1. The problem is to find the Pearson product-moment correlation coefficient, which measures the linear relationship between two variables, $X$ and $Y$. 2. Given data includes sums: $\sum X = 131235$, $\sum Y = 378.11$, $\sum X^2 = 203454169$, $\sum Y^2 = 958954.612$, $\sum XY = 3517981.9$, and sample size $n=2$. 3. The formula for Pearson correlation coefficient $r$ is: $$ r = \frac{n\sum XY - (\sum X)(\sum Y)}{\sqrt{[n\sum X^2 - (\sum X)^2][n\sum Y^2 - (\sum Y)^2]}} $$ 4. Substitute the values: $$ r = \frac{2 \times 3517981.9 - 131235 \times 378.11}{\sqrt{[2 \times 203454169 - (131235)^2][2 \times 958954.612 - (378.11)^2]}} $$ 5. Compute numerator: $$ 2 \times 3517981.9 = 7035963.8 $$ $$ 131235 \times 378.11 = 49625626.285 $$ $$ 7035963.8 - 49625626.285 = -42589662.485 $$ 6. Compute denominator parts: $$ 2 \times 203454169 = 406908338 $$ $$ (131235)^2 = 17222209225 $$ $$ 406908338 - 17222209225 = -16815300987 $$ $$ 2 \times 958954.612 = 1917909.224 $$ $$ (378.11)^2 = 142964.6521 $$ $$ 1917909.224 - 142964.6521 = 1774944.5719 $$ 7. Negative value in the denominator's first square root term implies an error in sums or data inconsistency. 8. Assuming the data meant the sums for two data points: Calculate mean $\bar{X} = \frac{11235 + 8788}{2} = 10011.5$ Calculate mean $\bar{Y} = \frac{85.11 + 293}{2} = 189.055$ 9. Calculate numerator (covariance): $$\sum (X_i - \bar{X})(Y_i - \bar{Y}) = (11235 - 10011.5)(85.11 - 189.055) + (8788 - 10011.5)(293 - 189.055) = 1223.5 \times -103.945 + (-1223.5) \times 103.945 = -127250.2075 - 127250.2075 = -254500.415$$ 10. Calculate denominator (standard deviations): $$\sqrt{[(11235 - 10011.5)^2 + (8788 - 10011.5)^2] \times [(85.11 - 189.055)^2 + (293 - 189.055)^2]} = \sqrt{(1223.5^2 + (-1223.5)^2)(-103.945^2 + 103.945^2)} = \sqrt{(1496292.25 + 1496292.25)(10808.644 + 10808.644)}$$ $$= \sqrt{2992584.5 \times 21617.288} = \sqrt{64732665354.4} \approx 254477.953$$ 11. Therefore, the Pearson correlation coefficient: $$r = \frac{-254500.415}{254477.953} \approx -1.00009$$ 12. Values close to $-1$ indicate a strong negative linear correlation.