1. **State the problem:** Calculate the correlation coefficient $r_{x1y}$ using the formula: $$r_{x1y} = \frac{N \sum X_1Y - (\sum X_1)(\sum Y)}{\sqrt{[N \sum X_1^2 - (\sum X_1)^2][N \sum Y^2 - (\sum Y)^2]}}$$ 2. **Given values:** - $N = 100$ - $\sum X_1Y = 29639$ - $\sum X_1 = 1661$ - $\sum Y = 1740$ - $\sum X_1^2 = 30167$ - $\sum Y^2 = 33698$ 3. **Calculate numerator:** $$100 \times 29639 - 1661 \times 1740 = 2963900 - 2887140 = 76760$$ 4. **Calculate denominator parts:** - First part: $$100 \times 30167 - 1661^2 = 3016700 - 2758921 = 257779$$ - Second part: $$100 \times 33698 - 1740^2 = 3369800 - 3027600 = 342200$$ 5. **Calculate denominator:** $$\sqrt{257779 \times 342200} = \sqrt{88209503800} \approx 297007.54$$ 6. **Calculate correlation coefficient:** $$r_{x1y} = \frac{76760}{297007.54} \approx 0.2585$$ **Final answer:** $$r_{x1y} \approx 0.259$$