1. **State the problem:** We need to calculate the Pearson correlation coefficient $r$ to measure the strength and direction of the linear relationship between advertising spend and monthly sales. 2. **Formula:** The Pearson correlation coefficient is given by: $$r = \frac{n\sum xy - \sum x \sum y}{\sqrt{(n\sum x^2 - (\sum x)^2)(n\sum y^2 - (\sum y)^2)}}$$ where $x$ is advertising spend, $y$ is monthly sales, and $n$ is the number of data points. 3. **Data:** Advertising Spend $x$: 1, 3, 5, 7, 9 Monthly Sales $y$: 4, 6, 10, 13, 15 4. **Calculate sums:** $$\sum x = 1+3+5+7+9 = 25$$ $$\sum y = 4+6+10+13+15 = 48$$ $$\sum xy = (1\times4)+(3\times6)+(5\times10)+(7\times13)+(9\times15) = 4+18+50+91+135 = 298$$ $$\sum x^2 = 1^2+3^2+5^2+7^2+9^2 = 1+9+25+49+81 = 165$$ $$\sum y^2 = 4^2+6^2+10^2+13^2+15^2 = 16+36+100+169+225 = 546$$ 5. **Plug values into formula:** $$r = \frac{5\times298 - 25\times48}{\sqrt{(5\times165 - 25^2)(5\times546 - 48^2)}} = \frac{1490 - 1200}{\sqrt{(825 - 625)(2730 - 2304)}} = \frac{290}{\sqrt{200 \times 426}}$$ 6. **Calculate denominator:** $$\sqrt{200 \times 426} = \sqrt{85200} \approx 291.92$$ 7. **Calculate $r$:** $$r = \frac{290}{291.92} \approx 0.993$$ **Final answer:** The Pearson correlation coefficient is approximately $0.993$, indicating a very strong positive linear relationship between advertising spend and monthly sales.