Lecture+1+Review+SLR

# I i i i i i the error term the unobservable is not

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: residual is not the same as the error term, since ˆˆ ˆ u = y − α − β x , whereas u = y − α − β x (i = 1, 2,..., n) . i • i i i i i The error term (the unobservable) is not observed, while residual is observed. ˆˆˆ The sample regression function (the OLS regression line): Y = α + β X . ˆ ˆ Recall residual is defined as ui = yi − yi . It is the difference between the true value yi ˆ and the predicted value yi . Residual is the part that is not explained by the ˆˆ ˆ regression line yi = α + β xi . • • ˆˆˆˆ ˆ So yi = yi + ui = α + β xi + ui (i = 1, 2,..., n) ˆ Note that ui ≠ ui , i.e., residual is not the same as the error term, since ˆˆ ˆ u = y − α − β x , whereas u = y − α − β x (i = 1, 2,..., n) . i • i i i i i The error term (the unobservable) is not observed, while residual is observed. Figure: Scatter plot, the estimated regression line, and residuals Ordinary Least Squares (OLS) ˆ ˆ How do we calculate α and β ? We need to choose a criterion. OLS Criterion Intuitively, OLS fits a line thro...
View Full Document

Ask a homework question - tutors are online