Consider the Following Set of Quarterly Sales Data Given in Thousands

question 99

Essay

Consider the following set of quarterly sales data given in thousands of dollars.The following dummy variable model that incorporates a linear trend and constant seasonal variation was used: y_t = β₀+ β₁t + β_Q1(Q1)+ β_Q2(Q2)+ β_Q3(Q3)+ ε_t
In this model there are 3 binary seasonal variables (Q1,Q₂,and Q₃).
Where
Qi is a binary (0,1)variable defined as:
Qi = 1,if the time series data is associated with quarter i;
Qi = 0,if the time series data is not associated with quarter i.
The results associated with this data and model are given in the following computer output.
The prediction equation is
Sales = 2442 + 6.2 Time - 693 Q1 - 1499 Q2 + 153 Q3 $\begin{array} { l c c c c } \text { Predictor } & \text { Coef } & \text { StDev } & \text { T } & \text { P } \\ \text { Constant } & 2441.7 & 151.9 & 16.08 & 0.000 \\\text { Time } & 6.25 & 14.70 & 0.43 & 0.684 \\\text { Q1 } & -692.9 & 142.8 & -4.85 & 0.002 \\\text { Q2 } & -1499.2 & 139.0 & -10.79 & 0.000 \\\text { Q3 } & 152.9 & 136.6 & 1.12 & 0.300 \end{array}$
$\mathrm { S } = 166.4 \quad \mathrm { R } - \mathrm { Sq } = 96.4 \% \quad \mathrm { R } - \mathrm { Sq } ( \mathrm { adj } ) = 94.4 \%$
Analysis of Variance
$\begin{array} { l r r r c c } \text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F } & \text { P } \\ \text { Regression } & 4 & 5209942 & 1302485 & 47.06 & 0.000 \\ \text { Residual Error } & 7 & 193733 & 27676 & & \\ \text { Total } & 11 & 5403675 & & & \end{array}$
-Provide a managerial interpretation of the regression coefficient for the variable "time."