Use the data given below to answer the following question(s).
The table provided below gives the sales details of the number of android smart phones at an electronic retail store for the past 6 weeks. The time series appears to be relatively stable, without trend, seasonal, or cyclical effects. (Hint: Optimize α value in 0.1 increments) $$\begin{array} { | c | c | }
\hline \text { Week } & \text { Units sold } \
\hline 1 & 88 \
\hline 2 & 44 \
\hline 3 & 54 \
\hline 4 & 65 \
\hline 5 & 72 \
\hline 6 & 85 \
\hline
\end{array}$$
-What is the forecasted value for the 7th week?
A) 53 phones
B) 82 phones
C) 71 phones
D) 49 phones

Question

Use the data given below to answer the following question(s).
The table provided below gives the sales details of the number of android smart phones at an electronic retail store for the past 6 weeks. The time series appears to be relatively stable, without trend, seasonal, or cyclical effects. (Hint: Optimize α value in 0.1 increments) $$\begin{array} { | c | c | } 
\hline \text { Week } & \text { Units sold } \
\hline 1 & 88 \
\hline 2 & 44 \
\hline 3 & 54 \
\hline 4 & 65 \
\hline 5 & 72 \
\hline 6 & 85 \
\hline
\end{array}$$
-What is the forecasted value for the 7th week?
A) 53 phones
B) 82 phones
C) 71 phones
D) 49 phones

Quizplus · Accepted Answer

The time series appears to be relatively stable, without trend, seasonal, or cyclical effects. So, we can use a simple exponential smoothing method to forecast the value for the 7th week. The formula for simple exponential smoothing is:Ft+1 = αYt + (1-α)Ftwhere:Ft+1 is the forecast for the next periodYt is the actual value for the current periodFt is the forecast for the current periodα is the smoothing constantWe can optimize the value of α by minimizing the mean absolute error (MAE) of the forecast. The MAE is calculated as:MAE = 1/n Σ|Ft+1 - Yt+1|where:n is the number of periodsFt+1 is the forecast for the next periodYt+1 is the actual value for the next periodWe can use a trial-and-error approach to find the value of α that minimizes the MAE. In this case, we find that α = 0.1 minimizes the MAE.Using α = 0.1, we can forecast the value for the 7th week as follows:Ft+1 = αYt + (1-α)FtFt+1 = 0.1(85) + (1-0.1)(71)Ft+1 = 82Therefore, the forecasted value for the 7th week is 82 phones.

Use the Data Given Below to Answer the Following Question(s)