Question

find the correlation coefficient, r, of the data described below. sharon isnt getting enough sleep and suspects its due to playing too many video games before bed. to find out, she decided to track how much time she spends gaming. over several days, sharon recorded how many hours of sleep she had gotten each night, x, as well as how many hours she had spent playing video games before bed, y. hours of video games hours of sleep 0.5 10 1.3 10 1.6 7 2.5 4 3.5 6 round your answer to the nearest thousandth. r =

Explanation:

Explicación:

Paso 1: Calcular las medias

Sea $x$ las horas de sueño y $y$ las horas de juegos de video.
$n = 5$
$\bar{x}=\frac{10 + 10+7+4+6}{5}=\frac{37}{5} = 7.4$
$\bar{y}=\frac{0.5+1.3+1.6+2.5+3.5}{5}=\frac{9.4}{5}=1.88$

Paso 2: Calcular las diferencias y los productos

$x$	$y$	$x - \bar{x}$	$y-\bar{y}$	$(x - \bar{x})(y - \bar{y})$	$(x - \bar{x})^2$	$(y - \bar{y})^2$
10	1.3	$10 - 7.4 = 2.6$	$1.3 - 1.88=-0.58$	$2.6\times(-0.58)=-1.508$	$2.6^2=6.76$	$(-0.58)^2 = 0.3364$
7	1.6	$7 - 7.4=-0.4$	$1.6 - 1.88=-0.28$	$(-0.4)\times(-0.28)=0.112$	$(-0.4)^2=0.16$	$(-0.28)^2 = 0.0784$
4	2.5	$4 - 7.4=-3.4$	$2.5 - 1.88 = 0.62$	$(-3.4)\times0.62=-2.108$	$(-3.4)^2 = 11.56$	$0.62^2=0.3844$
6	3.5	$6 - 7.4=-1.4$	$3.5 - 1.88 = 1.62$	$(-1.4)\times1.62=-2.268$	$(-1.4)^2=1.96$	$1.62^2 = 2.6244$

Suma de $(x - \bar{x})(y - \bar{y})$: $S_{xy}=-3.588-1.508 + 0.112-2.108-2.268=-9.36$
Suma de $(x - \bar{x})^2$: $S_{xx}=6.76+6.76 + 0.16+11.56+1.96=27.2$
Suma de $(y - \bar{y})^2$: $S_{yy}=1.9044+0.3364+0.0784+0.3844+2.6244=5.328$

Paso 3: Calcular el coeficiente de correlación

$r=\frac{S_{xy}}{\sqrt{S_{xx}S_{yy}}}=\frac{-9.36}{\sqrt{27.2\times5.328}}=\frac{-9.36}{\sqrt{144.9216}}=\frac{-9.36}{12.0383}\approx - 0.778$

Respuesta:

$-0.778$

Answer:

Explicación:

Paso 1: Calcular las medias

Sea $x$ las horas de sueño y $y$ las horas de juegos de video.
$n = 5$
$\bar{x}=\frac{10 + 10+7+4+6}{5}=\frac{37}{5} = 7.4$
$\bar{y}=\frac{0.5+1.3+1.6+2.5+3.5}{5}=\frac{9.4}{5}=1.88$

Paso 2: Calcular las diferencias y los productos

$x$	$y$	$x - \bar{x}$	$y-\bar{y}$	$(x - \bar{x})(y - \bar{y})$	$(x - \bar{x})^2$	$(y - \bar{y})^2$
10	1.3	$10 - 7.4 = 2.6$	$1.3 - 1.88=-0.58$	$2.6\times(-0.58)=-1.508$	$2.6^2=6.76$	$(-0.58)^2 = 0.3364$
7	1.6	$7 - 7.4=-0.4$	$1.6 - 1.88=-0.28$	$(-0.4)\times(-0.28)=0.112$	$(-0.4)^2=0.16$	$(-0.28)^2 = 0.0784$
4	2.5	$4 - 7.4=-3.4$	$2.5 - 1.88 = 0.62$	$(-3.4)\times0.62=-2.108$	$(-3.4)^2 = 11.56$	$0.62^2=0.3844$
6	3.5	$6 - 7.4=-1.4$	$3.5 - 1.88 = 1.62$	$(-1.4)\times1.62=-2.268$	$(-1.4)^2=1.96$	$1.62^2 = 2.6244$

Suma de $(x - \bar{x})(y - \bar{y})$: $S_{xy}=-3.588-1.508 + 0.112-2.108-2.268=-9.36$
Suma de $(x - \bar{x})^2$: $S_{xx}=6.76+6.76 + 0.16+11.56+1.96=27.2$
Suma de $(y - \bar{y})^2$: $S_{yy}=1.9044+0.3364+0.0784+0.3844+2.6244=5.328$

Paso 3: Calcular el coeficiente de correlación

$r=\frac{S_{xy}}{\sqrt{S_{xx}S_{yy}}}=\frac{-9.36}{\sqrt{27.2\times5.328}}=\frac{-9.36}{\sqrt{144.9216}}=\frac{-9.36}{12.0383}\approx - 0.778$

Respuesta:

$-0.778$