Cluster 1 Results:

LR Slope: -0.007284025968538165

R-squared: 0.27525153202504027

t-statistic: -2.5409474310335876

p-value: 0.021099052456581946

Similarly for clusters 2 and 3…

Cluster 2 Results:

LR Slope: -0.0077117141767901794

R-squared: 0.36953339540415586

t-statistic: -3.156605168807558

p-value: 0.00576068502698579

Cluster 3 Results:

LR Slope: -0.01193051964700224

R-squared: 0.48944498115367974

t-statistic: -4.036966314785228

p-value: 0.0008558581836797252

Cluster 1: The average cone drill time for Power Players has been decreasing by approximately 0.0073 seconds each year. The R-squared value of 0.2752 suggests that about 28% of the variance in the average cone drill speed for this cluster can be explained by the year. The negative t-statistic and p-value suggest that there is a significant negative linear relationship between the year of the NFL Combine and the average cone drill speed. Therefore, we reject the null hypothesis and conclude that the average cone drill speed for Power Players has been decreasing over the years.

Cluster 2: Agile Players have also seen cone drill performance improve with their average completion time decreasing by approximately 0.0077 seconds each year. An R-squared value of 0.3695 suggests that about 37% of the variance in the average cone drill speed for this cluster can be explained by the year. The negative t-statistic and p-value suggest that there is a significant negative linear relationship between the year of the NFL Combine and the average cone drill speed. Therefore, we reject the null hypothesis and conclude that the average cone drill speed for Agile Players has been decreasing over the years.

Cluster 3: Hybrid Players have seen the greatest improvement of all with their average cone drill time decreasing by 0.0119 seconds each year. The R-squared value of 0.4894 suggests that about 49% of the variance in the average cone drill speed for this cluster can be explained by the year. The negative t-statistic and p-value suggest that there is a significant negative linear relationship between the year of the NFL Combine and the average cone drill speed. We again reject the null hypothesis and conclude that the average cone drill speed for Hybrid Players has been decreasing over the years.

To investigate these results further, we will plot all three clusters alongside their regression models for comparison.