Question
Fit a straight line trend by the method of least squares and estimate the trend for the year 2023.
| Year | 2014 | 2015 | 2016 | 2017 | 2018 | 2019 | 2020 |
| Sales (in ₹ lacs) | 26 | 26 | 44 | 42 | 108 | 120 | 166 |
Solution
| Year | Y | X = Year – 2017 | `X^2` | XY |
| 2014 | 26 | -3 | 9 | -78 |
| 2015 | 26 | -2 | 4 | -52 |
| 2016 | 44 | -1 | 1 | -44 |
| 2017 | 42 | 0 | 0 | 0 |
| 2018 | 108 | 1 | 1 | 108 |
| 2019 | 120 | 2 | 4 | 240 |
| 2020 | 166 | 3 | 9 | 498 |
| bn | `\sum "Y"` = 532 | `\sum "x"^2″` = 28 | `\sum "XY"` = 672 |
a = ∑y/n = 532/7 = 76,
b = ∑xy/∑x2 = 672/28 = 24
yc = a + bx, yc = 76 + 24x
Estimated sales = yc for 2023 = 76 + 24 × 6 = ₹220 lacs
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