Question

Osteoporosis is a degenerative disease that primarily affects women over the age of 50. A research analyst wants to forecast sales of StrongBones, a prescription drug for treating this debilitating disease. She uses the model Sales = β₀ + β₁Population + β₂Income + ε,where Sales refers to the sales of StrongBones (in $1,000,000s), Population is the number of women over the age of 50 (in millions), and Income is the average income of women over the age of 50 (in $1,000s). She collects data on 36 cities across the United States and obtains the following regression results:

	Coefficients	Standard Error	t Stat	p-Value
Intercept	10.09	3.97	2.54	0.0218
Population	8.34	1.34	6.22	0.0084
Income	7.30	6.23	1.17	0.3626

a. What is the sample regression equation? (Enter your answers in millions rounded to 2 decimal places.)

Sales = __(answer)__ + _(answer)__ Population + __(answer)__ Income.

b-1. Interpret the coefficient of population.

• As the number of women over the age of 50 increases by 1 million, sales of StrongBones is predicted to increase by $8.34 million.

• As the number of women over the age of 50 increases by 1 million, sales of StrongBones is predicted to increase by $7.30 million.

• As the number of women over the age of 50 increases by 1 million, sales of StrongBones is predicted to increase by $8.34 million, holding income constant.

• As the number of women over the age of 50 increases by 1 million, sales of StrongBones is predicted to increase by $7.30 million, holding income constant.

b-2. Interpret the coefficient of income.

• As the average income of women over the age of 50 increases by $1,000, sales of StrongBones is predicted to increase by $8.34 million.

• As the average income of women over the age of 50 increases by $1,000, sales of StrongBones is predicted to increase by $7.30 million.

• As the average income of women over the age of 50 increases by $1,000, sales of StrongBones is predicted to increase by $8.34 million, holding population constant.

• As the average income of women over the age of 50 increases by $1,000, sales of StrongBones is predicted to increase by $7.30 million, holding population constant.

c. Predict sales if a city has 2.5 million women over the age of 50 and their average income is $36,000. (Enter your answer in millions rounded to 2 decimal places.)

Sales = ???

Answer 1

Ans:

1)

Sales=10.09+8.34*population+7.30*income

b-1)As the number of women over the age of 50 increases by 1 million, sales of StrongBones is predicted to increase by $8.34 million, holding income constant.

b-2)As the average income of women over the age of 50 increases by $1,000, sales of StrongBones is predicted to increase by $7.30 million, holding population constant.

c)when population=2.5 million and income=36 thousands

sales=10.09+8.34*2.5+7.30*36=293.74