SCENARIO 16-13
Given Below Is the Monthly Time Series Data

question 17

Short Answer

SCENARIO 16-13
Given below is the monthly time series data for U.S. retail sales of building materials over a
specific year. $$\begin{array} { | c | c | } \hline \text { Month } & \text { Retail Sales } \\\hline 1 & 6,594 \\\hline 2 & 6,610 \\\hline 3 & 8,174 \\\hline 4 & 9,513 \\\hline 5 & 10,595 \\\hline 6 & 10,415 \\\hline 7 & 9,949 \\\hline 8 & 9,810 \\\hline 9 & 9,637 \\\hline 10 & 9,732 \\\hline 11 & 9,214 \\\hline 12 & 9,201 \\\hline\end{array}$$ The results of the linear trend, quadratic trend, exponential trend, first-order autoregressive,
second-order autoregressive and third-order autoregressive model are presented below in which
the coded month for the 1st month is 0: $\text { Linear trend model: }$
$\begin{array}{lrrrr} & \text { Coefficients } & \text { Standard Error } & \text { t Stat } & \text { P-value } \\\hline \text { Intercept } & 7950.7564 & 617.6342 & 12.8729 & 0.0000 \\\text { Coded Month } & 212.6503 & 95.1145 & 2.2357 & 0.0494\end{array}$

$\text { Quadratic trend model: }$


$\text { Exponential trend model: }$
$\begin{array}{lrrrr}\hline & \text { Coefficients } & \text { Standard Error } & \text { t Stat } & \text { P-value } \\\hline \text { Intercept } & 3.8912 & 0.0315 & 123.3674 & 0.0000 \\\text { Coded Month } & 0.0116 & 0.0049 & 2.3957 & 0.0376\end{array}$


$\text { First-order autoregressive: }$
$\begin{array}{lrrrr} & \text { Coefficients } & \text { Standard Error } & t \text { Stat } & {\text { P-value }} \\\hline \text { Intercept } & 3132.0951 & 1287.2899 & 2.4331 & 0.0378 \\\text { YLag1 } & 0.6823 & 0.1398 & 4.8812 & 0.0009 \\\hline\end{array}$


-Referring to Scenario 16-13, what is the exponentially smoothed value for the $12 ^ { \text {th } }$ month
using a smoothing coefficient of W = 0.5 if the exponentially smooth value for the $10 ^ { \text {th } }$ and
11th month are 9,746.3672 and 9,480.1836, respectively?

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Definitions:

Psychological Reactance

A reaction to regain freedom or control when one feels it is being threatened or reduced, often leading to resistance or doing the opposite of what is being sought.

Empathy

The ability to understand and share the feelings of another, often leading to a deeper connection and emotional support.

Cognitive Dissonance Theory

A psychological theory suggesting that individuals experience discomfort when holding two or more contradictory beliefs, attitudes, or values, leading them to attempt to reduce the dissonance.

Theory of Planned Behavior

A theory in psychology that forecasts a person's likelihood of performing a specific action at a given time and location, taking into account their attitudes, societal expectations, and their sense of control over the behavior.