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| 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, such extrapolation may pretend to see into the future, but the predictions should not be trusted |
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| any data point that stands away from the others; in a regression it can have a large residual or have high leverage |
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| data points whose x-values are far from the mean of x exert leverage on a linear model; pulls the line close to them, has large effect on the line, sometimes completely determining the slope and intercept, can make residuals deceptively small |
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| if omitting a point from the data results in a very different regression model, then that point is called an influential point |
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| a variable that is not explicitly part of a model but affects the way the variables in the model appear to be related |
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| we re-express data by taking the logarithm, the square root, the reciprocal, or some other mathematical operation on all values of a variable |
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| the Ladder of Powers places in order the effects that many re-expressions have on the data |
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