According to a straight-line trend fitted by the method of least squares, the trend values of the yearly exports (in crore Rs.) of a firm for the years 2020 and 2024 are 38 and 50 respectively. The trend value of the exports (in crore Rs.) for the year 2027 is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 59
On a straight-line trend the trend value changes by the same amount every year. From 2020 to 2024 there are 4 years:
\( \displaystyle \text{yearly rise} = \frac{50 - 38}{4} = \frac{12}{4} = 3 \)
From 2024 to 2027 there are 3 more years:
\(50 + 3 \times 3 = 50 + 9 = 59\)
Why the other options are incorrect
Option (1) 56 — Incorrect. This is the trend value for 2026, two years after 2024.
Option (2) 62 — Incorrect. This is the trend value for 2028, four years after 2024.
Option (4) 65 — Incorrect. This takes the yearly rise as 5 instead of 12 ÷ 4 = 3.