一元线性回归(SLR)

• 资源
• 实践

1 资源

• Using python statsmodels for OLS linear regression

• Introduction to Linear Regression Analysis(5th)-Douglas

• 数据集-百度云

2 模型

Population Regression Model: $y = \beta_0 + \beta_1 x + \epsilon$

Sample Regression Model: $y_i = \beta_0 + \beta_1 x_i + \epsilon_i, \quad i = 1,2,\cdots,n$

Simple Linear Regression Model: $\hat{y} = \hat{\beta_0} + \hat{\beta_1} x$

the least - squares criterion is $$S(\beta_0, \beta_1) = \sum_{i = 0}^{n} (y_i - \beta_0 - \beta_1 x_i)^2$$

Residual: $e_i = y_i - \hat{y_i} = y_i - (\hat{\beta_0} + \hat{\beta_1} x), \quad i = 1,2,\cdots,n$

3 问题

after fit:

1. How well does this equation fi t the data?
2. Is the model likely to be useful as a predictor?
3. Are any of the basic assumptions (such as constant variance and uncorrelated errors) violated, and if so, how serious is this?

4 实践