tailieunhanh - Kinh tế ứng dụng_ Lecture 3: Outliers, Leverage and Influence

1) Introduction The estimates of the regression parameters are influenced by a few extreme observations. The residual plot may let us pick out, which the individual data points are high or low. We may use the residual plot to find the outlier, which are inadequately captured by the regression model itself. | Applied Econometrics 1 Outliers Leverage and Influence Applied Econometrics Lecture 3 Outliers Leverage and Influence Life is the art of drawing sufficient conclusions from insufficient premises SAMUEL BUTLER 1 Introduction The estimates of the regression parameters are influenced by a few extreme observations. The residual plot may let us pick out which the individual data points are high or low. We may use the residual plot to find the outlier which are inadequately captured by the regression model itself. 2 Identification of outliers The percentiles that cut the data up into four quarters have special names The 25 th percentiles and the 75th percentiles are called the lower and upper quartiles QL and QU The lower quartile will be the integer n 1 2 1 2 value from the bottom of the ordered list. the upper quartile is the integer n 1 2 1 2 value from the top A data point Y0 is considered to be an outliers if Yo IQR or Yo Qu IQR where IQR is the inter - quartile range IQR QU - QL Source Hoaglin 1983 3 Outliers An outlier is a point which is far removed from its fitted value . has large residual . Large in this context does not refer to the absolute size of a residual but to its size relative to most of the other residuals in the regression. When a point is an outlier in univariate analysis it is defined with reference to its own mean. When a point is an outlier in bivariate analysis it has a large residual . Y value is far removed from its fitted value . Apart from the graphical methods we can also rely on special statistics to detect outliers. In order to compare the large residual to the other residual we may calculate the standardized residual which is simply the residual divided by the standard error of the estimate ei s . But an outlier in the data set will inflate the standard error of the regression. Hence we use the studentized residual Written by Nguyen Hoang Bao May 20 2004 Applied Econometrics 2 Outliers Leverage and Influence ti s i ạ 1