Question

Osteoporosis is a degenerative disease that primarily affects women over the age of 42. 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 42 (in millions), and Income is the average income of women over the age of 42 (in $1,000s). She collects data on 26 cities across the United States and obtains the following regression results:

	Coefficients	Standard Error	t Stat	p-Value
Intercept	10.28	3.73	2.76	0.0186
Population	8.19	2.15	3.80	0.0320
Income	7.00	6.01	1.16	0.3658

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

Sales= _____ +_____ Population + _____Income.

b-1. Interpret the coefficient of population.

• As the number of women over the age of 42 increases by 1 million, sales of StrongBones is predicted to increase by $8.19 million.

• As the number of women over the age of 42 increases by 1 million, sales of StrongBones is predicted to increase by $7.00 million.

• As the number of women over the age of 42 increases by 1 million, sales of StrongBones is predicted to increase by $8.19 million, holding income constant.

• As the number of women over the age of 42 increases by 1 million, sales of StrongBones is predicted to increase by $7.00 million, holding income constant.

b-2. Interpret the coefficient of income.

• As the average income of women over the age of 42 increases by $1,000, sales of StrongBones is predicted to increase by $8.19 million.

• As the average income of women over the age of 42 increases by $1,000, sales of StrongBones is predicted to increase by $7.00 million.

• As the average income of women over the age of 42 increases by $1,000, sales of StrongBones is predicted to increase by $8.19 million, holding population constant.

• As the average income of women over the age of 42 increases by $1,000, sales of StrongBones is predicted to increase by $7.00 million, holding population constant.

c. Predict sales if a city has 1.0 million women over the age of 42 and their average income is $42,000. (Enter your answer in millions rounded to 2 decimal places.)

Sales:   

Answer 1

(A) Given regression equation based on the data table is

sales = 10.28 + 8.19(population)+7.00(income)

(B-1) coefficient of population is 8.19. Coefficient is positive, which means that it will increase the sales by 8.19 units for every unit increase in population, holding income constant

option C

(b-2) coefficient of income is 7. Coefficient is positive, which means that it will increase the sales by 7 units for every unit increase in income, holding population constant

option D

(C) sales = 10.28 + 8.19(population)+7.00(income)

setting population 1 and income. =42

= 10.28 +8.19(1) + 7(42)

= 312.47