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

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

Besides, we consider [tex]a_{1}[/tex] and [tex]a_{2}[/tex], such that [tex]a_{1}\ne a_{2}[/tex], we define the difference between predicted milk productions ([tex]\Delta M[/tex]) below:

[tex]\Delta M = -1.1\cdot (a_{2}-a_{1})[/tex] (1)

If we know that [tex]a_{1} = 5\,yr[/tex] and [tex]a_{2} = 10\,yr[/tex], then the difference between predicted milk productions is:

[tex]\Delta M = -1.1\cdot (10-5)[/tex]

[tex]\Delta M = -5.5\,\frac{gal}{week}[/tex]

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.