A time series regression equation for a surfboard manufacturing company in Australia is given below: yt = 35 + 4Q₁ + 0.5Q₃ + 8Q₄ + 3t
With t in quarters, the origin is December 2010 and Q₁ is the indicator variable for March, Q₃ is the indicator variable for September and Q₄ is the indicator variable for December.
Which of the following is the correct value of the estimate for the number of surfboards sold by this manufacturing company in June 2013?

Question

Quizplus · Accepted Answer

First, we need to identify the appropriate variables that correspond to June 2013, which is two quarters after December 2012. Therefore, t = 2. Next, we plug in the values for the indicator variables: Q₁ = 0 Q₃ = 0 Q₄ = 1 Substituting these values and solving for yt, we get: yt = 35 + 4(0) + 0.5(0) + 8(1) + 3(2) yt = 35 + 0 + 0 + 8 + 6 yt = 49 Therefore, the estimated number of surfboards sold by the manufacturing company in June 2013 is 49. None of the answer choices provided match this value, but the closest option is C) 65. However, this is not the correct estimate according to the given regression equation.

A Time Series Regression Equation for a Surfboard Manufacturing Company