Question

website x sells 5 products. it has a user rating system for the products they sell. website xs user rating system ranges from 1 to 5. the average rating for website x products sold on the website is shown in the table below. average rating for each product determine the equation that models the average user rating, y, for website xs product x. round your answers to the nearest hundredths y = x +

Explanation:

Step1: Calcular la pendiente \(m\)

La fórmula para la pendiente \(m=\frac{n(\sum xy)-(\sum x)(\sum y)}{n(\sum x^{2})-(\sum x)^{2}}\)
Donde \(n = 5\) (número de productos), \(x=\{1,2,3,4,5\}\), \(y = \{1.7,3.6,3.2,3.2,4.8\}\)
\(\sum x=1 + 2+3+4+5=15\)
\(\sum y=1.7 + 3.6+3.2+3.2+4.8 = 16.5\)
\(\sum xy=1\times1.7+2\times3.6+3\times3.2+4\times3.2+5\times4.8=1.7 + 7.2+9.6+12.8+24=55.3\)
\(\sum x^{2}=1^{2}+2^{2}+3^{2}+4^{2}+5^{2}=1 + 4+9+16+25 = 55\)
\(m=\frac{5\times55.3-15\times16.5}{5\times55 - 15^{2}}=\frac{276.5-247.5}{275 - 225}=\frac{29}{50}=0.58\)

Step2: Calcular la intersección \(b\)

La fórmula de la recta de regresión es \(y=mx + b\), despejando \(b\): \(b=\frac{\sum y-m\sum x}{n}\)
\(b=\frac{16.5-0.58\times15}{5}=\frac{16.5 - 8.7}{5}=\frac{7.8}{5}=1.56\)

Answer:

\(y = 0.58x+1.56\)