Answer:
a. ![\hat{amount} \ \hat{ spent} = -91.67 - (229.47* ownhome)-(604.90 * close) +(0.02216 * salary) + (42.62 * catalogs)](https://tex.z-dn.net/?f=%5Chat%7Bamount%7D%20%5C%20%5Chat%7B%20spent%7D%20%20%3D%20-91.67%20-%20%28229.47%2A%20ownhome%29-%28604.90%20%2A%20close%29%20%2B%280.02216%20%2A%20salary%29%20%2B%20%2842.62%20%2A%20catalogs%29)
b. the expected amount spent by Amy is $1144.47
c. the expected amount that Brenda is going to spend is $1749.37
Step-by-step explanation:
(a)
From the regression output; the equation for the regression model can be written as:
![\hat{amount} \ \hat{ spent} = -91.67 - (229.47* ownhome)-(604.90 * close) +(0.02216 * salary) + (42.62 * catalogs)](https://tex.z-dn.net/?f=%5Chat%7Bamount%7D%20%5C%20%5Chat%7B%20spent%7D%20%20%3D%20-91.67%20-%20%28229.47%2A%20ownhome%29-%28604.90%20%2A%20close%29%20%2B%280.02216%20%2A%20salary%29%20%2B%20%2842.62%20%2A%20catalogs%29)
From the information given in the question;
(b)
Amy does not own a home but rent; the variables given also stated that ;
Own Home = 1 if customer owns home, 0 if renting
So for Amy ; Own Home = 0 (since it is rented)
Close = Yes(1)
Salary = $60,000
Catalogs = 12
Therefore;
the mean amount spent by Amy is by using the regression model is ;
![\hat{amount} \ \hat{ spent} = -91.67 - (229.47* 0)-(604.90 * 1) +(0.02216 * 60000) + (42.62 * 12)](https://tex.z-dn.net/?f=%5Chat%7Bamount%7D%20%5C%20%5Chat%7B%20spent%7D%20%20%3D%20-91.67%20-%20%28229.47%2A%200%29-%28604.90%20%2A%201%29%20%2B%280.02216%20%2A%2060000%29%20%2B%20%2842.62%20%2A%2012%29)
![\hat{amount} \ \hat{ spent} = -91.67 -0-604.90 +1329.6 + 511.44](https://tex.z-dn.net/?f=%5Chat%7Bamount%7D%20%5C%20%5Chat%7B%20spent%7D%20%20%3D%20-91.67%20-0-604.90%20%2B1329.6%20%2B%20511.44)
![\hat{amount} \ \hat{ spent} =1144.47](https://tex.z-dn.net/?f=%5Chat%7Bamount%7D%20%5C%20%5Chat%7B%20spent%7D%20%20%3D1144.47)
Thus; the expected amount spent by Amy is $1144.47
(c)
If Brenda has the same characteristics as Amy but does not live close to store with similar merchandise.
Then the Close for Brenda will be = No (0)
Thus; the amount spent by Brenda will be:
![\hat{amount} \ \hat{ spent} = -91.67 - (229.47* 0)-(604.90 * 0) +(0.02216 * 60000) + (42.62 * 12)](https://tex.z-dn.net/?f=%5Chat%7Bamount%7D%20%5C%20%5Chat%7B%20spent%7D%20%20%3D%20-91.67%20-%20%28229.47%2A%200%29-%28604.90%20%2A%200%29%20%2B%280.02216%20%2A%2060000%29%20%2B%20%2842.62%20%2A%2012%29)
![\hat{amount} \ \hat{ spent} = -91.67 -0-0 +1329.6 + 511.44](https://tex.z-dn.net/?f=%5Chat%7Bamount%7D%20%5C%20%5Chat%7B%20spent%7D%20%20%3D%20-91.67%20-0-0%20%2B1329.6%20%2B%20511.44)
![\hat{amount} \ \hat{ spent} = 1749.37](https://tex.z-dn.net/?f=%5Chat%7Bamount%7D%20%5C%20%5Chat%7B%20spent%7D%20%20%3D%201749.37)
Thus, the expected amount that Brenda is going to spend is $1749.37