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). The data is shown in the accompanying table; the data set is found on the text website, labeled Purchase.

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

1. Estimate the linear probability model using Under Armour as the response variable and Age as the predictor variables. Interpret the coefficient.

2. Compute the predicted probability of an Under Armour purchase for a 20-year-old customer and a 30-year-old customer.

3. Test Annabel's belief that the Under Armour brand attracts young customers at the 5% level.

4. Now by using the logistic regression model using Under Armour as the response variable and Age as the predictor variables. Interpret the coefficient.

5. Compute the predicted probability of an Under Armour purchase for a 20-year-old customer and a 30-year-old customer. Use a logistic regression model.

6. Test Annabel's belief that the Under Armour brand attracts young customers at the 5% level. Use a logistic regression model.