# week7 - Diagnostics and Transformation for SLR In general...

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STA302/1001 week 7 1 Diagnostics and Transformation for SLR In general, it makes sense to base inference and conclusions only on valid models. So we need to make sure we are fitting an appropriate model. For this we need to plot the data! Example…

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STA302/1001 week 7 2 Influential Points, Outliers and Leverage Points Observations whose inclusion/exclusion result in substantial changes in the fitted model are said to be influential. A point can be outlying in any (or all) of the value of the explanatory variable, the dependent variable or its residual. Outlier with respect to the residual represents model failure, i.e., line doesn’t fit this point adequately. These are typically outliers with respect to the dependent variable. Outlier with respect to the explanatory variable are called leverage points . They may be influential, uniquely determine the regression coefficient and possibly cause the S.E. of the regression coefficient to be smaller than they would be if the point was removed. Textbook distinguish between “good” leverage points that follow the pattern of the data and “bad” leverage points that are influential.
STA302/1001 week 7 3 Quantifying Leverage To determine if a point is a leverage point we calculate the following…

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STA302/1001 week 7 4 Measuring Influence of the i th Observation There are three main measurements for assessing the influence of an observation. Each of these measures uses different aspect of the fitted model to assess the influence of an observation. Notation: Subscript ( i ) indicates that the i th observation has been deleted from the data and regression was re-fit using remaining n -1 data points.
5 Measurement I for Influence – DFBETAS This measure examines how estimates of β 0 and β 1 change with and without the i th observation. It is the difference in beta’s defined by…

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week7 - Diagnostics and Transformation for SLR In general...

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