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Grfico MSGraph.Chart.804Grfico de Microsoft GraphGrfico Excel.Chart.804Grfico de Microsoft Excel !Grfico Excel.Chart.804Grfico de Microsoft Excel "Grfico Excel.Chart.804Grfico de Microsoft ExcelC:\Documents and Settings\miguel\Escritorio\MIDISMURCIA\introduccion.wavF/ 0|DArialgsRomanllT0"DArial BlackmanllT0" DTimes New RomanllT00DWingdingsRomanllT0@DTahomagsRomanllT0" A .  @n?" dd@  @@`` !**  %a!># ( +- /01235689;<>B P! Q TWX ] ^  ,,prsvhR$2gҜjKi> z~SYb$^0 z_T - )'1% SYR$oqLo*C^h]};}xeR$2r08oح7 h <FF"${xC'73P"$_68TDr"$/X]vX oMR$"9ᵴi0GB"$6z7ov jp2`b$~ad_R$.Kb|Mm 0AA0 Ta^&1A6@$%&'-. woO ʚ;Zd8ʚ;g4jdjd\ŗ T06ppp@ <4dddd8!0l|<4!d!d8!0l| 80___PPT10 pp?  %$"DISTRIBUCIONES BIDIMENSIONALES Estadstica'Qu es una distribucin bidimensional?(('$Es un conjunto de pares de valores (xi ,yi) donde cada uno de los valores representa una magnitud. En la siguiente tabla se observa las caractersticas de peso y altura de 14 soldados. P-PP%  ,$Cul es el objetivo?Conocer si las magnitudes estn relacionadas y si lo estn de que manera. Poder prever de manera aproximada el valor de una magnitud conociendo la otra$o$ Cmo se nos presenta?1. En tablas simples  2. En tablas de doble entrada En el ejemplo se ve una tabla donde Y es el numero de hijos y X el numero de hermanos de un individuo .PjPi  53. Nube de puntos, nos dan un grafico con los datos 46  Para saber la distribucin de las variables x e y por separado no hay ms que sumar filas y columnas As se obtienen las DISTRIBUCIONES MARGINALES,xTa ,Parmetros de las distribuciones marginales --(Ahora que conocemos como calcular las marginales , hay que obtener sus parmetros estadsticos, la media , la desviacin tpica y la covarianza   La media  (La media se calcula XM = Sumamos todos los datos y los dividimos por el numero total de datos, al punto (XM,YM) se le llama centro de gravedad TY"s" La desviacin tpicaBSe calcula Sx2=" "xi2/N - xm2~  La covarianza (: Sxy = "xiyi /N  XmYm $ $$ $$ $$ $  &Qu relacin hay entre las variables?''($En un estudio de dos variables nos puede interesar saber que relacin existe entre las dos variables, por ejemplo, horas de estudio y nmero de suspensos infraccin y renta per cpita de un pas etc.. Esto se conseguir mediante el COEFICIENTE DE CORRELACION DE PEARSON: r= Sxy/ Sx*Sy bZ   s  YEl coeficiente de correlacin r est entre -1 y 1. Si su valor absoluto es cercano a 1 , se dice que existe una CORRELACIN FUERTE entre las variables. Si es prximo a 0 se dice que la correlacin es dbil Si r es positivo quiere decir que cuando una magnitud tambin lo hace. Si es negativo, mientras una crece la otra disminuye y viceversa  YZEjemplo(Qu relacin existe entre las notas conseguidas en fsica (variable x) y las horas que ven la televisin los alumnos de 4ESO (variable y)? Sx = 1.23 Sy = 3 Sxy= - 3.19 Zz- 2Calculamos el coeficiente de correlacin r= - 3.19/1.23*3=- 0.864 Como el valor absoluto de r es prximo a r se dice que las variables tienen una correlacin fuerte. Adems r es negativo por tanto tienen correlacin negativa. Es decir a ms horas de televisin menos nota en la asignatura de fsica *3;Podemos predecir resultados?Como hemos visto antes los datos pueden venir dados en una nube de puntos. El objetivo es encontrar una recta que aproximo de la mejor manera los puntos de la distribucin  7Sabemos que para calcular una recta basta con saber un punto y la pendiente de la misma. El punto que es ms prximo a todos los datos de la distribucin es (Xm,Ym), por tanto ya tenemos un punto de la recta buscada. Ahora bien, las pendientes dependern de si queremos predecir un dato de la variable x e y. B6Rectas de regresinyRecta de regresin de Y sobre X Y= Ym + Sxy/Sx2 * (X-Xm) Recta de regresin de X sobre Y X= Xm + Sxy/Sy2 * (Y-Ym)   &+,7* EEs decir, si conozco solamente una magnitud y deseo saber la otra de manera aproximada no tengo ms que construir su recta de regresin, sustituir su valor en la recta de regresin y obtener as el valor aproximado. Hay que tener en cuenta que cuanto mayor sea el coeficiente de correlacin mas fiable ser nuestra prediccinEjemplo  (En la siguiente tabla se muestra el ndice de mortalidad y el porcentaje de personas mayores de 64 aos de algunos pases europeos  SAhora calculamos la media y desviacin tpica de las marginales, y la covarianza: TT Y el coeficiente de correlacin es r = Es decir, un coeficiente de correlacin medio, con lo que podemos concluir que la correlacin entre ndice de mayores de 65 aos y mortalidad no es muy alta $#PP  ZY las rectas de regresin que son: Y= 1.34/1.46(x- 9.59)+13.22 X= 1.71/1.46(y-13.22)+9.59 *#8#8# %Si deseramos conocer el porcentaje de mayores suponiendo que hay un pas con un ndice de mortalidad del 6%, hay que sustituir en la recta de regresin de y el valor 6, obteniendo 9.95% de mayores. Aunque no presenta mucha fiabilidad por no tener un buen coeficiente de correlacin de Pearson&&,Cuidado al seleccionar variable (La estadstica bidimensional es un arma eficaz si se utiliza correctamente, un coeficiente r alto no quiere decir que necesariamente las variables tengan relacin ya que puede ser debido al azar. El matemtico debe seleccionar unas variables lgicas. 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