A time series regression equation measuring the number of surfboards sold by a surfboard manufacturing company in Australia is given below: Y = 35 + 4Q₁ + 0.5Q₃ + 8Q₄ + 3t With t in quarters and 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 statements is correct regarding the trend component? A)There were 43 surfboards sold in December 2010, and this increases by 3 surfboards per quarter, irrespective of the season of the year. B)There were 35 surfboard sold in December 2010, and this increases by 15.5 surfboards per quarter, irrespective of the season of the year. C)There were 35 surfboard sold in December 2010, and this increases by 3 surfboards per quarter, irrespective of the season of the year. D)None of these choices are correct.

Question

Quizplus · Accepted Answer

The trend component in the given regression equation is represented by the term 3t, which means that the number of surfboards sold is increasing by 3 units per quarter. The initial value of Y (the number of surfboards sold in December 2010) is given as 35. Therefore, the correct statement is: There were 35 surfboard sold in December 2010, and this increases by 3 surfboards per quarter, irrespective of the season of the year.

A Time Series Regression Equation Measuring the Number of Surfboards