Lesson plan
Partial leverage
In regression analysis, partial leverage (PL) is a measure of the contribution of the individual independent variables to the total leverage of each observation. That is, if h i is the i th element of the diagonal of the hat matrix, PL is a measure of how h i changes as a variable is added to the regression model. It is computed as: : \left(\mathrm{PL}_j\right)_i = \frac{\left(X_{j\bullet[j]}\right)_i^2}{\sum_{k=1}^n\left(X_{j\bullet[j]}\right)_k^2} where :j = index of independent variable :i = index of observation :X j·[j] = residuals from regressing X j against the remaining independent variables Note that the partial leverage is the leverage of the i th point in the partial regression plot for the j th variable. Data points with large partial leverage for an independent variable can exert undue influence on the selection of that variable in automatic regression model building procedures.
Article summary
In regression analysis, partial leverage (PL) is a measure of the contribution of the individual independent variables to the total leverage of each observation. That is, if h i is the i th element of the diagonal of the hat matrix, PL is a measure of how h i changes as a variable is added to the regression model. It is computed as: : \left(\mathrm{PL}_j\right)_i = \frac{\left(X_{j\bullet[j]}\right)_i^2}{\sum_{k=1}^n\left(X_{j\bullet[j]}\right)_k^2} where :j = index of independent variable :i = index of observation :X j·[j] = residuals from regressing X j against the remaining independent variables Note that the partial leverage is the leverage of the i th point in the partial regression plot for the j th variable. Data points with large partial leverage for an independent variable can exert undue influence on the selection of that variable in automatic regression model building procedures.
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
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Key claims and bibliography are generated from the same tracked claims and sources as the article page.