Question

Mark Cotteleer owns a company that manufacturers canoes. Actual demand for Mark’s canoes during each season in 2012 through 2015 was as follow. Based on this data and the additive seasonal model, what will the demand level be for Mark’s canoes in the spring of 2017.

		Year
Season	2012	2013	2014	2015
Winter	1400	1200	1000	900
Spring	1500	1400	1600	1500
Summer	1000	2100	2000	1900
Fall	600	750	650	500

You can use excel to solve this problem

Answer 1

Additive Model: y_t = T_t + S_t + ε_t

For the four quarters the regression equation by the additive method is given as:

y_t = β₀ + β₁t + β₂S₁ + β₃S₂ + β₄S₃ + β₅S₄ + ε_t

S₁, S₂, S₃ and S₄ are dummy variables for corresponding to seasons winter, spring, summer and fall respectively:

The combination of 0’s and 1’s for each of the dummy variables at each period indicate the quarter corresponding to the time series value.

Winter: S₁ = 1, S₂ = 0, S₃ = 0, S₄ = 0

Spring: S₁ = 0, S₂ = 1, S₃ = 0 ,S₄ = 0

Summer: S₁ = 0, S₂ = 0, S₃ = 1, S₄ = 0

Fall: S₁ = 0, S₂ = 0, S₃ = 0, S₄ = 0

Simplified regression equation is: y_t = β₀ + β₁t + β₂S₁ + β₃S₂ + β₄S₃ + ε_t

Multiple regression is then done on with t, S₁, S₂, and S₃ as the independent variables and the time series values y_t as the dependent variable.

y_t = 581.25 + 4.375t + 513.125S₁ + 883.75S₂ + 1129.375S₃ + 0*S₄

The excel model is as follows:

Formulas:

Solution:

Season	Forecast for year 2016
Winter	1168.75
Spring	1543.75
Summer	1793.75
Fall	668.75