Let \(y = 138.86 + 7.64(x - 2021)\) be a straight line of best fit by using least square method to the following data:
| Year(x) | 2018 | 2019 | 2020 | 2021 | 2022 | 2023 | 2024 |
| Profit(y) (in Rs. '000) | 114 | 130 | 126 | 144 | 138 | 156 | 164 |
Then the trend value for the year 2024 is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 161.78
The trend value for a year is the value of y on the fitted line, not the observed value. For 2024, \(x - 2021 = 3\):
\(y = 138.86 + 7.64 \times 3\)
\(= 138.86 + 22.92\)
\(= 161.78\)
So the trend value for 2024 is 161.78 (thousand rupees).
Why the other options are incorrect
Option (1) 164 — Incorrect. This is the observed profit for 2024 in the table, not the trend value.
Option (2) 154.14 — Incorrect. This is the trend value for 2023: \(138.86 + 7.64 \times 2 = 154.14\).
Option (4) 162.86 — Incorrect. It is not the value of the line at x = 2024, which is 161.78.