Model

I used the same model for all graphs, but a different formula for yardage.

I used a Gaussian Predictive Model (GPM) to calculate the average score to par, driving distance, and course yardage based on data from 91 PGA golf courses.

For the first two graphs -

The model follows the formula:

\[ y_i = \mu + \epsilon_i \]

Where:

y_i is the average score or driving distance of course i.
\(\mu\) is the average score or driving distance across all PGA courses.
The error term i, the difference between the observed and predicted value, follows a normal distribution with mean 0 which can be written as:

\[ \epsilon_i \sim \mathcal{N}(0, \sigma^2) \]

For the last graph, the model follows the formula

\[ score_i = \beta_0 + \beta_1 \cdot yardage_i + \epsilon_i \] Where:

\(\beta_0\) is the intercept term
\(\beta_1\) is the coefficient for the yardage
yardage_i is the yardage for the i-th observation
\(\epsilon_i\), the error term, is difference between the observed and predicted value, follows a normal distribution with mean 0 which can be written as:

\[ \epsilon_i \sim \mathcal{N}(0, \sigma^2) \]

Details about results of the model for the first graph -

Characteristic	Beta	95% CI ¹
(Intercept)	-0.01	-0.33, 0.32
¹ CI = Credible Interval

Details about results of the model for the second graph -

Characteristic	Beta	95% CI ¹
(Intercept)	288	287, 290
¹ CI = Credible Interval

Details about results of the model for third graph -

Characteristic	Beta	95% CI ¹
(Intercept)	7,221	7,183, 7,261
¹ CI = Credible Interval