Quarterly sales of a department store for the last seven years are given in the following table. The scatterplot shows that the quarterly sales have an increasing trend and seasonality. A linear regression model given by, Sales = β₀ + β₁Qtr1 + β₂Qtr2 + β₃Qtr3 + β₄t + ε, where t is the time period (t = 1, ..., 28) and Qtr1, Qtr2, and Qtr3 are quarter dummies, is estimated and then used to make forecasts. For the regression model, the following partial output is available. Using the decomposition method:
A) Compute the adjusted seasonal indices for the four quarters.
B) Find the linear trend equation for the seasonally adjusted quarterly sales.
C) Make the sales forecasts for the first and fourth quarter of Year 8.

Question

Quarterly sales of a department store for the last seven years are given in the following table.

The scatterplot shows that the quarterly sales have an increasing trend and seasonality. A linear regression model given by, Sales = β₀ + β₁Qtr1 + β₂Qtr2 + β₃Qtr3 + β₄t + ε, where t is the time period (t = 1, ..., 28) and Qtr1, Qtr2, and Qtr3 are quarter dummies, is estimated and then used to make forecasts. For the regression model, the following partial output is available.

Using the decomposition method:
A) Compute the adjusted seasonal indices for the four quarters.
B) Find the linear trend equation for the seasonally adjusted quarterly sales.
C) Make the sales forecasts for the first and fourth quarter of Year 8.

Quizplus · Accepted Answer

The Answer of Quarterly sales of a department store for the last seven years are given in the following table. The scatterplot shows that the quarterly sales have an increasing trend and seasonality. A linear regression model given by, Sales = β₀ + β₁Qtr1 + β₂Qtr2 + β₃Qtr3 + β₄t + ε, where t is the time period (t = 1, ..., 28) and Qtr1, Qtr2, and Qtr3 are quarter dummies, is estimated and then used to make forecasts. For the regression model, the following partial output is available. Using the decomposition method: A) Compute the adjusted seasonal indices for the four quarters. B) Find the linear trend equation for the seasonally adjusted quarterly sales. C) Make the sales forecasts for the first and fourth quarter of Year 8.

Quarterly Sales of a Department Store for the Last Seven