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