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 MSE and MAD, compare the linear trend equation with seasonal dummy variables, _t = 31,9261 - 7.855Qtr1 - 4.7362Qtr2 - 7.1656Qtr3 + 1.0749t, and the decomposition method equation _t= _t× _twith t = 26.8819 + 1.0780t and the quarterly seasonal indices: 0.9322, 1.0066, 0.9441, and 1.1171. Which of the two corresponding forecasting models is recommended?

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 MSE and MAD, compare the linear trend equation with seasonal dummy variables,

_t = 31,9261 - 7.855Qtr1 - 4.7362Qtr2 - 7.1656Qtr3 + 1.0749t, and the decomposition method equation

_t=

_t×

_twith

t = 26.8819 + 1.0780t and the quarterly seasonal indices: 0.9322, 1.0066, 0.9441, and 1.1171. Which of the two corresponding forecasting models is recommended?

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 MSE and MAD, compare the linear trend equation with seasonal dummy variables, _t = 31,9261 - 7.855Qtr1 - 4.7362Qtr2 - 7.1656Qtr3 + 1.0749t, and the decomposition method equation _t= _t× _twith t = 26.8819 + 1.0780t and the quarterly seasonal indices: 0.9322, 1.0066, 0.9441, and 1.1171. Which of the two corresponding forecasting models is recommended?

Quarterly Sales of a Department Store for the Last Seven