For the following data:
| Year | 2022 | 2023 | 2024 | 2025 | 2026 |
| Earning (in lakh Rs.) | 32 | 40 | 55 | 65 | 72 |
Using fit a straight line trend by the method of least squares, the predicted earning (in lakh, Rs.) for the 2027 is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 84.3
There are 5 years (odd), so take the middle year 2024 as origin: u = year − 2024. The trend line is \( y=a+bu \), with \( \sum u=0 \), so
\( \displaystyle a=\frac{\sum y}{n},\qquad b=\frac{\sum uy}{\sum u^2} \)
For the years 2022 to 2026, u = −2, −1, 0, 1, 2.
\( \displaystyle \sum y=32+40+55+65+72=264 \)
\( \displaystyle \sum uy=(-2)(32)+(-1)(40)+0(55)+1(65)+2(72) \)
\( \displaystyle =-64-40+0+65+144=105 \)
\( \displaystyle \sum u^2=4+1+0+1+4=10 \)
\( \displaystyle a=\frac{264}{5}=52.8 \)
\( \displaystyle b=\frac{105}{10}=10.5 \)
\( \displaystyle y=52.8+10.5u \)
For 2027, u = 3:
\( \displaystyle y=52.8+10.5\times 3 \)
\( \displaystyle =52.8+31.5=84.3 \)
So the predicted earning is 84.3 lakh.