Overview of this Lesson
In this lesson we'll look at some of the main things that can go wrong with a multiple linear regression model. We'll also consider methods for overcoming some of these pitfalls. In particular, we'll cover:
- Nonconstant variance and weighted least squares
- Autocorrelation and time series methods
- Multicollinearity, which exists when two or more of the predictors in a regression model are moderately or highly correlated with one another.
- Excluding important predictor variables
- Missing data
- Power and sample size
|Key Learning Goals for this Lesson:
- Know the main issues surrounding nonconstant variance.
- Use weighted least squares to mitigate some nonconstant variance problems.
- Know the main issues surrounding autocorrelation.
- Use time series methods to mitigate autocorrelation problems.
- Know what multicollinearity means.
- Distinguish between structural multicollinearity and data-based multicollinearity.
- Understand the effects of uncorrelated predictors on various aspects of regression analyses.
- Understand the effects of multicollinearity on various aspects of regression analyses.
- Understand variance inflation factors and how to use them to help detect multicollinearity.
- Know the two ways of reducing data-based multicollinearity.
- Understand how centering the predictors in a polynomial regression model helps to reduce structural multicollinearity.
- Know the main issues surrounding other regression pitfalls, including overfitting, excluding important predictor variables, extrapolation, missing data, and power and sample size.