User:Songpengyx/sandbox

First of all, in order to create a regression model, graph is a definitely important tool to assist us to decide what we are supposed to do. In fact, regression diagnostics are used to check if a fitted mean or an assumption is related to the observed data. The basic concept of statistics is to decide the residuals or possible rescaled residuals. However, if the model is unable to provide a set of residuals that seem to be reasonable, some part of the model will call into problem, such as the assumed mean function or assumptions concerning the variance function. Additionally, the estimation of this study and other aspects of the analysis also need to cause an attention. If some data are deleted or missing, the observed statistics will change unexpectedly. This type of cases is called influential which places a very important role in the study of statistics so we need to learn how to use it to detect such cases. Last but not least, we will be required to study and use two relatively diagnostics statistics which are distance measures and leverage values. Although we focus on graphical diagnostics most of time, the numerical quantities are not supposed to be ignored because they are aiding us to interpret the meaning of the graphs.

Cook [ 1977, 1979 ] provided an approach to do this-utilizing a measure for the squared distance from the least-squares estimate in terms of all n points estimate Beta to the estimate acquired by removing the i th point, say the ith estimate Beta This distance measure is Cook’s distance.