-Do heavier lifters tend to bench press more?
-Use a simple data set of lifters with body weight, training years, and bench press max.
-Apply simple linear regression and correlation to quantify the relationship.
Objective
R Code:Linear Regression (Body Weight vs Bench Max)
ggplot(Lifters, aes(x = BodyWeight, y = BenchMax)) +
geom_point(size = 4, color = "grey") +
geom_smooth(method = "lm", se = FALSE, color = "maroon", linewidth = 1.2) +
theme_minimal(base_size = 18) +
labs(title = "Linear Regression:BodyWeight vs BenchMax ",
x = "Body Weight lbs", y = "Predicted Bench Max lbs")
Linear Regression (Body Weight vs Bench Max)
Training Years vs Bench Press
3D Visualization: Body Weight, Training Years, Bench Max
Math: Regression and Correlation
\[ \hat{y} = \beta_0 + \beta_1 x \]
\[ r = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})} {\sqrt{\sum (x_i - \bar{x})^2 \sum (y_i - \bar{y})^2}} \]
- \(\beta_1\): slope (change in Bench Max per lb Body Weight)
- \(r\): strength of linear relationship
Correlation Summary
| Term | Value |
|---|---|
| Intercept | -10.950 |
| Slope | 1.200 |
| R-squared | 0.997 |
| Correlation (r) | 0.999 |
Conclusion
-Strong positive correlation between body weight and bench press strength.
-Heavier lifters tend to lift more; training years probably also contribute.
-Simple regression provides a clear, interpretable understanding of the strength trends.