M5_Golf Putting 2
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School
Georgia Institute Of Technology *
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Course
7406
Subject
Industrial Engineering
Date
Jan 9, 2024
Type
Pages
2
Uploaded by schooler18
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**Title: Predicting Golf Putting Success with Logistic Regression**
**Instructor: Dr. Yajun Mei**
**Objective:**
To leverage logistic regression for predicting golf putting success rates and understand its
practical application.
**Golf Putting Data Analysis:**
- **Data Source:** Berry’s book on professional golf putting statistics.
- **Data Points:** For example, at less than 2 feet, there were 1,443 putts with 1,346 successes,
indicating a 93.28% success rate.
- **Challenge:** Predict the success rate for putts at a given distance 'x'.
**Limitation of Linear Models:**
- Previously, we observed that linear regression models may predict success rates outside the
0-100% range, leading to unrealistic probabilities.
**Introduction to Logistic Regression:**
- **Modeling Approach:** Model the number of successes 'Yi' as a binomial distribution with
parameters 'ni' (total trials) and 'pi i' (success rate).
- **Link Function:** Use a logistic link function to relate the log-odds of 'pi i' to the distance 'xi',
allowing for predictions within a 0-1 range.
**Implementing Logistic Regression in R:**
- **Data Preparation:** Define variables for distance, trials, and successes.
- **Model Fitting:** Use two methods to fit the model:
1. Define a two-dimensional variable with successes and failures (`trials - successes`).
2. Define the response as the success rate with weights equal to the number of trials.
- **Model Output:** The R summary shows significant coefficients for both the intercept and
distance, confirming their influence on putting success.
**Model Interpretation:**
- The logistic regression equation is: \( \log\left(\frac{p}{1-p}\right) = \beta_0 + \beta_1 \times
\text{distance} \).
- The model predicts a decrease in success rate with increasing distance, aligning with
expectations.
**Visual Representation and Prediction:**
- **Plotting:** Estimate success probabilities for distances up to 40 feet.
- **Predict Function:** Use `predict` with `type = "response"` to obtain estimated probabilities.
**Comparison to Linear Models:**
- Logistic regression ensures probabilities remain between 0 and 100% and approach zero for
long putts.
- However, the model predicts a success rate of only 90.3% for zero distance, which may not
align with practical golf putting outcomes.
**Summary:**
This lecture showcased how logistic regression provides more realistic success rate predictions
than multiple linear regression for golf putting, despite some limitations.
**Closing Remarks:**
Understanding the strengths and weaknesses of logistic regression is essential for its practical
application in sports analytics and beyond. Thank you for your attention.
---
In this detailed lecture summary, we dissect the application of logistic regression in predicting
golf putting outcomes, emphasizing the model's practicality and inherent limitations when
applied to real-world data.
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