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:

Cortical Arousal

The level of activation in the cerebral cortex, which can affect attention, perception, and the ability to process information.

Extraverts

Individuals characterized by an outgoing, socially confident behavior, often energized by interactions with others.

Introverts

Individuals who prefer solitary activities and environments where they can focus on internal thoughts and feelings, distinct from extroverts.

Source Traits

Fundamental dimensions of personality that are hypothesized to be the origin for all individual differences in personality traits.