Answer to Question #173559 in Statistics and Probability for ANJU JAYACHANDRAN

Question

9(b) 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 (4)

Answer 1

For exponential smoothing, forecasts are calculated using;

$F_{t+1}=\alpha A_t+(1-\alpha )F_t$

where A are the actual sales and F are the forecast sales. The table below shows the forecast sale values.

Focusing on the last value (2988,2767.84) and a slope of 80, the equation of the straight line that was fit is;

y-2767.84=80(x-2988)

y=80x-239040+2767.84

y=80x-236272.16