Question

payton collected data to show the relationship between the number of hours he practices and the number of errors he makes when playing a new piece of music. the table shows his data.
practice makes better

number of hours	1	2	3	4	5	6	7	8
number of errors	36	34	30	31	23	16	11	5

which is the approximate slope of the line of best fit for the data?
-5.5
-4.5
-2.0
-1.0

Explanation:

Step1: Definir variables

Sean $x$ el número de horas de práctica y $y$ el número de errores.

Step2: Usar la fórmula de la pendiente

La fórmula para la pendiente $m$ de la recta de mejor ajuste es $m=\frac{n(\sum xy)-(\sum x)(\sum y)}{n(\sum x^{2})-(\sum x)^{2}}$.
Calculamos $\sum x = 1 + 2+3+4+5+6+7+8=36$.
Calculamos $\sum y=36 + 34+30+31+23+16+11+5 = 186$.
Calculamos $\sum xy=1\times36+2\times34 + 3\times30+4\times31+5\times23+6\times16+7\times11+8\times5=1\times36+68+90+124+115+96+77+40 = 646$.
Calculamos $\sum x^{2}=1^{2}+2^{2}+3^{2}+4^{2}+5^{2}+6^{2}+7^{2}+8^{2}=1 + 4+9+16+25+36+49+64 = 204$.
$n = 8$.

Step3: Sustituir valores en la fórmula

$m=\frac{8\times646-36\times186}{8\times204 - 36^{2}}=\frac{5168-6696}{1632 - 1296}=\frac{-1528}{336}\approx - 4.55\approx - 4.5$.

Answer:

-4.5