Discussion
The equation of the linear trend fitted to the annual data is yt = 214.4 + 5.86x of an industry for the years 1998 to 2004, where x = t - 2001 and yt is the annual production in thousand tonnes in time period t. What is the estimate of the annual production for the year 2005 ?
Answer: D
The estimate for 2005 is 237.84 thousand tonnes.
The origin is at 2001, so for 2005 \(x = 2005 - 2001 = 4\):
\[ \begin{aligned} y &= 214.4 + 5.86 \times 4 \\ &= 214.4 + 23.44 = 237.84 \end{aligned} \]
216.84 and 227.84 do not fit \(x = 4\), and 2017.84 is far too large to follow the trend of about 214 thousand tonnes a year.
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