PulsePlay, a mobile sports game, noticed that players who spend more time in training mode tend to win more ranked matches. The product team wants to know whether training time actually causes better performance, or whether the relationship is only correlational.
You are given summary statistics from 200 players. First, quantify the observed association between weekly training hours and weekly ranked wins. Then assess whether this proves causation, especially after accounting for player skill level as a potential confounder.
| Metric | Value |
|---|---|
| Number of players | 200 |
| Correlation between training hours and ranked wins | 0.42 |
| Significance level | 0.05 |
| Mean training hours per week | 6.8 |
| SD of training hours | 2.4 |
| Mean ranked wins per week | 15.2 |
| SD of ranked wins | 5.1 |
| Simple regression slope: wins on training hours | 0.89 |
| Multiple regression slope after controlling for skill rating | 0.18 |
| Standard error of adjusted slope | 0.11 |
| Additional context | Top-skill players are more likely to use training mode |