\( r_{x y}=r_{y x} \) Where \( r_{x y} \) is the correlation between \( x \) and \( y \) and \( r_{y x} \) is the correlation between \( y \) and \( x \). True

Yes, the statement is **true**. ### Explanation: The Pearson correlation coefficient is a measure of the linear relationship between two variables. It is defined as: \[ r_{xy} = \frac{\text{Cov}(x, y)}{\sigma_x \sigma_y} \] Where: - \(\text{Cov}(x, y)\) is the covariance between variables \(x\) and \(y\). - \(\sigma_x\) and \(\sigma_y\) are the standard deviations of \(x\) and \(y\), respectively. **Key Point:** Covariance is symmetric, meaning \(\text{Cov}(x, y) = \text{Cov}(y, x)\). Given this symmetry, the correlation coefficient also inherits this property: \[ r_{xy} = \frac{\text{Cov}(x, y)}{\sigma_x \sigma_y} = \frac{\text{Cov}(y, x)}{\sigma_y \sigma_x} = r_{yx} \] Therefore, \( r_{xy} = r_{yx} \). ### Implications: - **Interpretation:** Whether you consider the correlation from \(x\) to \(y\) or from \(y\) to \(x\), the strength and direction of the linear relationship remain the same. - **Usage:** This symmetry allows flexibility in statistical analyses and ensures consistency in results regardless of the order of variables. ### Example: If the correlation between height and weight is \( r_{\text{height, weight}} = 0.8 \), then the correlation between weight and height is also \( r_{\text{weight, height}} = 0.8 \). --- If you have any more questions or need further clarification on correlation or other statistical concepts, feel free to ask!