In: Statistics and Probability
Annabel, a retail analyst, has been following Under Armour,
Inc., the pioneer in the compression-gear market....
Annabel, a retail analyst, has been following Under Armour,
Inc., the pioneer in the compression-gear market. Compression
garments are meant to keep moisture away from a wearer’s body
during athletic activities in warm and cool weather. Annabel
believes that the Under Armour brand attracts a younger customer,
whereas the more established companies, Nike and Adidas, draw an
older clientele. In order to test her belief, she collects data on
the age of the customers and whether or not they purchased Under
Armour (1 for Under Armour, 0 otherwise). A portion of the data is
shown in the accompanying table.
Under Armour |
Age |
1 |
30 |
0 |
19 |
0 |
34 |
0 |
29 |
1 |
39 |
1 |
24 |
0 |
34 |
0 |
17 |
1 |
16 |
0 |
22 |
0 |
38 |
0 |
33 |
1 |
22 |
0 |
44 |
0 |
33 |
1 |
19 |
0 |
43 |
0 |
41 |
0 |
32 |
0 |
21 |
0 |
39 |
0 |
42 |
0 |
38 |
0 |
45 |
0 |
35 |
0 |
30 |
0 |
40 |
0 |
28 |
0 |
21 |
1 |
24 |
|
a-1. Use the appropriate statistical software
to estimate a logit model using Under Armour as the response
variable and age as the explanatory variable.
(Negative values should be indicated by a
minus sign. Round your answers to 2 decimal
places.)
|
|
|
Coefficient |
Intercept |
|
Age |
|
|
a-2. Compute the predicted probability of an Under
Armour purchase for a 20-year-old customer and a 30-year-old
customer. (Round coefficient estimates to at least 4
decimal places and final answer to 2 decimal places.)
|
|
|
ŷ |
20-year-old customer |
|
30-year-old customer |
|
|