Leverage

Leverage measures how unusual or extreme the explanatory variables are for each observation. Very roughly, a high leverage means that the explanatory variable has values that are different to other points in the dataset. In the case of simple linear regression, where there is only one explanatory value, this typically means values with a very high or very low explanatory value.

Here, you'll look at highly leveraged values in the model of house price versus the square root of distance from the nearest MRT station in the Taiwan real estate dataset.

Guess which observations you think will have a high leverage, then move the slider to find out.

Which statement is true?

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Introduction to Regression in R

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Introduction to Regression in R

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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!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

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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