Question

question 23 (1 point)
listen
the mean square error (mse) for the forecasts shown in the following table is:
month forecast demand actual demand
april 170 180
may 225 200
june 210 200
july 260 240
august 200 230
more than 250 but less than or equal to 300.
more than 300 but less than or equal to 350.
more than 350 but less than or equal to 400.
more than 400 but less than or equal to 450.
question 24 (1 point)
listen
in the context of data patterns in a time series, regular patterns in a data series that take place over long periods of time are called ______ patterns.
orthographic
seasonal
cyclical
parallel patterns
question 25 (1 point)
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a moving average (ma) method is most appropriate for data with major identifiable trends.
true
false

Explanation:

Question 23

Step1: Calculate error for each month

Error = Forecast - Actual. For April: $170 - 180=- 10$; May: $225 - 200 = 25$; June: $210 - 200 = 10$; July: $260 - 240 = 20$; August: $200 - 230=-30$.

Step2: Calculate squared - error for each month

Squared - error = Error$^2$. For April: $(-10)^2 = 100$; May: $25^2 = 625$; June: $10^2 = 100$; July: $20^2 = 400$; August: $(-30)^2 = 900$.

Step3: Calculate MSE

MSE=$\frac{\sum_{i = 1}^{n}e_{i}^{2}}{n}$, where $n = 5$, $\sum_{i = 1}^{5}e_{i}^{2}=100 + 625+100 + 400+900=2125$, MSE=$\frac{2125}{5}=425$.

Seasonal patterns occur over short - term regular intervals (e.g., daily, weekly, yearly). Cyclical patterns occur over long periods of time in a time - series data. Orthographic is related to spelling and parallel patterns are not relevant here.

A moving average method is best for data with no trend or a very stable trend. It smooths out random fluctuations. For data with major identifiable trends, other methods like trend - adjusted exponential smoothing are more appropriate.

Answer:

more than 400 but less than or equal to 450.

Question 24