Question

A relatively recent firm has been active for the last five years and now wants to forecast annual sales for the current year, 2020, based on the following historical data: Sales YEAR t (y) t*y t? 1 2015 1 3.000 3.000 2016 2 6.000 12.000 4 2017 3 8.000 24.000 9 2018 4 7.000 28.000 16 2019 5 10.000 50.000 25 SUM 15 34000 117.000 55 a. What is the forecast for this year, 2020, using a four-year simple moving average? (2 pts) b. What is the forecast for this year using exponential smoothing with alpha -0.6, if the forecast for 2018 was 8,000? (4 pts) c. What is the least squares regression equation that shows the best relationship between demand and year? (4 pts) d. What is the forecast for this year using the least squares trendline you found in partc? (2 ptsj e. In fact, within a year, demand changes over four quarters of a year. Over the past five years, the firm's sales have averaged 2000 units in the first quarter (Q1), 1500 units in the second quarter(Q2), 1000 units in the third quarter (03), and 2300 units in the fourth quarter(Q4). What are appropriate quarter(seasonal) relatives for this firm's sales? (4 pts)

Answer 1

Answer a:

Let,

At = Actual Value for the Year 't'

Then,

Ft = Forecast value using the four years simple moving averages method = (At-1 + At-2 + At-3 + At-4) / 4

Answer b:

Let,

At-1 = Actual sales for the previous year

Ft-1 = Forecast sales for the previous year

α = Alpha = 0.6 (As given in the question)

Ft = Simple exponential smoothing forecast for the current year = Ft-1 + α (At-1 - Ft-1)

Thus, we get:

Calculations:

Answer c:

Step 1: Find the mean values for both the variables:

Where x = Independent Variable = No. of a particular year and y = Dependent Variable = Sales

Step 2: Find the three columns as mentioned below:

Where,

xy = x * y

x2 = x * x

y2 = y * y

Step 3: Find the value of byx:

Step 4: Find the linear trend equation:

Answer d:

Here, we take x = 6 in the linear trend equation as obtained in the previous answer:

∴ y = 1500 (6) + 2300

= 11300

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