Question

Osteoporosis is a degenerative disease that primarily affects women over the age of 61. 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 61 (in millions), and Income is the average income of women over the age of 61 (in $1,000s). She collects data on 33 cities across the United States and obtains the following regression results: Coefficients Standard Error t Stat p-Value Intercept 10.13 3.12 3.25 0.0058 Population 8.26 1.49 5.54 0.0116 Income 7.59 6.42 1.18 0.3593 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 61 increases by 1 million, sales of StrongBones is predicted to increase by $8.26 million. As the number of women over the age of 61 increases by 1 million, sales of StrongBones is predicted to increase by $7.59 million. As the number of women over the age of 61 increases by 1 million, sales of StrongBones is predicted to increase by $8.26 million, holding income constant. As the number of women over the age of 61 increases by 1 million, sales of StrongBones is predicted to increase by $7.59 million, holding income constant. b-2. Interpret the coefficient of income. As the average income of women over the age of 61 increases by $1,000, sales of StrongBones is predicted to increase by $8.26 million. As the average income of women over the age of 61 increases by $1,000, sales of StrongBones is predicted to increase by $7.59 million. As the average income of women over the age of 61 increases by $1,000, sales of StrongBones is predicted to increase by $8.26 million, holding population constant. As the average income of women over the age of 61 increases by $1,000, sales of StrongBones is predicted to increase by $7.59 million, holding population constant. c. Predict sales if a city has 2.0 million women over the age of 61 and their average income is $40,000. (Enter your answer in millions rounded to 2 decimal places.) Salesˆ Sales ^

Answer 1

(a)

The sample regression equation

(b)

As the number of women over the age of 61 increases by 1 million, sales of StrongBones is predicted to increase by $8.26 million, holding income constant.

(c)

As the average income of women over the age of 61 increases by $1,000, sales of StrongBones is predicted to increase by $7.59 million, holding population constant.

(d)

Income in millions = 40000/1000000 = $0.04

Predict sales if a city has 2.0 million women over the age of 61 and their average income is $40,000 is$26.95 million