Question

The average number of customers per day at a home improvement store is given in the following table. Let x represent the day where 1 = Sun of the first week, 7 = Sat of the first week, 8 = Sun of the second week, and 14 = Sat of the second week. Use a graphing calculator to produce a sine regression model for the data. Round a, b, c, and d to the nearest thousandth.

Day.. sun...mon..tues..wed..thur..fri..sat
Number of Customers..115..77..60..51..68..86..120
a.
33.690sin(0.887x + 1.337) + 81.684
b.
34.081sin(0.888x - 1.341) + 82.822
c.
34.081sin(0.888x + 1.341) + 82.822
d.
33.690sin(0.887x + 1.337) - 81.684

Answer 1

Answer (EDGE 2020):

C. 34.081sin(0.888x + 1.341) + 82.822

Answer 2

A.
`33.690\sin (0.887x + 1.337) + 81.684`.

Explanation:

We are given that,

x = Number of days where 1 = Sun of 1st week and 7 = Sat of first week.

The corresponding table for the data is given by,

Days Day Number Number of Customers

Sun 1 115

Mon 2 77

Tue 3 60

Wed 4 51

Thur 5 68

Fri 6 86

Sat 7 120

The general form of the regression model is
`a\sin (bx+c)+d`.

Using the sinusoidal regression calculator, we get that,

a = 33.690

b = 0.887

c = 1.337

d = 81.684

That is, the sine regression model is
`33.690\sin (0.887x + 1.337) + 81.684`.

Thus, option A is the sine regression model for the given data.