<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>2007-2422</journal-id>
<journal-title><![CDATA[Tecnología y ciencias del agua]]></journal-title>
<abbrev-journal-title><![CDATA[Tecnol. cienc. agua]]></abbrev-journal-title>
<issn>2007-2422</issn>
<publisher>
<publisher-name><![CDATA[Instituto Mexicano de Tecnología del Agua, Coordinación de Comunicación, Participación e Información]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S2007-24222016000400161</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Una aplicación hidrológica de la regresión lineal múltiple ponderada]]></article-title>
<article-title xml:lang="en"><![CDATA[An Hydrological Application of Weighted Multiple Linear Regression]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Campos-Aranda]]></surname>
<given-names><![CDATA[Daniel Francisco]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Autónoma de San Luis Potosí  ]]></institution>
<addr-line><![CDATA[San Luis Potosí San Luis Potosí]]></addr-line>
<country>México</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>08</month>
<year>2016</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>08</month>
<year>2016</year>
</pub-date>
<volume>7</volume>
<numero>4</numero>
<fpage>161</fpage>
<lpage>173</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S2007-24222016000400161&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S2007-24222016000400161&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S2007-24222016000400161&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen: La regresión lineal múltiple tiene dos aplicaciones hidrológicas básicas: (1) ampliar registros cortos con base en series largas cercanas, y (2) deducir ecuaciones empíricas que permiten estimar, en sitios de interés sin aforos, crecientes de diseño (QTr). Como ambas aplicaciones se realizan en un contexto regional, siempre está presente la multicolinealidad en el primer caso, y la falta de homocedasticidad en el segundo. Para corregir la no uniformidad que tienen las varianzas de la variable dependiente (Yi) se usa una función de ponderado (wi) en el ajuste de mínimos cuadrados, lo cual conduce a la técnica de mínimos cuadrados ponderados (MCP). En este trabajo se exponen con detalle dos procedimientos para estimar las wi óptimas. El primero toma en cuenta la teoría de los residuales y el error medio del ajuste de mínimos cuadrados ordinarios y el segundo se basa en los datos que son vecinos cercanos, para buscar la manera en que varían las varianzas de Yi. Ambos métodos se aplican a las ecuaciones empíricas que permiten estimar el gasto máximo medio anual (Qma) de la Región Hidrológica 10 (Sinaloa, México). Con base en los resultados, se concluye que es recomendable aplicar siempre el método de MCP, al obtener ecuaciones empíricas que estiman el Qma, o bien las QTr, pues sus indicadores de desempeño evaluados en el dominio real muestran mejoría de ajuste.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract: Multiple linear regression has two basic hydrological applications: (1) to extend short records based on long series that are close and (2) to derive empirical equations to estimate flood design (QTr) at sites of interest where records are not available. Since both applications are made in a regional context, multicollinearity is always present in the first case, and the lack of homoscedasticity in the second. In order to correct the non-uniformity with the variances of the dependent variable (Yi) a weighting function (wi) in the least squares fit is used, which leads to the weighted least squares (WLS) technique. In this work two methods to estimate the optimal w. are discussed in detail; the first one takes into account the theory of residuals and the mean error of setting ordinary least squares and the second one is based on data that are close neighbors, seeking for changes on the variances of Yi. Both methods are applied to empirical equations that estimate the average annual maximum flow (Qaa) of Hydrological Region No. 10 (Sinaloa). Based on the results it is concluded that it is advisable to always apply the method of WLS, to obtain empirical equations that estimate the Qaa or the QTr, due to the improvement of adjustment of the performance indicators evaluated in the real domain.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[homocedasticidad]]></kwd>
<kwd lng="es"><![CDATA[mínimos cuadrados ordinarios]]></kwd>
<kwd lng="es"><![CDATA[mínimos cuadrados ponderados]]></kwd>
<kwd lng="es"><![CDATA[desviación absoluta media]]></kwd>
<kwd lng="es"><![CDATA[error estándar medio]]></kwd>
<kwd lng="es"><![CDATA[error relativo estándar medio]]></kwd>
<kwd lng="es"><![CDATA[creciente media anual]]></kwd>
<kwd lng="es"><![CDATA[Región Hidrológica 10]]></kwd>
<kwd lng="en"><![CDATA[Homoscedasticity]]></kwd>
<kwd lng="en"><![CDATA[ordinary least squares]]></kwd>
<kwd lng="en"><![CDATA[weighted least squares]]></kwd>
<kwd lng="en"><![CDATA[mean absolute deviation]]></kwd>
<kwd lng="en"><![CDATA[mean standard error]]></kwd>
<kwd lng="en"><![CDATA[means standard relative error]]></kwd>
<kwd lng="en"><![CDATA[average annual flood]]></kwd>
<kwd lng="en"><![CDATA[Hydrological Region No. 10]]></kwd>
</kwd-group>
</article-meta>
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