Question

Osteoporosis is a degenerative disease that primarily affects women over the age of 45. 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 45 (in millions), and Income is the average income of women over the age of 45 (in $1,000s). She collects data on 29 cities across the United States and obtains the following regression results:

	Coefficients	Standard Error	t Stat	p-Value
Intercept	10.15	3.13	3.24	0.0071
Population	8.45	1.11	7.61	0.0047
Income	7.45	6.12	1.22	0.3468

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

Salesˆ=Sales^=    +  Population +  Income.

b-1. Interpret the coefficient of population.

• As the number of women over the age of 45 increases by 1 million, sales of StrongBones is predicted to increase by $8.45 million.

• As the number of women over the age of 45 increases by 1 million, sales of StrongBones is predicted to increase by $7.45 million.

• As the number of women over the age of 45 increases by 1 million, sales of StrongBones is predicted to increase by $8.45 million, holding income constant.

• As the number of women over the age of 45 increases by 1 million, sales of StrongBones is predicted to increase by $7.45 million, holding income constant.

b-2. Interpret the coefficient of income.

• As the average income of women over the age of 45 increases by $1,000, sales of StrongBones is predicted to increase by $8.45 million.

• As the average income of women over the age of 45 increases by $1,000, sales of StrongBones is predicted to increase by $7.45 million.

• As the average income of women over the age of 45 increases by $1,000, sales of StrongBones is predicted to increase by $8.45 million, holding population constant.

• As the average income of women over the age of 45 increases by $1,000, sales of StrongBones is predicted to increase by $7.45 million, holding population constant.

c. Predict sales if a city has 1.6 million women over the age of 45 and their average income is $43,000. (Enter your answer in millions rounded to 2 decimal places.)

SalesˆSales^               

Answer 1

Part a) The regression equation is given as

Sales^ = 10.15 + 8.45Population + 7.45Income

Part b-1) The coefficient of population is 8.45 which means that as the number of women over the age of 45 increases by 1 million, sales of StrongBones is predicted to increase by $8.45 million, holding income constant.

Part b-2) The coefficient of income is 7.45 which means that as the average income of women over the age of 45 increases by $1,000, sales of StrongBones is predicted to increase by $7.45 million, holding population constant.

Part c) We have the following values

Population = 1,600,000

Income = $43,000

Sales^ = 10.15 + 8.45Population + 7.45Income

Sales^ = 10,150,000 + (8.45 × 1,600,000) + (7.45 × 43,000)

Sales^ = 23.99 million