A Time Series Regression Equation Measuring the Number of Surfboards

question 40

Multiple Choice

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.

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Definitions:

Normal Distribution

A symmetric, bell-shaped distribution of values in which the mean, median, and mode are all equal and located at the center of the distribution.

Standard Deviation

Standard deviation is a measure of the amount of variation or dispersion of a set of values; a low standard deviation indicates that the values tend to be close to the mean, while a high standard deviation indicates that the values are spread out over a wider range.

Mean High Temperature

The average of the highest temperatures recorded over a specific period.

Normal Distribution

A bell-shaped probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.