Question

2. Sales of air conditioners have grown consistently over the years and the follow represents sales:

Year           Sales
1                  520
2                  550
3 600
4                  610
5                  680
6                  710

7 810

8 820

9 900

b. Using smoothing constants of .6 and .9, develop forecasts for the sales of air conditioners.
c. What effect did the smoothing constant have on the forecast for air conditioners. Which smoothing constant gives the most accurate forecast?
d. Forecast year 7 using linear regression and the regression equation.

Answer 1

The forecast using smoothing constant can be developed using the following equation:

S_t+1= C * y_t + (1-C) * S_t, where C is the smoothing constant and S_t is the forecast for period t.

b) Using the above forecast formula, we get the following forecast table for the smoothing constants 0.6 and 0.9. (For the first period, we use the actual sale for the period as the forecast as we don't have previous period sales data, though there can be difference approaches like multiplying the actual sales for first period with smoothing constant, etc)

		Forecast
Year	Sales	Smooth Const=0.6	Smooth Const=0.9
1	520	520.00	520.00
2	550	520.00	520.00
3	600	538.00	547.00
4	610	575.20	594.70
5	680	596.08	608.47
6	710	646.43	672.85
7	810	684.57	706.28
8	820	759.83	799.63
9	900	795.93	817.96

c)  The smoothing constant seems to get nearer to the actual Sales as time passes. Smoothing constant of 0.9 seems to give better forecasts than 0.6 as can be seen from the forecast table above.

d)  Let's fit a linear regression line on the given data (In excel go to Data - > Data Analysis -> Regression, and choose Year as X-column and Sales as Y-columns). We get the following regression output:

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	451.3888889	16.27685679	27.73194	2.04E-08	412.9002	489.8775	412.9002	489.8775
Year	47.5	2.892473356	16.42193	7.57E-07	40.66039	54.33961	40.66039	54.33961

Hence, the regression equation is:

Sales = 47.5 * Year + 451.39

=> For Year 7, Sales = 47.5 * 7 + 451.39 = 783.89 ~ 784