Consider the Following Set of Quarterly Sales Data Given in Thousands

question 102

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 coefficients for the variable "Q1" (quarter 1),"Q2" (quarter 2)and "Q3" (quarter 3).

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Definitions:

Merge

The combination of two or more entities (such as companies) into a single entity, often with the goal of enhancing competitive advantage or expanding market reach.

Vertically Integrated

A company's consolidation of all or part of the production process and supply chain within itself, controlling different stages of production usually to increase the company's power in the marketplace.

Competitive Market

A market structure where numerous producers compete to sell their goods or services to many buyers, leading to efficient pricing and innovation.

Market Price

The present cost at which a product or service is available for purchase or sale in the marketplace.