Home run!

Regression to the mean is an important concept in many areas, including sports.

Here you can see a dataset of baseball batting data in 2017 and 2018. Each point represents a player, and more home runs is better. A naive prediction might be that the performance in 2018 would be that it is the same as the performance in 2017. That is, a linear regression would lie on the "y equals x" line.

Explore the plot and make predictions. What does regression to the mean say about the number of home runs in 2018 for a player who was very successful in 2017?

This exercise is part of the course

Introduction to Regression in R

Hands-on interactive exercise

Turn theory into action with one of our interactive exercises

This exercise is part of the course

Introduction to Regression in R

IntermediateSkill Level

4.8+

Start Course for Free

You’ll learn the basics of this popular statistical model, what regression is, and how linear and logistic regressions differ. You’ll then learn how to fit simple linear regression models with numeric and categorical explanatory variables, and how to describe the relationship between the response and explanatory variables using model coefficients.

Exercise 1: A tale of two variables Exercise 2: Which one is the response variable?Exercise 3: Visualizing two variables Exercise 4: Fitting a linear regression Exercise 5: Estimate the intercept Exercise 6: Estimate the slope Exercise 7: Linear regression with lm()Exercise 8: Categorical explanatory variables Exercise 9: Visualizing numeric vs. categorical Exercise 10: Calculating means by category Exercise 11: lm() with a categorical explanatory variable

In this chapter, you’ll discover how to use linear regression models to make predictions on Taiwanese house prices and Facebook advert clicks. You’ll also grow your regression skills as you get hands-on with model objects, understand the concept of "regression to the mean", and learn how to transform variables in a dataset.

Exercise 1: Making predictions Exercise 2: Predicting house prices Exercise 3: Visualizing predictions Exercise 4: The limits of prediction Exercise 5: Working with model objects Exercise 6: Extracting model elements Exercise 7: Manually predicting house prices Exercise 8: Using broom Exercise 9: Regression to the mean Exercise 10: Home run!

Current Exercise

Exercise 11: Plotting consecutive portfolio returns Exercise 12: Modeling consecutive returns Exercise 13: Transforming variables Exercise 14: Transforming the explanatory variable Exercise 15: Transforming the response variable too

In this chapter, you’ll learn how to ask questions of your model to assess fit. You’ll learn how to quantify how well a linear regression model fits, diagnose model problems using visualizations, and understand the leverage and influence of each observation used to create the model.

Exercise 1: Quantifying model fit Exercise 2: Coefficient of determination Exercise 3: Residual standard error Exercise 4: Visualizing model fit Exercise 5: Residuals vs. fitted values Exercise 6: Q-Q plot of residuals Exercise 7: Scale-location Exercise 8: Drawing diagnostic plots Exercise 9: Outliers, leverage, and influence Exercise 10: Leverage Exercise 11: Influence Exercise 12: Extracting leverage and influence

Learn to fit logistic regression models. Using real-world data, you’ll predict the likelihood of a customer closing their bank account as probabilities of success and odds ratios, and quantify model performance using confusion matrices.

Exercise 1: Why you need logistic regression Exercise 2: Exploring the explanatory variables Exercise 3: Visualizing linear and logistic models Exercise 4: Logistic regression with glm()Exercise 5: Predictions and odds ratios Exercise 6: Probabilities Exercise 7: Most likely outcome Exercise 8: Odds ratio Exercise 9: Log odds ratio Exercise 10: Quantifying logistic regression fit Exercise 11: Calculating the confusion matrix Exercise 12: Measuring logistic model performance Exercise 13: Accuracy, sensitivity, specificity Exercise 14: Congratulations