Question

read the following description of a data set.
an opera company is planning its repertory for next season. to help choose which operas to include, a company employee looked at the ticket sales data from last season.
the employee noted the running time (in hours), x, and the total number of tickets sold, y, for the various operas that were performed.
the least squares regression line of this data set is:
$y = -383.365x + 5,427.117$
how many tickets does this line predict a 2.14 - hour opera would have sold?
round your answer to the nearest integer.
tickets

Explanation:

Step1: Sustituir el valor de \(x\) en la ecuación

Dada la ecuación de la recta de regresión \(y = - 383.365x+5427.117\), donde \(x = 2.14\).
Sustituimos \(x\) en la ecuación: \(y=-383.365\times2.14 + 5427.117\).

Step2: Realizar la multiplicación

Calculamos \(-383.365\times2.14\).
\(-383.365\times2.14=-383.365\times(2 + 0.14)=-383.365\times2-383.365\times0.14=-766.73-53.6711=-820.4011\).

Step3: Realizar la suma

Ahora sumamos el resultado de la multiplicación al término independiente: \(y=-820.4011 + 5427.117\).
\(y = 4606.7159\).

Step4: Redondear al entero más cercano

Redondeando \(4606.7159\) al entero más cercano, obtenemos \(4607\).

Answer:

\(4607\)