If \(y = 38.85 +7.64(x-2020)\) is the equation of the straight line trend for the following data:
| Year \((x)\) | 2017 | 2018 | 2019 | 2020 | 2021 | 2022 | 2023 |
| Profit (Rs. '000) \((y)\) | 14 | 30 | 26 | 44 | 38 | 56 | 64 |
The trend value for the year 2021 by least square method is :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 46.49
The trend value of a year is read from the fitted trend line, not from the data table. Putting \(x = 2021\) in the given line:
\(x - 2020 = 1\)
\(y = 38.85 + 7.64(1) = 46.49\)
So the trend value for 2021 is 46.49 (thousand rupees). The actual profit of 2021, 38, is a different quantity.