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

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