Quarterly sales of a department store for the last seven years are given in the
ID: 3223401 • Letter: Q
Question
Quarterly sales of a department store for the last seven years are given in the following table.
The Excel scatterplot shown indicates that the quarterly sales have an increasing trend and seasonality. Therefore, the linear regression model, Sales = 0 + 1Qtr1 + 2Qtr2 + 3Qtr3 + 4t + , with three seasonal dummy variables Qtr1, Qtr2, and Qtr3, and the decomposition method are proposed to make sales forecasts. For the regression model, the following Excel partial output is available.
What is the regression equation for the linear trend model with seasonal dummy variables?
Coefficients Standard Error t stat p-value Intercept 31.9261 1.1028 28.9511 0.0000 Qtr1 –7.8555 1.1124 –7.0617 0.0000 Qtr2 –4.7362 1.1071 –4.2781 0.0003 Qtr3 –7.1656 1.1038 –6.4916 0.0000 t 1.0749 0.0487 22.0563 0.0000 Year 1 11 1 2 3 3 3 3 4 Qtr Sales 26.331 29.886 29.492 37.522 31.390 33.653 33.361 41.318 35.478 35.909 33.814 42.866 36.150 43.581 3 4 11 3 4 3 1 2 3 Qtr Sales 38.924 47.903 37.391 45.698 45.552 49.581 47.304 50.881 50.005 60.006 52.268 56.064 55.042 64.678Explanation / Answer
Using the coefficients given in the table, the regression equation is
Sales = 31.9261 - 7.8555 Qtr1 - 4.7362 Qtr2 - 7.1656 Qtr3 + 1.0749t
All the decision variables are significant in this regression model.