A linear trend equation. (Round your intermediate calculations and final answer

Question

A linear trend equation.(Round your intermediate calculations and final answer to 2 decimal places.)

A five-month moving average. (Round your answer to 2 decimal places.)

Exponential smoothing with a smoothing constant equal to .20, assuming a March forecast of 19(000). (Round your intermediate calculations and final answer to 2 decimal places.)

A weighted average using .60 for August, .10 for July, and .30 for June. (Round your answer to 2 decimal places.)

Please show work I need to learn...

Month Sales (000)Units   Feb. 18   Mar. 19   Apr. 12   May. 28   Jun. 16   Jul. 24   Aug. 27

Explanation / Answer

1. Linear trend, by least squares fit:
b = (n * xy – x*y)/(n * x^2 - (x)^2) = 1.21
a = (y – b*x)/n = 14.64,
where x is month number, 2, 3, … 8;
y is score – monthly sales.
For September, x = 9
So forecast is 14.64 + 1.21 * 9 = 25.53 (thousand).

2. 5-month moving average: use months April to August to estimate September.
Estimate = 106/5 = 21.2

3. New smoothed value = 0.2 * old forecast + 0.3 * new observation
month fcst obs
Mar 19 19
Apr 19 12
May 16.9 28
Jun 20.23 16
Jul 18.96 22
Aug 19.87 28
Sep 22.31


4. Naive:
Either average of all observations, = 145 / 7 = 20.71
or the last observation: 27

5. Weighted average (of last 3 months)
0.6 + 0.1 + 0.3 = 1.0 OK
0.7 * 27 + 0.1 * 24 + 0.3 * 16 = 26.01
0.94

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