Question

Dairy farmers are aware there is often a linear relationship between the age, in years, of a dairy cow and the amount of milk produced in gallons per week The least squares regression line

produced from a random sample is Milk = 40.8 – 1.1 (Age). Based on the model, what is the difference in predicted amounts of milk produced between a cow of 5 years and a cow of 10 years?

A cow of 5 years is predicted to produce 5.5 fewer gallons per week

B A cow of 5 years is predicted to produce 5.5 more gallons per week

c) A cow of 5 years is predicted to produce 1.1 fewer gallons per week

D) A cow of 5 years is predicted to produce 1.1 more gallons per week

A cow of 5 years and a cow of 10 years are both predicted to produce 40.8 gallons per week

Answer 1

B. A cow of 5 years is predicted to produce 5.5 more gallons per week.

Explanation:

Let
`M(a) = 40.8-1.1\cdot a`, where
`a` is the age of the dairy cow, measured in years, and
`M(a)` is the predicted milk production, measured in gallons per week.

Besides, we consider
`a_(1)` and
`a_(2)`, such that
`a_(1)\\e a_(2)`, we define the difference between predicted milk productions (
`\Delta M`) below:

`\Delta M = -1.1\cdot (a_(2)-a_(1))` (1)

If we know that
`a_(1) = 5\,yr` and
`a_(2) = 10\,yr`, then the difference between predicted milk productions is:

`\Delta M = -1.1\cdot (10-5)`

`\Delta M = -5.5\,(gal)/(week)`

That is, a cow of 5 years is predicted to produce 5.5 more gallons per week than a cow of 10 years. Hence, the right answer is B.