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={1 if female 0 if male,

?₂={1if black 0 otherwise,

?₃={1if white 0 otherwise,

?₄={1if orange 0 otherwise

A regression model was fit and produced the following results:
?̂=23.41 + 4.67?₁ − 1.3?₂ + 2.13?₃ + 6.87?₄

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

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

c) Is a calico cat more popular as a female or male?
Female calico: ?̂= ______
Male calico: ?̂= ______

Which is more popular?
male OR female

Answer 1

The regression model is:

y = 23.41 + 4.67x1 − 1.3x2 + 2.13x3 + 6.87x4

x1={1 if female 0 if male,

x2={1 if black 0 otherwise,

x3={1 if white 0 otherwise,

x4={1 if orange 0 otherwise

a) For an orange female cat; x1 = 1, x2 = 0, x3 = 0, x4 = 1

y = 23.41 + 4.67*1 − 1.3*0 + 2.13*0 + 6.87*1

y = 34.95

b) For a black male cat, x1 = 0, x2 = 1, x3 = 0, x4 = 0

y = 23.41 + 4.67*0 − 1.3*1 + 2.13*0 + 6.87*0

y = 22.11

c) The effect of being a female increase the popularity by 4.67 units which is the coefficient of x1 (positive and magnitude being 4.67) for any cat

Hence, the female cat is more popular