multiple regression :include monthly dummies

*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: Sat, 13 Dec 2008 08:26:12 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/13/t1229182071vzkc2uj90md27ak.htm/, Retrieved Sat, 13 Dec 2008 16:28:01 +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/2008/Dec/13/t1229182071vzkc2uj90md27ak.htm/}, year = {2008}, } @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 = {2008}, 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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32.68 10967.87 31.54 10433.56 32.43 10665.78 26.54 10666.71 25.85 10682.74 27.6 10777.22 25.71 10052.6 25.38 10213.97 28.57 10546.82 27.64 10767.2 25.36 10444.5 25.9 10314.68 26.29 9042.56 21.74 9220.75 19.2 9721.84 19.32 9978.53 19.82 9923.81 20.36 9892.56 24.31 10500.98 25.97 10179.35 25.61 10080.48 24.67 9492.44 25.59 8616.49 26.09 8685.4 28.37 8160.67 27.34 8048.1 24.46 8641.21 27.46 8526.63 30.23 8474.21 32.33 7916.13 29.87 7977.64 24.87 8334.59 25.48 8623.36 27.28 9098.03 28.24 9154.34 29.58 9284.73 26.95 9492.49 29.08 9682.35 28.76 9762.12 29.59 10124.63 30.7 10540.05 30.52 10601.61 32.67 10323.73 33.19 10418.4 37.13 10092.96 35.54 10364.91 37.75 10152.09 41.84 10032.8 42.94 10204.59 49.14 10001.6 44.61 10411.75 40.22 10673.38 44.23 10539.51 45.85 10723.78 53.38 10682.06 53.26 10283.19 51.8 10377.18 55.3 10486.64 57.81 10545.38 63.96 10554.27 63.77 10532.54 59.15 10324.31 56.12 10695.25 57.42 10827.81 63.52 10872.48 61.71 10971.19 63.01 11145.65 68.18 11234.68 72.03 11333.88 69.75 10997.97 74.41 11036.89 74.33 11257.35 64.24 11533.59 60.03 11963.12 59.44 12185.15 62.5 12377.62 55.04 12512.89 58.34 12631.48 61.92 12268.53 67.65 12754.8 67.68 13407.75 70.3 13480.21 75.26 13673.28 71.44 13239.71 76.36 13557.69 81.71 13901.28 92.6 13200.58 90.6 13406.97 92.23 12538.12 94.09 12419.57 102.79 12193.88 109.65 12656.63 124.05 12812.48 132.69 12056.67 135.81 11322.38 116.07 11530.75 101.42 11114.08 75.73 9181.73 55.48 8614.55

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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Olieprijs[t] = -86.2842757208807 + 0.0134215355293647DowJones[t] -3.353375836221M1[t] -3.6578005891384M2[t] -7.84443873350316M3[t] -14.7678676832942M4[t] -12.9353385813789M5[t] -11.5357318133792M6[t] -7.35542204852444M7[t] -7.10533150746131M8[t] -6.0923874525072M9[t] -3.8493014624562M10[t] + 1.30089658596615M11[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) -86.2842757208807 17.401376 -4.9585 4e-06 2e-06 DowJones 0.0134215355293647 0.001488 9.0217 0 0 M1 -3.353375836221 10.057783 -0.3334 0.739636 0.369818 M2 -3.6578005891384 10.066976 -0.3633 0.717238 0.358619 M3 -7.84443873350316 10.060205 -0.7797 0.437679 0.21884 M4 -14.7678676832942 10.352955 -1.4264 0.157362 0.078681 M5 -12.9353385813789 10.350568 -1.2497 0.214791 0.107396 M6 -11.5357318133792 10.350011 -1.1146 0.268143 0.134072 M7 -7.35542204852444 10.348326 -0.7108 0.479141 0.239571 M8 -7.10533150746131 10.350536 -0.6865 0.494264 0.247132 M9 -6.0923874525072 10.357648 -0.5882 0.557938 0.278969 M10 -3.8493014624562 10.353908 -0.3718 0.710976 0.355488 M11 1.30089658596615 10.348229 0.1257 0.900253 0.450127 Multiple Linear Regression - Regression Statistics Multiple R 0.706625299856318 R-squared 0.499319314397031 Adjusted R-squared 0.429456893150105 F-TEST (value) 7.14718020768572 F-TEST (DF numerator) 12 F-TEST (DF denominator) 86 p-value 7.20546966537228e-09 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 20.6964505214673 Sum Squared Residuals 36837.5035201287 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 32.68 57.568005329351 -24.888005329351 2 31.54 50.0923199277388 -18.5523199277388 3 32.43 49.0224307640032 -16.5924307640032 4 26.54 42.1114838422544 -15.5714838422544 5 25.85 44.1591601587054 -18.3091601587054 6 27.6 46.8268336035195 -19.2268336035195 7 25.71 41.2816302930861 -15.5716302930861 8 25.38 43.6975540225228 -18.3175540225228 9 28.57 49.1778561784259 -20.6078561784259 10 27.64 54.3787801684383 -26.7387801684383 11 25.36 55.1978487015347 -29.8378487015347 12 25.9 52.1545683731464 -26.2545683731464 13 26.29 31.72738875931 -5.43738875930999 14 21.74 33.8145474223701 -12.0745474223701 15 19.2 36.3533065164147 -17.1533065164147 16 19.32 32.8750515216563 -13.5550515216563 17 19.82 33.9731541994047 -14.1531541994047 18 20.36 34.9533379821118 -14.5933379821118 19 24.31 47.2995783937426 -22.9895783937426 20 25.97 43.2329004624962 -17.2629004624962 21 25.61 42.918857299662 -17.3088572996620 22 24.67 37.2695435370254 -12.5995435370254 23 25.59 30.6631475385008 -5.07314753850076 24 26.09 30.2871289658631 -4.19712896586312 25 28.37 19.8910707913186 8.4789292086814 26 27.34 18.0757837838606 9.26421621613938 27 24.46 21.8495925773173 2.61040742268267 28 27.46 13.3883240865717 14.0716759134283 29 30.23 14.5172962960377 15.7127037039623 30 32.33 8.42661251580957 23.9033874841904 31 29.87 13.4324809310756 16.4375190689244 32 24.87 18.4733885793454 6.3966114206546 33 25.48 23.3620694491142 2.11793055088584 34 27.28 31.9759557088887 -4.69595570888867 35 28.24 37.8819204229695 -9.64192042296955 36 29.58 38.3310578546772 -8.75105785467725 37 26.95 37.766140240037 -10.8161402400370 38 29.08 40.0099282227248 -10.9299282227248 39 28.76 36.8939259675375 -8.1339259675375 40 29.59 34.8359378624964 -5.24593786249641 41 30.7 42.2440412540204 -11.5440412540204 42 30.52 44.4698777492078 -13.9498777492078 43 32.67 44.9206112211627 -12.2506112211627 44 33.19 46.4413185307908 -13.2513185307908 45 37.13 43.0863580630684 -5.95635806306844 46 35.54 48.9794306403302 -13.4394306403302 47 37.75 51.2732574973931 -13.5232574973931 48 41.84 48.3713059381291 -6.53130593812906 49 42.94 47.3236156904976 -4.38361569049762 50 49.14 44.2947534404745 4.84524655952551 51 44.61 45.6129580934787 -1.00295809347865 52 40.22 42.2010054842353 -1.98100548423527 53 44.23 42.2367936248345 1.99320637516546 54 45.85 46.1095867448303 -0.259586744830265 55 53.38 49.7299500473999 3.65004995260008 56 53.26 44.6265927118654 8.63340728813461 57 51.8 46.9010268912245 4.89897310877551 58 55.3 50.6132341603197 4.68676583968028 59 57.81 56.5518132057369 1.25818679426305 60 63.96 55.3702340706269 8.58976592937313 61 63.77 51.7252082673528 12.0447917326472 62 59.15 48.6260171711558 10.5239828288443 63 56.12 49.4179634160535 6.70203658394646 64 57.42 44.2736932160351 13.1463067839649 65 63.52 46.7057623100471 16.8142376899529 66 61.71 49.4302088501504 12.2797911498496 67 63.01 55.9520397034581 7.0579602965419 68 68.18 57.3970495527006 10.7829504472994 69 72.03 59.7414099321676 12.2885900678324 70 69.75 57.4760679225497 12.2739320774503 71 74.41 63.148632133775 11.2613678662250 72 74.33 64.8066472706126 9.52335272938742 73 64.24 65.1608364090232 -0.920836409023253 74 60.03 70.6213638120339 -10.5913638120339 75 59.44 69.4147092012539 -9.97470920125393 76 62.5 65.0745231947997 -2.57452319479971 77 55.04 68.7225834077722 -13.6825834077722 78 58.34 71.7138500741992 -13.3738500741992 79 61.92 71.0228135186711 -9.1028135186711 80 67.65 77.7993941415984 -10.1493941415983 81 67.68 87.5759298204511 -19.8959298204511 82 70.3 90.7915402749599 -20.4915402749599 83 75.26 98.5330341880367 -23.2730341880367 84 71.44 91.4129624426039 -19.9729624426039 85 76.36 92.3273664740103 -15.9673664740103 86 81.71 96.6344471136273 -14.9244471136273 87 92.6 83.0433390238367 9.5566609761633 88 90.6 78.8899807919512 11.7100192080488 89 92.23 69.061208749178 23.1687912508220 90 94.09 68.8696924801716 25.2203075198285 91 102.79 70.020895891404 32.769104108596 92 109.65 76.4818019986806 33.1681980013194 93 124.05 79.5864923658862 44.4635076341138 94 132.69 71.6854475874881 61.0045524125118 95 135.81 66.9803463120533 68.8296536879467 96 116.07 68.4760950843409 47.5939049156591 97 101.42 59.5303680390995 41.8896319609005 98 75.73 33.2908391060143 42.4391608939857 99 55.48 21.4917744401045 33.9882255598955 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.0104161603324054 0.0208323206648109 0.989583839667595 17 0.00173529242227759 0.00347058484455518 0.998264707577722 18 0.000271778973988173 0.000543557947976346 0.999728221026012 19 6.48113911061855e-05 0.000129622782212371 0.999935188608894 20 9.59434969246659e-06 1.91886993849332e-05 0.999990405650308 21 1.33421265742259e-06 2.66842531484518e-06 0.999998665787343 22 3.69513745071019e-07 7.39027490142038e-07 0.999999630486255 23 4.77114624501284e-07 9.54229249002567e-07 0.999999522885376 24 1.84486178003431e-07 3.68972356006863e-07 0.999999815513822 25 5.3906981111823e-08 1.07813962223646e-07 0.99999994609302 26 1.79342624797815e-08 3.58685249595630e-08 0.999999982065737 27 3.27734309671591e-09 6.55468619343183e-09 0.999999996722657 28 2.40186191803172e-09 4.80372383606344e-09 0.999999997598138 29 2.80256551099467e-09 5.60513102198934e-09 0.999999997197434 30 2.74774158062368e-09 5.49548316124736e-09 0.999999997252258 31 7.97937141125204e-10 1.59587428225041e-09 0.999999999202063 32 1.56811960666544e-10 3.13623921333088e-10 0.999999999843188 33 3.13713750282095e-11 6.2742750056419e-11 0.999999999968629 34 6.24730978135797e-12 1.24946195627159e-11 0.999999999993753 35 1.48142362273554e-12 2.96284724547109e-12 0.999999999998519 36 3.81022197378446e-13 7.62044394756892e-13 0.99999999999962 37 8.57651640657879e-14 1.71530328131576e-13 0.999999999999914 38 1.92954991415666e-14 3.85909982831332e-14 0.99999999999998 39 4.9480375167603e-15 9.8960750335206e-15 0.999999999999995 40 1.72171644851950e-15 3.44343289703901e-15 0.999999999999998 41 7.07151043551988e-16 1.41430208710398e-15 1 42 2.07800040284648e-16 4.15600080569297e-16 1 43 1.06680380420308e-16 2.13360760840616e-16 1 44 1.00173258752738e-16 2.00346517505476e-16 1 45 2.30861232658917e-16 4.61722465317834e-16 1 46 3.53418553291179e-16 7.06837106582358e-16 1 47 1.16258660900286e-15 2.32517321800573e-15 0.999999999999999 48 7.74486287638521e-15 1.54897257527704e-14 0.999999999999992 49 2.97262736933135e-14 5.94525473866271e-14 0.99999999999997 50 8.77254367801041e-13 1.75450873560208e-12 0.999999999999123 51 3.73030783539989e-12 7.46061567079979e-12 0.99999999999627 52 4.99030113211587e-12 9.98060226423175e-12 0.99999999999501 53 1.15619292870289e-11 2.31238585740579e-11 0.999999999988438 54 2.22650028628283e-11 4.45300057256567e-11 0.999999999977735 55 1.44769794951021e-10 2.89539589902042e-10 0.99999999985523 56 9.75876752696678e-10 1.95175350539336e-09 0.999999999024123 57 3.14019526985959e-09 6.28039053971919e-09 0.999999996859805 58 1.73028312757926e-08 3.46056625515851e-08 0.999999982697169 59 9.23403537489708e-08 1.84680707497942e-07 0.999999907659646 60 4.03128000171712e-07 8.06256000343425e-07 0.999999596872 61 1.06558296759934e-06 2.13116593519868e-06 0.999998934417032 62 1.41071172535471e-06 2.82142345070941e-06 0.999998589288275 63 1.58086608600030e-06 3.16173217200059e-06 0.999998419133914 64 2.1409321203181e-06 4.2818642406362e-06 0.99999785906788 65 3.37387765361794e-06 6.74775530723588e-06 0.999996626122346 66 3.69516834337618e-06 7.39033668675236e-06 0.999996304831657 67 3.64335883081229e-06 7.28671766162458e-06 0.99999635664117 68 4.65152928012284e-06 9.30305856024567e-06 0.99999534847072 69 7.00336214059825e-06 1.40067242811965e-05 0.99999299663786 70 1.5067915636696e-05 3.0135831273392e-05 0.999984932084363 71 3.2452083567286e-05 6.4904167134572e-05 0.999967547916433 72 3.26741021699308e-05 6.53482043398616e-05 0.99996732589783 73 2.67618913348015e-05 5.35237826696031e-05 0.999973238108665 74 1.45207967128720e-05 2.90415934257441e-05 0.999985479203287 75 6.5287515557391e-06 1.30575031114782e-05 0.999993471248444 76 4.92067900106984e-06 9.84135800213968e-06 0.999995079320999 77 4.91829947946793e-06 9.83659895893586e-06 0.99999508170052 78 4.39570094573748e-06 8.79140189147495e-06 0.999995604299054 79 5.40159234119982e-06 1.08031846823996e-05 0.99999459840766 80 7.52033496860831e-06 1.50406699372166e-05 0.999992479665031 81 3.61890072221355e-05 7.2378014444271e-05 0.999963810992778 82 0.000412039411009589 0.000824078822019178 0.99958796058899 83 0.00940923570335064 0.0188184714067013 0.99059076429665 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 66 0.970588235294118 NOK 5% type I error level 68 1 NOK 10% type I error level 68 1 NOK

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/13/t1229182071vzkc2uj90md27ak/10to4j1229181967.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/13/t1229182071vzkc2uj90md27ak/10to4j1229181967.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/13/t1229182071vzkc2uj90md27ak/19ag81229181967.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/13/t1229182071vzkc2uj90md27ak/19ag81229181967.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/13/t1229182071vzkc2uj90md27ak/2nwki1229181967.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/13/t1229182071vzkc2uj90md27ak/2nwki1229181967.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/13/t1229182071vzkc2uj90md27ak/3x3f71229181967.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/13/t1229182071vzkc2uj90md27ak/3x3f71229181967.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/13/t1229182071vzkc2uj90md27ak/4ljdd1229181967.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/13/t1229182071vzkc2uj90md27ak/4ljdd1229181967.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/13/t1229182071vzkc2uj90md27ak/5i8n61229181967.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/13/t1229182071vzkc2uj90md27ak/5i8n61229181967.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/13/t1229182071vzkc2uj90md27ak/6loo31229181967.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/13/t1229182071vzkc2uj90md27ak/6loo31229181967.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/13/t1229182071vzkc2uj90md27ak/77an71229181967.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/13/t1229182071vzkc2uj90md27ak/77an71229181967.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/13/t1229182071vzkc2uj90md27ak/8whb41229181967.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/13/t1229182071vzkc2uj90md27ak/8whb41229181967.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/13/t1229182071vzkc2uj90md27ak/9vfdr1229181967.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/13/t1229182071vzkc2uj90md27ak/9vfdr1229181967.ps (open in new window)

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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