Answer to Question #163078 in Statistics and Probability for Ajay

Question

Suppose the quarterly sales for a particular make of a car in Delhi were 2682, 2462

and 3012, respectively. From the past data prior to these three data points, a straight

line was to fit. The value on the line corresponding to the last observed time is 2988

and the slope is 80. Use exponential smoothing based upon the three observations

given above to forecast sales for the quarterly period following these observations,

using α = β = 0 ⋅ .2

Answer 1

Given values of $\alpha$ is 0.2.

By using the exponential smoothing, The forecast sales for the quarterly period is given by the formula-

$F_{i+1}=\alpha A_i+(1-\alpha)F_i$ , Where i>0

Where F= Forecst sales

A= Sales

The forecast clculated for each quarter is distributed in the table as-

Let us consider the two latest observation (2988,2767.84)

Slope=80

The staright line is -

$y-2767.84=80(x-2988)$

$y=80x-239040+2767.84$

$y=80x-236272.16$