Question

- + Fit to page ID Page view A) Read alouc * Q3. Based on the time series values from problem number 2, consider the following table of exponential smoothing values using a = 0.3 for the time series. Units Sold Forecast (F) error Month (Thousands) Squared error 9 2 3 (i)? (ii)? 36 3 6 7.2000 -1.2000 1.44 4 6 6.8400 -0.8400 0.7056 5 12 6.5880 5.4120 29.2897 6 9 8.2116 0.7884 0.6216 (iii)? 1 7 a) (3pt) Compute the number (i): Show your work for full credit b) (3pt) Compute the number (ii): Show your work for full credit c) (5pt) Compute the number (iii): Show your work for full credit d) (pt) What is the mean square error (MSE)? Show your work for full credit e) (pt) Compare the MSE for part (Q3.d) using exponential smoothing values and (Q2.e) using the 3-month moving average. Which method is better and why? Q4.

Answer 1

The necessary table is done below

Month Squared error -6 Unit sold 1 2 3 4 5 6 7 Forecast(t) error 9 - 3 9 6 7.2 6 6.84 12 6.588 9 8.2116 8.44812 -1.2 -0.84 5.412 0.7884 36 1.44 0.7056 29.289744 0.62157456 68.05691856

a) Forecast value of month 2 = Actual value of month 1 =9

b) error for month 2 = Actual value of month 1-Forecast value of month 2 = 3-9 = -6

c) Here alpha=0.3

Forecast value of month 7 = 0.3 * actual value of month 6 + (1-0.3) * forecast value of month 6

= 0.3 * 9+ 0.7 *8.2116= 8.44812

d) Mean squared error = MSE = sum( Squared error)/5

     MSE= (36+1.44+0.7056 +29.2897 + 0.6216)/ 5

           =68.05691856 / 5

           = 13.61138371

e) Provide, value form question 2.,

If MSE(Q2)> MSE=13.61 , then the exponential smoothin model is good,

If MSE(Q2)< MSE=13.61 , then the 3-month moving average is good,