1. **State the problem:** We need to find the correlation coefficient $r$ for the given data table relating temperature and drying time. 2. **Recall the formula:** The correlation coefficient $r$ measures the strength and direction of a linear relationship between two variables. It is calculated as: $$r = \frac{n\sum xy - \sum x \sum y}{\sqrt{(n\sum x^2 - (\sum x)^2)(n\sum y^2 - (\sum y)^2)}}$$ where $n$ is the number of data points, $x$ and $y$ are the variables. 3. **List the data:** | Temperature ($x$) | Drying time ($y$) | |-------------------|------------------| | 17 | 18 | | 19 | 15 | | 29 | 10 | | 30 | 15 | | 31 | 12 | 4. **Calculate sums:** $$\sum x = 17 + 19 + 29 + 30 + 31 = 126$$ $$\sum y = 18 + 15 + 10 + 15 + 12 = 70$$ $$\sum xy = (17)(18) + (19)(15) + (29)(10) + (30)(15) + (31)(12) = 306 + 285 + 290 + 450 + 372 = 1703$$ $$\sum x^2 = 17^2 + 19^2 + 29^2 + 30^2 + 31^2 = 289 + 361 + 841 + 900 + 961 = 3352$$ $$\sum y^2 = 18^2 + 15^2 + 10^2 + 15^2 + 12^2 = 324 + 225 + 100 + 225 + 144 = 1018$$ 5. **Plug values into formula:** $$r = \frac{5(1703) - (126)(70)}{\sqrt{[5(3352) - 126^2][5(1018) - 70^2]}}$$ 6. **Simplify numerator:** $$5(1703) = 8515$$ $$126 \times 70 = 8820$$ $$\text{Numerator} = 8515 - 8820 = -305$$ 7. **Simplify denominator:** $$5(3352) = 16760$$ $$126^2 = 15876$$ $$5(1018) = 5090$$ $$70^2 = 4900$$ $$\sqrt{(16760 - 15876)(5090 - 4900)} = \sqrt{884 \times 190} = \sqrt{167960}$$ 8. **Calculate denominator:** $$\sqrt{167960} \approx 409.82$$ 9. **Calculate $r$:** $$r = \frac{-305}{409.82} \approx -0.744$$ 10. **Round to nearest hundredth:** $$r \approx -0.74$$ **Final answer:** The correlation coefficient $r$ is approximately **-0.74**, indicating a moderate negative linear relationship between temperature and drying time.