Residuals and fitted values

Summary

• Given data $x_1,x_2,…,x_n$ and $y_1,y_2,…,y_n$ and the OLS linear trendline

$$y=b_1+b_2x$$

• ( $b_1$ and $b_2$ are calculated using the OLS formula)
• The OLS fitted values are defined as

$${\hat{y}}_i=b_1+b_2x_i i=1,…,n$$

• The OLS residuals are defined as

$$e_i=y_i-{\hat{y}}_i=y_i-b_1-b_2x_i i=1,…,n$$

• The OLS RSS (residual Sum of Squares) is defined as

$$RSS=\sum_{i=1}^{n}{ e_i^2 }$$