1. **Problem statement:** Find the coefficients $a$ and $b$ in the linear regression equation $y = bx + a$ for the given data points where $x$ is the % level of engagement and $y$ is the % volume of sales. Given data points: $(69, 73), (63, 67), (33, 38), (40, 43), (81, 84)$ 2. **Formula for linear regression coefficients:** $$b = \frac{n\sum xy - \sum x \sum y}{n\sum x^2 - (\sum x)^2}$$ $$a = \frac{\sum y - b \sum x}{n}$$ where $n$ is the number of data points. 3. **Calculate sums:** $$\sum x = 69 + 63 + 33 + 40 + 81 = 286$$ $$\sum y = 73 + 67 + 38 + 43 + 84 = 305$$ $$\sum xy = 69\times73 + 63\times67 + 33\times38 + 40\times43 + 81\times84 = 5037 + 4221 + 1254 + 1720 + 6804 = 19036$$ $$\sum x^2 = 69^2 + 63^2 + 33^2 + 40^2 + 81^2 = 4761 + 3969 + 1089 + 1600 + 6561 = 17980$$ 4. **Calculate $b$:** $$b = \frac{5 \times 19036 - 286 \times 305}{5 \times 17980 - 286^2} = \frac{95180 - 87230}{89900 - 81796} = \frac{6950}{8104}$$ 5. **Simplify $b$ with cancellation:** $$b = \frac{\cancel{6950}}{\cancel{8104}} \approx 0.8577$$ 6. **Calculate $a$:** $$a = \frac{305 - 0.8577 \times 286}{5} = \frac{305 - 245.99}{5} = \frac{59.01}{5} = 11.802$$ **Final answer:** $$a \approx 11.80, \quad b \approx 0.86$$