b== a= Thus, the equation is = 7.129 + 4.275x. yx x yx= = 5, 7.129 + 4.275(5) = 28.50. National mixer, Inc., sells can openers. Monthly sales for a seven-month period were as follows: Month Feb. Mar. Apr. May Jun. Jul. Aug. Sales (1000 units) 19 18 15 20 18 22 20 Plot the monthly data on a sheet of graph paper Forecast September sales volume using each of the following: A linear regression A five-month moving average Exponential smoothing with a smoothing constant equal to 0.2, assuming a March forecast of 19000 units The naive approach Aweighted average using 0.6, 0.3, and 0.1 wieghts Which method seems least appropariate? Why? Solution : Plot the monthly data Forcasting the septamper value using : 1. linear regrission : Month ( t ) Sales ( Y ) Ty ---- --- ---- 0 Feb. (2) 4 19 38 Mar. (3) 9 18 54 Apr. (4) 16 15 60 May (5) 25 20 100 Jun. (6) 36 18 108 Jul (7) 49 22 154 Aug (8) 64 20 160 35 203 132 674 = 1225 = 203 ∑ = a + bt b= Yt where a= t = specified number of time periods from t=0 n=number of periods = 7 = forecast for period t Yt y=value of time series a=value of at t=0 Yt b=slope of the line 2. a five month moving average : MAn =where
b== a= Thus, the equation is yx = 7.129 + 4.275x. x = 5, yx= 7.129 + 4.275(5) = 28.50. National mixer, Inc., sells can openers. Monthly sales for a seven-month period were as follows: Month Feb. Mar. Apr. May Jun. Jul. Aug. Sales (1000 units) 19 18 15 20 18 22 20 Plot the monthly data on a sheet of graph paper Forecast September sales volume using each of the following: A linear regression A five-month moving average Exponential smoothing with a smoothing constant equal to 0.2, assuming a March forecast of 19000 units The naive approach Aweighted average using 0.6, 0.3, and 0.1 wieghts Which method seems least appropariate? Why? Solution : Plot the monthly data Forcasting the septamper value using : 1. linear regrission : Month ( t ) Sales ( Y ) Ty ---- --- ---- 0 Feb. (2) 4 19 38 Mar. (3) 9 18 54 Apr. (4) 16 15 60 May (5) 25 20 100 Jun. (6) 36 18 108 Jul (7) 49 22 154 Aug (8) 64 20 160 35 203 132 674 = 1225 ∑ = 203 Yt = a + bt where t = specified number of time periods from t=0 Yt = forecast for period t a=value of Yt at t=0 b=slope of the line b= a= n=number of periods = 7 y=value of time series 2. a five month moving average : MAn =where