 2906.51247428389 -466.262474283886 63 2408.64 2833.03251273144 -424.392512731436 64 2472.81 2915.77110094659 -442.961100946592 65 2407.6 2629.32047198321 -221.720471983214 66 2454.62 2834.98632654039 -380.366326540391 67 2448.05 2652.21085686839 -204.160856868388 68 2497.84 2666.58111973673 -168.741119736731 69 2645.64 2764.68137646383 -119.041376463833 70 2756.76 2713.96608140969 42.7939185903105 71 2849.27 2814.98607472351 34.2839252764931 72 2921.44 2875.0298243142 46.4101756858017 73 2981.85 2964.79231409996 17.0576859000381 74 3080.58 3184.00178564041 -103.421785640410 75 3106.22 3192.1191489299 -85.899148929897 76 3119.31 2952.39283719018 166.917162809819 77 3061.26 2869.9037232058 191.356276794202 78 3097.31 2969.09655585297 128.21344414703 79 3161.69 3112.62466496433 49.0653350356719 80 3257.16 3162.86636866311 94.2936313368915 81 3277.01 3184.51983303367 92.4901669663344 82 3295.32 3259.02114752499 36.2988524750109 83 3363.99 3377.21330917197 -13.2233091719671 84 3494.17 3501.86223964972 -7.69223964971827 85 3667.03 3694.60984705601 -27.5798470560133 86 3813.06 3746.80043132041 66.2595686795931 87 3917.96 3675.65776147452 242.302238525481 88 3895.51 3706.01865950118 189.491340498825 89 3801.06 3586.76707792798 214.292922072024 90 3570.12 3314.18140378979 255.938596210209 91 3701.61 3349.25910807833 352.350891921674 92 3862.27 3511.29728185908 350.972718140922 93 3970.1 3680.75923189107 289.340768108933 94 4138.52 3998.38115866742 140.138841332576 95 4199.75 4005.30591265847 194.444087341531 96 4290.89 3913.29420654587 377.595793454128 97 4443.91 4194.01683732498 249.893162675018 98 4502.64 4275.88370420499 226.756295795007 99 4356.98 4013.94715652773 343.032843472272 100 4591.27 4213.93221133105 377.337788668951 101 4696.96 4431.15397063312 265.806029366885 102 4621.4 4349.20243048809 272.197569511910 103 4562.84 4409.84056454571 152.999435454289 104 4202.52 4129.83331065031 72.6866893496911 105 4296.49 4307.92401769693 -11.4340176969336 106 4435.23 4641.52263044847 -206.292630448468 107 4105.18 4145.41452511886 -40.2345251188606 108 4116.68 4240.07740634523 -123.397406345227 109 3844.49 3798.90759393396 45.5824060660444 110 3720.98 3852.17118176078 -131.191181760783 111 3674.4 3738.85546496286 -64.4554649628629 112 3857.62 3933.65824339979 -76.0382433997869 113 3801.06 3943.5865605569 -142.526560556897 114 3504.37 3525.13660820987 -20.7666082098690 115 3032.6 3096.90468604373 -64.3046860437313 116 3047.03 3161.49679542101 -114.466795421005 117 2962.34 3160.73838475211 -198.398384752110 118 2197.82 2165.89717742234 31.9228225776631 119 2014.45 1912.72507459910 101.724925400897 120 1862.83 1875.25624960617 -12.4262496061659 121 1905.41 1985.78762416858 -80.377624168581 122 1810.99 1758.32342841183 52.6665715881659 123 1670.07 1592.06105023068 78.008949769321 124 1864.44 1905.96884013565 -41.5288401356504 125 2052.02 2066.60035978536 -14.5803597853576 126 2029.6 2090.00547897607 -60.405478976066 127 2070.83 2126.99603054467 -56.1660305446732 128 2293.41 2531.63106736077 -238.221067360769 129 2443.27 2640.88275897021 -197.612758970214 130 2513.17 2715.69240468249 -202.522404682485 131 2466.92 2810.89541327531 -343.975413275310 132 2502.66 2795.76723507134 -293.107235071345 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 23 0.143247789393016 0.286495578786031 0.856752210606984 24 0.0732187004096181 0.146437400819236 0.926781299590382 25 0.0419992370665825 0.083998474133165 0.958000762933418 26 0.0191903994248866 0.0383807988497733 0.980809600575113 27 0.00786426484181974 0.0157285296836395 0.99213573515818 28 0.00308691176632982 0.00617382353265963 0.99691308823367 29 0.00167644886891851 0.00335289773783703 0.998323551131082 30 0.000686318851684574 0.00137263770336915 0.999313681148315 31 0.000283745001087341 0.000567490002174683 0.999716254998913 32 9.16980217966155e-05 0.000183396043593231 0.999908301978203 33 8.15818149243974e-05 0.000163163629848795 0.999918418185076 34 2.94520390031158e-05 5.89040780062315e-05 0.999970547960997 35 1.32053104965165e-05 2.6410620993033e-05 0.999986794689503 36 4.98916633374654e-06 9.97833266749309e-06 0.999995010833666 37 1.68930743681456e-06 3.37861487362912e-06 0.999998310692563 38 1.70186631587016e-06 3.40373263174032e-06 0.999998298133684 39 1.71965361642185e-06 3.43930723284371e-06 0.999998280346384 40 1.69902256589049e-05 3.39804513178098e-05 0.999983009774341 41 0.000191004184415169 0.000382008368830337 0.999808995815585 42 0.000106593380326529 0.000213186760653059 0.999893406619673 43 6.664122640398e-05 0.00013328245280796 0.999933358773596 44 7.18558563335686e-05 0.000143711712667137 0.999928144143666 45 7.80155308520417e-05 0.000156031061704083 0.999921984469148 46 0.000149738141610941 0.000299476283221882 0.99985026185839 47 0.000751761738458942 0.00150352347691788 0.99924823826154 48 0.00186148654607147 0.00372297309214294 0.998138513453928 49 0.00272656236577629 0.00545312473155259 0.997273437634224 50 0.00221787743648747 0.00443575487297494 0.997782122563513 51 0.00137993554129367 0.00275987108258734 0.998620064458706 52 0.00230708897519843 0.00461417795039685 0.997692911024802 53 0.00490470654700325 0.0098094130940065 0.995095293452997 54 0.00591821378480476 0.0118364275696095 0.994081786215195 55 0.0067121456382241 0.0134242912764482 0.993287854361776 56 0.0111048519645621 0.0222097039291241 0.988895148035438 57 0.00899337271409132 0.0179867454281826 0.991006627285909 58 0.0225153324008424 0.0450306648016848 0.977484667599158 59 0.0199142521041237 0.0398285042082475 0.980085747895876 60 0.0172518703787952 0.0345037407575904 0.982748129621205 61 0.0178832581758222 0.0357665163516444 0.982116741824178 62 0.0196510882206221 0.0393021764412442 0.980348911779378 63 0.059822687814717 0.119645375629434 0.940177312185283 64 0.294389233261681 0.588778466523361 0.705610766738319 65 0.717130186194287 0.565739627611426 0.282869813805713 66 0.878549364860064 0.242901270279873 0.121450635139936 67 0.950939041020576 0.0981219179588488 0.0490609589794244 68 0.974348368734017 0.051303262531967 0.0256516312659835 69 0.988811744590947 0.0223765108181061 0.0111882554090531 70 0.996438643060433 0.00712271387913469 0.00356135693956735 71 0.99881954906655 0.00236090186689779 0.00118045093344890 72 0.999736010364855 0.000527979270288991 0.000263989635144495 73 0.999955249419973 8.95011600547486e-05 4.47505800273743e-05 74 0.999991821979787 1.63560404269183e-05 8.17802021345915e-06 75 0.999999447949086 1.10410182817721e-06 5.52050914088607e-07 76 0.999999865998808 2.68002383356715e-07 1.34001191678358e-07 77 0.999999979805916 4.03881671518795e-08 2.01940835759397e-08 78 0.999999986667262 2.66654758810450e-08 1.33327379405225e-08 79 0.999999977865618 4.42687631609296e-08 2.21343815804648e-08 80 0.999999977214162 4.55716763995504e-08 2.27858381997752e-08 81 0.999999959396677 8.12066455311474e-08 4.06033227655737e-08 82 0.999999912264889 1.75470222245799e-07 8.77351111228994e-08 83 0.999999879994226 2.40011547178971e-07 1.20005773589486e-07 84 0.999999803053181 3.93893637745505e-07 1.96946818872752e-07 85 0.999999808670733 3.82658533651996e-07 1.91329266825998e-07 86 0.99999987530396 2.49392082151797e-07 1.24696041075899e-07 87 0.999999955571951 8.8856097620371e-08 4.44280488101855e-08 88 0.999999992641132 1.47177356644605e-08 7.35886783223024e-09 89 0.999999998360742 3.27851516313736e-09 1.63925758156868e-09 90 0.99999999979845 4.03098284684173e-10 2.01549142342086e-10 91 0.999999999430083 1.13983382385728e-09 5.6991691192864e-10 92 0.999999998284002 3.43199576747599e-09 1.71599788373799e-09 93 0.999999994139588 1.17208237361543e-08 5.86041186807713e-09 94 0.999999993537153 1.29256948434256e-08 6.46284742171282e-09 95 0.999999982049185 3.59016296426999e-08 1.79508148213500e-08 96 0.999999935271894 1.29456211224920e-07 6.47281056124602e-08 97 0.999999852787932 2.94424135901040e-07 1.47212067950520e-07 98 0.999999748986427 5.02027145903405e-07 2.51013572951703e-07 99 0.999999382101446 1.23579710809519e-06 6.17898554047593e-07 100 0.999997558830858 4.88233828503801e-06 2.44116914251901e-06 101 0.99999065437025 1.86912595016216e-05 9.34562975081078e-06 102 0.9999764503599 4.70992801995718e-05 2.35496400997859e-05 103 0.999945499661665 0.000109000676670785 5.45003383353927e-05 104 0.999780154010238 0.000439691979523398 0.000219845989761699 105 0.999366997717847 0.00126600456430651 0.000633002282153255 106 0.99889255877815 0.00221488244369992 0.00110744122184996 107 0.99852509786321 0.00294980427357802 0.00147490213678901 108 0.993753085995501 0.0124938280089973 0.00624691400449863 109 0.973807972256099 0.0523840554878024 0.0261920277439012 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 64 0.735632183908046 NOK 5% type I error level 77 0.885057471264368 NOK 10% type I error level 81 0.93103448275862 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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