1. **State the problem:** We need to find the correlation coefficient $r$ for the data pairs $(x, y)$ where $x$ is the number of breakfasts eaten and $y$ is the GPA. 2. **Recall the formula for the correlation coefficient:** $$r = \frac{n\sum xy - \sum x \sum y}{\sqrt{(n\sum x^2 - (\sum x)^2)(n\sum y^2 - (\sum y)^2)}}$$ where $n$ is the number of data points. 3. **List the data points:** $$(6, 2.8), (9, 2.0), (11, 1.8), (13, 2.0), (24, 3.9), (28, 2.5)$$ 4. **Calculate sums:** - $n = 6$ - $\sum x = 6 + 9 + 11 + 13 + 24 + 28 = 91$ - $\sum y = 2.8 + 2.0 + 1.8 + 2.0 + 3.9 + 2.5 = 14.999999999999998 \approx 15.0$ - $\sum x^2 = 6^2 + 9^2 + 11^2 + 13^2 + 24^2 + 28^2 = 36 + 81 + 121 + 169 + 576 + 784 = 1767$ - $\sum y^2 = 2.8^2 + 2.0^2 + 1.8^2 + 2.0^2 + 3.9^2 + 2.5^2 = 7.84 + 4 + 3.24 + 4 + 15.21 + 6.25 = 40.54$ - $\sum xy = (6)(2.8) + (9)(2.0) + (11)(1.8) + (13)(2.0) + (24)(3.9) + (28)(2.5) = 16.8 + 18 + 19.8 + 26 + 93.6 + 70 = 244.2$ 5. **Plug values into the formula:** $$r = \frac{6(244.2) - (91)(15)}{\sqrt{(6(1767) - 91^2)(6(40.54) - 15^2)}}$$ 6. **Calculate numerator:** $$6 \times 244.2 = 1465.2$$ $$91 \times 15 = 1365$$ $$\text{Numerator} = 1465.2 - 1365 = 100.2$$ 7. **Calculate denominator parts:** $$6 \times 1767 = 10602$$ $$91^2 = 8281$$ $$6 \times 40.54 = 243.24$$ $$15^2 = 225$$ 8. **Calculate denominator:** $$\sqrt{(10602 - 8281)(243.24 - 225)} = \sqrt{2321 \times 18.24}$$ 9. **Calculate product inside square root:** $$2321 \times 18.24 = 42356.64$$ 10. **Square root:** $$\sqrt{42356.64} \approx 205.8$$ 11. **Calculate $r$:** $$r = \frac{100.2}{205.8} \approx 0.487$$ **Final answer:** The correlation coefficient rounded to the nearest thousandth is **$r = 0.487$**.