1. **State the problem:** We need to find the regression line equation $y = mx + b$ based on the given data points $(x, y)$. 2. **Formula for regression line:** The slope $m$ and intercept $b$ are given by: $$m = \frac{n\sum xy - \sum x \sum y}{n\sum x^2 - (\sum x)^2}$$ $$b = \frac{\sum y - m \sum x}{n}$$ where $n$ is the number of data points. 3. **Calculate sums:** - $n = 15$ - $\sum x = 2 + 3 + \cdots + 16 = 135$ - $\sum y = 35.62 + 35.39 + \cdots + 2.8 = 311.25$ - $\sum x^2 = 2^2 + 3^2 + \cdots + 16^2 = 1535$ - $\sum xy = 2\times35.62 + 3\times35.39 + \cdots + 16\times2.8 = 2383.15$ 4. **Calculate slope $m$:** $$m = \frac{15 \times 2383.15 - 135 \times 311.25}{15 \times 1535 - 135^2} = \frac{35747.25 - 42018.75}{23025 - 18225} = \frac{-5271.5}{4800}$$ $$m = -1.10$$ 5. **Calculate intercept $b$:** $$b = \frac{311.25 - (-1.10) \times 135}{15} = \frac{311.25 + 148.5}{15} = \frac{459.75}{15}$$ $$b = 30.65$$ 6. **Final regression line:** $$y = -1.10x + 30.65$$ This line best fits the data with slope $-1.10$ and intercept $30.65$.