1. Following table shows the sales data of new satellite tv services by an agent of last 6 months.
|
Month
|
1
|
2
|
3
|
4
|
5
|
6
|
|
Sales
|
18
|
25
|
21
|
22
|
16
|
20
|
a. Using three-month moving average, what is the forecast for 7th month?
b. If the weights for last three months are 0.4, 0.3, and 0.3 (0.4 being for the most recent), what is the forecast for 7th month?
2. Forecasts and actual sales of Fidget spinners in a convenient store are as follows:
|
Month
|
Mar
|
Apr
|
May
|
Jun
|
Jul
|
Aug
|
Sep
|
Oct
|
|
Sales
|
150
|
220
|
205
|
256
|
250
|
260
|
270
|
280
|
|
Forecast
|
170
|
229
|
192
|
241
|
238
|
210
|
225
|
179
|
a. Plot the data. Provide insides about the time series.
b. What is the forecast for November using a two-period moving average?
c. What is the forecast for November using a three-period moving average?
d. What are the Mean Squared Error (MSE) for the two- and three-period moving average models?
e. Based on the MSE, which number of periods for the moving average should be used for the model? (2 period or 3 period)? Describe why.
f. What are the forecasts for November using single exponential smoothing with α=0.1 and α=0.5.
g. What is the best single exponential smoothing model by evaluating MSE? Describe why.
3. The following data relates the weekly sales figures of the bar to the number of guests registered in that week in a small bed-and-breakfast:
|
Week
|
Guest
|
Bar Sales
|
|
1
|
16
|
$330
|
|
2
|
12
|
$270
|
|
3
|
18
|
$380
|
|
4
|
14
|
$300
|
a) Perform a linear regression that relates bar sales to guests (not to time)
b) If the forecast for next week is 20 guests, what are the sales expected to be?
4. Tyrell Garden Supply is a manufacturer of outdoor gardening equipment and storage devices. Tyrell Garden Supply's storage shed sales for the past year is given in the table below:
5.
|
Month
|
Jan
|
Feb
|
Mar
|
Apr
|
May
|
Jun
|
Jul
|
Aug
|
Sep
|
Oct
|
Nov
|
Dec
|
|
Forecast
|
10
|
10
|
12
|
15
|
20
|
25
|
30
|
35
|
30
|
20
|
15
|
15
|
|
Shed Sales
|
10
|
12
|
13
|
16
|
19
|
23
|
26
|
30
|
28
|
18
|
16
|
14
|
a. What are the forecasts for January (next year), using a two-period and three-period moving average?
b. Compute MAPE for the two- and three-period moving average models and compare your results. What is the best number of periods for the moving average model based on MAPE?
c. Find the best single exponential smoothing model by evaluating the MSE from 0.1 to 0.9, in increments of 0.1.