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

Answer:

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

Step-by-step 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.