Regression Wisdom

Regression Wisdom - Transcript

Chapter 9 Regression Wisdom
Prediction is difficult especially about the future
Niels Bohr
Danish Physicist

Sifting Residuals for Groups


No regression analysis is complete without a display of the residuals


Is the linear model reasonable



Residuals are what is left over after the model describes the relationship


Reveal subtleties Additional details that confirm Reveal violations of regression conditions



Look a histogram of the residuals

Subsets


Another condition for fitting models


All data must come from the same group



If you discover that there is more than 1 group in a regression


Analyze the groups separately Use a different model for each group OR use the original model and note the different groups

Getting the Bends


Fundamental assumption for working with linear models


The relationship modeled is in fact linear



Sometimes it is hard to tell from the scatterplot


Plot regression residuals against predicted values to see if there is a bend The residual plot should have NO pattern if a linear model is appropriate

Extrapolation Reaching Beyond the Data


Linear models give a predicted value for each case in the data


Put a new x value into the equation The equation gives a predicted y value



The farther the x values lie from the data we used to build the regression the less we should trust the predicted y value

Extrapolation


Extrapolation


The use of a regression line for prediction outside the domain of values of x Extrapolation requires the assumption that the x y relationship never changes even at extreme values of y



NOT to be trusted


Predicting the Future




When the x variable in a linear model is time extrapolation is an attempt to predict the future If you must extrapolate into the future be wary


Don t believe that the prediction will come true

Outliers


Outliers strongly influence a regression


Outlier any point that stands away from the other data points Point that falls far from the regression line Compare the regression models with and without outlier Can especially influence regression model High Leverage



Model outliers




x Outliers


Influential Points


Influential points can hide in residual plots Points with high leverage pull the line close to them


Small residuals Look at the original scatterplot Find the regression model with and without the point s



To find influential points


Lurking Variables and Causation




With observational data there is no way to be sure that a lurking variable is not the cause of any apparent association Do NOT infer causality from a regression Resist the temptation to conclude that x causes y from a regression no matter how obvious that conclusion seems to you

Working with Summary Values


Scatterplots of statistics summarized over groups tend to show less variability than would be seen if we measured the same variable on individuals


Show less scatter Can give a false impression of how well a line summarizes the data

What Can Go Wrong


Make sure the relationship is straight


Check the residual plot Be cautious of extrapolating beyond the x values of the data Don t trust predicted values when x variable is time



Beware of extrapolating




Be on guard for different groups in your regression


Look at a histogram of the residual values

What Can Go Wrong


Look for outliers Beware of high leverage points especially influential ones Consider comparing two regressions


One with outlier and one without



Treat outliers honestly Beware of lurking variables Watch out for summary data