For the same sales 10, 12, 15, 17 and 21 (2021 to 2025, $x$ in years from 2023), what is the slope $b$ of the least-squares trend line?

Explanation

1. 01

   With $\sum x = 0$, $b = \frac{\sum xy}{\sum x^{2}}$. Here $\sum xy = -20 - 12 + 0 + 17 + 42 = 27$ and $\sum x^{2} = 4 + 1 + 0 + 1 + 4 = 10$.

2. 02

   $b = \frac{27}{10} = 2.7$: sales rise by about 2.7 a year.