payton collected data to show the relationship between the number of hours he practices and the number of…

Explanation:

Step1: Definir variables

Sean $x_i$ el número de horas de práctica y $y_i$ el número de errores, con $i = 1,2,\cdots,8$.

Step2: Calcular $\sum_{i = 1}^{n}x_i$, $\sum_{i = 1}^{n}y_i$, $\sum_{i = 1}^{n}x_i^2$ y $\sum_{i = 1}^{n}x_iy_i$

$\sum_{i = 1}^{8}x_i=1 + 2+3+4+5+6+7+8=\frac{8\times(8 + 1)}{2}=36$ $\sum_{i = 1}^{8}y_i=36+34+30+31+23+16+11+5 = 186$ $\sum_{i = 1}^{8}x_i^2=1^2+2^2+3^2+4^2+5^2+6^2+7^2+8^2=\frac{8\times(8 + 1)\times(2\times8 + 1)}{6}=204$ $\sum_{i = 1}^{8}x_iy_i=1\times36+2\times34+3\times30+4\times31+5\times23+6\times16+7\times11+8\times5$ $=36+68+90+124+115+96+77+40 = 646$

Step3: Aplicar fórmula de la pendiente

La fórmula para la pendiente $m$ de la línea de mejor ajuste es $m=\frac{n\sum_{i = 1}^{n}x_iy_i-\sum_{i = 1}^{n}x_i\sum_{i = 1}^{n}y_i}{n\sum_{i = 1}^{n}x_i^2-(\sum_{i = 1}^{n}x_i)^2}$, donde $n = 8$. $m=\frac{8\times646-36\times186}{8\times204 - 36^2}$ $=\frac{5168-6696}{1632 - 1296}$ $=\frac{- 1528}{336}\approx - 4.55\approx - 4.5$

Answer:

-4.5