Chapter 8: Regression Wisdom

Question 1

Define ‘Outlier’.

Answer 1

Any data point that stands away from the others can be called an outlier. In regression, cases can be extraordinary in two ways: by standing far apart in the y-direction and having a large residual or by standing far apart in the x-direction and having high leverage.

Question 2

Define ‘Leverage’.

Answer 2

Data points whose x-values are far from the mean of x are said to exert leverage on a linear model. High-leverage points pull the line close to them, and so they can have a large effect on the line, sometimes completely determining the slope and intercept. With high enough leverage, their residual can be deceptively small.

Question 3

Define ‘Influential point’.

Answer 3

A point that, if omitted from the data, results in a very different regression model.

Question 4

Define ‘Extrapolation’.

Answer 4

Although linear models provide an easy way to predict values of y for a given value of x, it is unsafe to predict for values of x far from the ones used to find the linear model equation. At times, such extrapolations may pretend to see into the future, but the predictions should not be trusted.

Question 5

Define ‘Lurking variable’.

Answer 5

A variable that is not explicitly part of a model but affects the way the variables in the model appear to be related. Because we can never be certain that observational data are not hiding a lurking variable that influences the relationship between x and y, it is never safe to conclude that a linear model demonstrates a causal relationship, no matter how strong the linear association.

Question 6

Be careful when you interpret regressions based on summarized data or with restricted data ranges. What do they due to regressions?

Answer 6

Regressions with summaries tend to look stronger than the regression based on all the individual cases, whereas restricting the ranges of variables usually makes regressions weaker.