Pitfalls of Regression (slides 43-52)

What is collinearity?

Two predictor variables are highly correlated, or even perfectly related to one another. This messes up the model.

What is extrapolation?

The model is used to make predictions outside the observed range of data.

• If this happens with the intercept, we can use “mean centering” to make it more interpretable or meaningful.

  • Subtract the mean of the X variable from every individual of X

What are outliers?

Values that are far away from most of the other values in the dataset.

What does leverage describe?

Describes an X value that is far away from its peers.

What does discrepancy describe?

Describes a Y value that is far away from its peers.

What happens when a data point has both high leverage and high discrepancy?

• Takes on a high “influence”

What is heteroscedasticity?

The model is more accurate for some values (ex. low ones) than others (ex. high ones)

• We want to see homoscedasticity, meaning “constant variance”

• We expect the range of errors to be the same regardless of whether we’re dealing with high values or low ones. We expect the variability or variance in the errors to be constant.