Professor Very Busy needs to allocate time next week to include time for office hours. He needs to forecast the number of students who will seek appointments. He has gathered the following data: $$\begin{array} { l l }
\text { Week } & \text {\# Students } \
\hline 6 \text { weeks ago } & 83 \
5 \text { weeks ago } & 110 \
4 \text { weeks ago } & 95 \
3 \text { weeks ago } & 80 \
2 \text { weeks ago } & 65 \
\text { Last week } & 50
\end{array}$$ What is this week's forecast using trend-adjusted (double) smoothing with alpha = .5 and beta = .1, if the forecast for last week was 65, the forecast for two weeks ago was 75, and the trend estimate for last week's forecast was -5?
A) 49.3
B) 50.6
C) 51.3
D) 65.4
E) 78.7

Question

Professor Very Busy needs to allocate time next week to include time for office hours. He needs to forecast the number of students who will seek appointments. He has gathered the following data: $$\begin{array} { l l } 
\text { Week } & \text {\# Students } \
\hline 6 \text { weeks ago } & 83 \
5 \text { weeks ago } & 110 \
4 \text { weeks ago } & 95 \
3 \text { weeks ago } & 80 \
2 \text { weeks ago } & 65 \
\text { Last week } & 50
\end{array}$$ What is this week's forecast using trend-adjusted (double) smoothing with alpha = .5 and beta = .1, if the forecast for last week was 65, the forecast for two weeks ago was 75, and the trend estimate for last week's forecast was -5?
A) 49.3
B) 50.6
C) 51.3
D) 65.4
E) 78.7

Quizplus · Accepted Answer

The formula for double smoothing with trend is:

Forecast for this week = alpha*actual value + (1-alpha)*(previous forecast + previous trend)
Trend estimate for this week = beta*(forecast for this week - previous forecast) + (1-beta)*previous trend

Using the given data and the initial conditions, we can calculate the forecast for this week and the trend estimate:

Forecast for this week = 0.5*50 + 0.5*(65 - 5) = 51.5
Trend estimate for this week = 0.1*(51.5 - 65) + 0.9*(-5) = -1.05

Then, we use these values to calculate the final forecast:

Forecast for this week = 0.5*80 + 0.5*(51.5 + (-1.05)) = 51.275

Therefore, the best choice is C) 51.3, which is the closest answer to the calculated forecast rounded to one decimal place.

Professor Very Busy Needs to Allocate Time Next Week to Include