1. Model evaluation

A good model:

• is not overly complicated.
• meets the four conditions of the linear regression model.
• allows you to answer your research question of interest.

Some criteria for evaluation:

• Adjusted R2（大好）
• MSE（小好）
  • Mean Square Error
  • SSE/(n-#params)
  • 和Adjusted R2等价
• RSE（小好）
  • Residual Standard Error
  • sqrt(SSE/(n-#params))
  • 其实residual e_i的真实标准误为「RSE×(1-h_ii)」
• Information criterion（小好，其中p为参数数量，包括截距项）
  • AIC = -2ln(L)+2p
  • BIC = -2ln(L) + pln(n)

2. Model building (variable selection)

2.1 Backward elimination

从全自变量开始，每次扔掉一个p值大自变量，直到模型中所有自变量的p值都足够小。过程如下：

1. Select a significance level ATR(alpha-to-remove)
2. Fit the full model with all possible regressors
3. Read the summary and find the regressor with highest p-value:
   • If p > SLS: remove the regressor and continue
   • If p ≤ SLS: stop, keep current model

2.2 Forward selection

每次挑一个p值小的自变量，直到p值太大、没有自变量可以进入模型。过程如下：