M5_Golf Putting 2

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School

Georgia Institute Of Technology *

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Course

7406

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Industrial Engineering

Date

Jan 9, 2024

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pdf

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2

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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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