Regression diagnostics and outliers

ABSTRACT If the regression model is correct and assumptions hold, inferences can be made confidently. Diagnostic techniques are designed to find contradictions between the assumptions of the model and the data at hand. The data set may contain extreme subsets that differ from the remaining of the data. Under the least squares method, a fitted line may be pulled toward on outlying observation because the sum of squares is minimized. This could cause a misleading fit if indeed the outlying observation is resulted from a mistake or other extraneous cause. It is therefore important to examine the outlying cases carefully and decide whether they should be retained or eliminated. It is reasonable to isolate outliers and to determine which parameter estimates are affected by them. In this work, agricultural activities of 60 countries were studied and a linear regression model was fitted. First of all single row effects were studied and influential observations were discovered. Then multiple row effects were calculated. At the end the results were interpreted together. In this thesis, by using the sample examined in the research, it was discovered which parameter estimate(s) was/were affected by the outliers. By investigating these effects, it was found that, the countries which were called outliers had special properties so they differed from the remaining of data. These properties give analysts important information about the interested variable(s). If the outliers are excluded from the model, the regression model can be fitted without causing any problems. But the relationship proposed by this new model doesn't reflect this property. Consequently, outliers give important information. So we shouldn't exclude them from the data set. Key Words: Least Squares Method, diagnostics, outlier and influential observations.