A straight-line trend $y = a + bx$ is fitted by least squares to the sales 10, 12, 15, 17 and 21 for 2021 to 2025, with $x$ measured in years from 2023. What is $a$?

Explanation

1. 01

   With $x$ running $-2, -1, 0, 1, 2$, $\sum x = 0$, and the first normal equation $\sum y = na + b\sum x$ becomes $\sum y = na$.

2. 02

   $a = \frac{\sum y}{n} = \frac{75}{5} = 15$, the mean of the sales.