Question

2. A consulting firm estimates the quarterly sales (in millions of dollars) of a Regional Airlines called “U Fly”, by the following significant model:

E(Sales) = 300.5 + 2.37(T) - 4.6Q₁ - 6.8Q₃ + 8.65Q₄

Where E(Sales) is the average sales for each quarter (in millions of dollars), T is a time index defined as 1, 2, 3, …………,20, and 20 represents the first quarter of 2020, Q₁ = 1 when in the first quarter, 0 otherwise, Q₃ =1 when in the third quarter, 0 otherwise, and Q₄ = 1 when in the fourth quarter, 0 otherwise,.

a. Briefly explain the meaning of estimated sample slopes for the trend (2.37) and the first quarter (-4.6).

b. Forecast actual sales (in dollars) for the second and third quarters of 2020. Explain your answers.

Answer 1

a. Briefly explain the meaning of estimated sample slopes for the trend (2.37) and the first quarter (-4.6).

The slope for the trend means for every increase in the time period, the quarterly sales will increase by 2.37.

The first quarter means for every first quarter, the quarterly sales will decrease by 4.6.

b. Forecast actual sales (in dollars) for the second and third quarters of 2020. Explain your answers

For the second quarter of 2020:

E(Sales) = 300.5 + 2.37(T) - 4.6Q1 - 6.8Q3 + 8.65Q4

E(Sales) = 300.5 + 2.37(21) - 4.6*0 - 6.8*0 + 8.65*0

E(Sales) = 350.27

For the third quarter of 2020:

E(Sales) = 300.5 + 2.37(T) - 4.6Q1 - 6.8Q3 + 8.65Q4

E(Sales) = 300.5 + 2.37(22) - 4.6*0 - 6.8*1 + 8.65*0

E(Sales) = 345.84