Question

A cat breeder is interested in what specific attributes people like most about cats. Specifically, they are interested to see whether the gender and color (black, white, orange, or other) have a significant impact on the popularity of the cat. The predictor variables are defined as follows:
?1={10if femaleif male,?2={10if blackotherwise,?3={10if whiteotherwise,?4={10if orangeotherwisex1={1if female0if male,x2={1if black0otherwise,x3={1if white0otherwise,x4={1if orange0otherwise

A regression model was fit and produced the following results:
?̂ =24.05+5.65?1−2.96?2+3.59?3+6.41?4y^=24.05+5.65x1−2.96x2+3.59x3+6.41x4

a) What is the estimated popularity for an orange female cat?
?̂ =y^=

b) What is the estimated popularity for a black male cat?
?̂ =y^=

c) Is a calico cat more popular as a female or male?
Female calico: ?̂ =y^=
Male calico: ?̂ =y^=
Which is more popular?

Answer 1

a)

estimated popularity for an orange female cat =24.05+5.65+6.41 =36.11

b)

estimated popularity for a black male cat =24.05-2.96 =21.09

c)

Female calico (other color) =24.05+5.65 =29.7

Male calico: =24.05

Which is more popular : Female Calico is more populat