The straight-line trend \(y = 46 + 3.2X\), where X = year − 2021, is fitted by the method of least squares to the yearly output \(y\) (in thousand tonnes) of a mill for the years 2018 to 2024. The trend value of the output (in thousand tonnes) for the year 2015 is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 26.8
The year 2015 lies before the origin 2021, so its X value is negative:
\(X = 2015 - 2021 = -6\)
\(y = 46 + 3.2 \times (-6) = 46 - 19.2 = 26.8\)
Why the other options are incorrect
Option (1) 65.2 — Incorrect. This takes X = +6, which is the year 2027, not 2015.
Option (2) 30 — Incorrect. This is the trend value for 2016 (X = −5).
Option (3) 23.6 — Incorrect. This is the trend value for 2014 (X = −7).