202211201933
Status:
Tags: Statistics Mathematics

Types

Linear Regression

Assumptions

  1. Linearity
  2. Homoscedasticity
    • Variance of residual is the same for any value of X
    • AKA heterogeneity of variances
  3. Independence
    • Observations are independent of each other
  4. Normality

Stepwise Regression

Forward selection

  • Start with no variables, test addition of each variable
    • Add variable whose inclusion gives most statistically significant improvement of fit
    • Repeat until none improve model to statistically significant extent
  • Drawbacks:
    • Variables whose statistical significance relies on a variable being held constant are not included

Backward elimination

  • Start with all candidate variables
    • Test deletion of each variable
    • Delete if loss gives most statistically insignificant deterioration of model fit
    • Repeat until no variables can be deleted without statistically insignificant loss of fit

Bidirectional elimination

  • Combination of forward & backward

Criticisms

  • Tests are biased, since they are based on the same data
  • May oversimplify real models of the data
  • Something to do with degrees of freedom

References