Question

consider the following sine regression model
$y = 18.614sin(0.521x - 1.984)+76.900$
predict $y(14)$.
a. 94.8
b. 61.5
c. 9.4
d. 77.3
please select the best answer from the choices provided

Explanation:

Step1: Substitute x = 14 into the model

$y=18.614\sin(0.521\times14 - 1.984)+76.900$
First, calculate the value inside the sine - function: $0.521\times14-1.984 = 7.294 - 1.984=5.31$.

Step2: Calculate the sine value

$\sin(5.31)\approx - 0.978$.

Step3: Calculate the value of y

$y = 18.614\times(-0.978)+76.900$.
$y=-18.1045+76.900\approx58.8$.
Since our calculated value is closest to 61.5 among the given options.

Answer:

B. 61.5