(20 points) Massachusetts Dog Chow company is interested in seeing how many poun

Question

(20 points) Massachusetts Dog Chow company is interested in seeing how many
pounds of dog treats a dog consumes in a season and whether this relates to the
dog being black, a retriever, or both.
A regression reveals the following results:
Treats = 43.2 + 2.5 (Spr) + 5.8 (Sum) + 4.1 (Fall) + 2.7 (Black) + 3.6 (Ret) + 9.4
(Black*Ret)
             (11.4)     (.81)        (1.7)           (2.3)            (1.2)           (1.9)         (3.2)
n = 1,110 R2 = 0.43
where Sum, Spr, and Fall are seasonal dummies that are equal to one for Summer,
Spring, and Fall season, respectively; Black=1 if the dog has a black coat and zero
otherwise, and Ret=1 if the dog is a retriever and zero otherwise. Treats is the
number of pounds of dog treats eaten in a season.
a. What is the average number of dog treats consumed by a dog (neither black
nor a retriever) in the summer season? How many treats are consumed in
Winter on average by a dog whose coat is not black and who is nor a
retriever?
b. On average, how many treats does a retriever which is not black eat in each
season? (List the number for each season.)
c. On average, how many treats does a black dog who is not a retriever eat in
each season? (List the number for each season.)
d. Which variables are insignificant here? How to determine whether the
seasonality explains significant amount of variation in the response variable?

Explanation / Answer

(a)

Average number of dog treats consumed by a dog (neither black
nor a retriever) in the summer season = 43.2 + 2.5 (0) + 5.8 (1) + 4.1 (0) + 2.7 (0) + 3.6 (0) + 9.4(0) = 49

Average number of dog treats consumed by a dog (neither black
nor a retriever) in the winter season = 43.2 + 2.5 (0) + 5.8 (0) + 4.1 (0) + 2.7 (0) + 3.6 (0) + 9.4(0) = 43.2

(b)

Spring:

Average number of treats that a retriever which is not black eats
= 43.2 + 2.5 (1) + 5.8 (0) + 4.1 (0) + 2.7 (0) + 3.6 (1) + 9.4(0) = 49.6

Summer:

Average number of treats that a retriever which is not black eats
= 43.2 + 2.5 (0) + 5.8 (1) + 4.1 (0) + 2.7 (0) + 3.6 (1) + 9.4(0) = 52.6

Fall:

Average number of treats that a retriever which is not black eats
= 43.2 + 2.5 (0) + 5.8 (0) + 4.1 (1) + 2.7 (0) + 3.6 (1) + 9.4(0) = 50.9

Winter:

Average number of treats that a retriever which is not black eats
= 43.2 + 2.5 (0) + 5.8 (0) + 4.1 (0) + 2.7 (0) + 3.6 (1) + 9.4(0) = 46.8

(c)

Spring:

Average number of treats that a black dog which is not a retriever eats
= 43.2 + 2.5 (1) + 5.8 (0) + 4.1 (0) + 2.7 (1) + 3.6 (0) + 9.4(0) = 48.4

Summer:

Average number of treats that a black dog which is not a retriever eats
= 43.2 + 2.5 (0) + 5.8 (1) + 4.1 (0) + 2.7 (1) + 3.6 (0) + 9.4(0) = 51.7

Fall:

Average number of treats that a black dog which is not a retriever eats
= 43.2 + 2.5 (0) + 5.8 (0) + 4.1 (1) + 2.7 (1) + 3.6 (0) + 9.4(0) = 50

Winter:

Average number of treats that a black dog which is not a retriever eats
= 43.2 + 2.5 (0) + 5.8 (0) + 4.1 (0) + 2.7 (1) + 3.6 (0) + 9.4(0) = 45.9

(d)

Rule of thumb says that if the t-value is greater than 2, then the variable is insignificant at the significance level of 0.05.

So we know that at the significance level of 5%, variables Spr, Sum, Black and Ret are significant and variables Fall and Black*Ret are insignificant.

Seansonality does not explain much variation as the value of R2 is quite low.

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