Job Stayers: y = 0.0614x + 4.1186 Job Changers: y = 0.0169x + 10.506 What do the two regression equations indicate about the independent variables Job Stayers and Job Changers?

The two regression equations provided represent the relationships between a dependent variable \( y \) and an independent variable \( x \) for two groups: Job Stayers and Job Changers. Let's break down what each equation indicates. 1. **Job Stayers: \( y = 0.0614x + 4.1186 \)** - **Slope (0.0614):** The positive slope indicates that there is a positive relationship between the independent variable \( x \) and the dependent variable \( y \) for Job Stayers. Specifically, for each one-unit increase in \( x \), \( y \) increases by approximately 0.0614 units. This suggests that as some aspect associated with \( x \) increases (could be years of experience, tenure, etc.), the corresponding outcome \( y \) also increases but at a relatively modest rate. - **Y-intercept (4.1186):** This value represents the expected value of \( y \) when \( x \) is zero. It provides a baseline level of \( y \) for Job Stayers, indicating that even without any contributions from \( x \), \( y \) starts at approximately 4.1186. 2. **Job Changers: \( y = 0.0169x + 10.506 \)** - **Slope (0.0169):** The slope for Job Changers is also positive but much smaller than that of Job Stayers. This indicates a weaker positive relationship between \( x \) and \( y \) for Job Changers. For each one-unit increase in \( x \), \( y \) increases by only about 0.0169 units. This suggests that the effect of \( x \) on \( y \) is less pronounced for Job Changers compared to Job Stayers. - **Y-intercept (10.506):** Similar to the first equation, this value suggests that when \( x \) is zero, the expected value of \( y \) for Job Changers is approximately 10.506. This is higher than the y-intercept for Job Stayers, indicating that the baseline level of \( y \) for Job Changers is greater. ### Comparison and Interpretation: - **Strength of Relationship:** The slope for Job Stayers is significantly steeper than that for Job Changers, indicating that whatever \( x \) represents has a more substantial impact on the outcomes for Job Stayers compared to Job Changers. - **Baseline Values:** The Job Changers start with a higher baseline value (y-intercept) than Job Stayers, suggesting that Job Changers may have some advantages or different characteristics compared to Job Stayers before considering the effect of \( x \). - **Implications:** If these equations relate to a specific measure (such as salary, job satisfaction, performance, etc.), you can infer that Job Stayers may benefit more from increases in \( x \) while Job Changers start from a better baseline but experience less growth in \( y \) as \( x \) increases. In conclusion, these regression equations highlight different growth patterns and baseline levels for two distinct groups, with Job Stayers potentially being more responsive to changes in \( x \) than Job Changers.