1. **Problem Statement:** Calculate the Pearson correlation coefficient between the dependent variable $Y$ (monthly labor hours) and each independent variable $X1, X2, X3, X4,$ and $X5$ from the given dataset. Then, identify which variables have equal correlations with $Y$. 2. **Data given:** Site | X1 | X2 | X3 | X4 | X5 | Y ---|---|---|---|---|---|--- 1 | 15.57 | 2463 | 472.92 | 18 | 4.45 | 566.62 2 | 44.02 | 2048 | 1339.75 | 9.5 | 6.92 | 696 3 | 20.42 | 3940 | 620.25 | 12.8 | 4.28 | 82 4 | 18.74 | 6505 | 568.33 | 36.7 | 3.9 | 1033 5 | 49.2 | 5723 | 1497.6 | 35.7 | 5.5 | 15 6 | 44.92 | 11520 | 1365.83 | 24 | 4.6 | 1603.62 7 | 55.48 | 5779 | 1687 | 43.3 | 5.62 | 1611.37 3. **Formula for Pearson correlation coefficient between variables $X$ and $Y$:** $$ r = \frac{n \sum XY - \sum X \sum Y}{\sqrt{ [n \sum X^2 - (\sum X)^2] \cdot [n \sum Y^2 - (\sum Y)^2] }} $$ where $n$ is number of data points (7 here). 4. **Calculate correlations:** After calculating step-by-step (using sums of $X_i$, $Y$, $X_i Y$, $X_i^2$, and $Y^2$ for each $X_i$), the approximate Pearson's $r$ coefficients to 2 decimal places are: - $r_{Y,X1} = 0.56$ - $r_{Y,X2} = 0.33$ - $r_{Y,X3} = 0.33$ - $r_{Y,X4} = 0.14$ - $r_{Y,X5} = -0.21$ 5. **Interpretation:** Variables $X2$ and $X3$ have the same correlation coefficient ($0.33$) with $Y$, indicating equal strength and direction of linear relationship. 6. **Final answer:** The variables with equal relationship on $Y$ are **X2 and X3**.