Question

find the equation for the least squares regression line of the data described below. ezra is a pr agent for an up - and - coming band. he wants to convince the band members that being active on social media is good for their careers. he claims that a large social media following typically translates into ticket sales. to prove his point, ezra looked up information about several successful bands. he compared the number of social media followers (in millions), x, to the average number of hours it takes these bands to sell out a concert, y. followers (in millions) hours 2.4 69 3.1 48 5.2 60 5.5 70 9.9 26 round your answers to the nearest thousandth. y = x +

Explanation:

Explicación:

Paso 1: Calcular sumatorias

Sean $x_i$ el número de seguidores (en millones) y $y_i$ el número de horas.
Tenemos $n = 5$ datos.
$\sum_{i = 1}^{n}x_i=2.4 + 3.1+5.2 + 5.5+9.9=26.1$
$\sum_{i = 1}^{n}y_i=69 + 48+60 + 70+26=273$
$\sum_{i = 1}^{n}x_i^2=2.4^2+3.1^2 + 5.2^2+5.5^2+9.9^2=5.76+9.61+27.04+30.25+98.01 = 170.67$
$\sum_{i = 1}^{n}x_iy_i=(2.4\times69)+(3.1\times48)+(5.2\times60)+(5.5\times70)+(9.9\times26)=165.6+148.8+312+385+257.4 = 1268.8$

Paso 2: Calcular la pendiente $m$

La fórmula para la pendiente $m$ de la línea de regresión es $m=\frac{n\sum_{i = 1}^{n}x_iy_i-\sum_{i = 1}^{n}x_i\sum_{i = 1}^{n}y_i}{n\sum_{i = 1}^{n}x_i^2 - (\sum_{i = 1}^{n}x_i)^2}$
Sustituyendo los valores:
$n = 5$, $\sum_{i = 1}^{n}x_i = 26.1$, $\sum_{i = 1}^{n}y_i=273$, $\sum_{i = 1}^{n}x_i^2 = 170.67$ y $\sum_{i = 1}^{n}x_iy_i=1268.8$
$m=\frac{5\times1268.8-26.1\times273}{5\times170.67-(26.1)^2}$
$m=\frac{6344 - 7125.3}{853.35 - 681.21}$
$m=\frac{-781.3}{172.14}\approx - 4.539$

Paso 3: Calcular la intersección $b$

La fórmula para la intersección $b$ es $b=\bar{y}-m\bar{x}$, donde $\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}$ y $\bar{y}=\frac{\sum_{i = 1}^{n}y_i}{n}$
$\bar{x}=\frac{26.1}{5}=5.22$
$\bar{y}=\frac{273}{5}=54.6$
$b = 54.6-(-4.539)\times5.22$
$b = 54.6 + 4.539\times5.22$
$b = 54.6+23.69358\approx78.294$

Respuesta:

$y=-4.539x + 78.294$

Answer:

Explicación:

Paso 1: Calcular sumatorias

Sean $x_i$ el número de seguidores (en millones) y $y_i$ el número de horas.
Tenemos $n = 5$ datos.
$\sum_{i = 1}^{n}x_i=2.4 + 3.1+5.2 + 5.5+9.9=26.1$
$\sum_{i = 1}^{n}y_i=69 + 48+60 + 70+26=273$
$\sum_{i = 1}^{n}x_i^2=2.4^2+3.1^2 + 5.2^2+5.5^2+9.9^2=5.76+9.61+27.04+30.25+98.01 = 170.67$
$\sum_{i = 1}^{n}x_iy_i=(2.4\times69)+(3.1\times48)+(5.2\times60)+(5.5\times70)+(9.9\times26)=165.6+148.8+312+385+257.4 = 1268.8$

Paso 2: Calcular la pendiente $m$

La fórmula para la pendiente $m$ de la línea de regresión es $m=\frac{n\sum_{i = 1}^{n}x_iy_i-\sum_{i = 1}^{n}x_i\sum_{i = 1}^{n}y_i}{n\sum_{i = 1}^{n}x_i^2 - (\sum_{i = 1}^{n}x_i)^2}$
Sustituyendo los valores:
$n = 5$, $\sum_{i = 1}^{n}x_i = 26.1$, $\sum_{i = 1}^{n}y_i=273$, $\sum_{i = 1}^{n}x_i^2 = 170.67$ y $\sum_{i = 1}^{n}x_iy_i=1268.8$
$m=\frac{5\times1268.8-26.1\times273}{5\times170.67-(26.1)^2}$
$m=\frac{6344 - 7125.3}{853.35 - 681.21}$
$m=\frac{-781.3}{172.14}\approx - 4.539$

Paso 3: Calcular la intersección $b$

La fórmula para la intersección $b$ es $b=\bar{y}-m\bar{x}$, donde $\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}$ y $\bar{y}=\frac{\sum_{i = 1}^{n}y_i}{n}$
$\bar{x}=\frac{26.1}{5}=5.22$
$\bar{y}=\frac{273}{5}=54.6$
$b = 54.6-(-4.539)\times5.22$
$b = 54.6 + 4.539\times5.22$
$b = 54.6+23.69358\approx78.294$

Respuesta:

$y=-4.539x + 78.294$