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Linearity - Reasons for Screening Data
Many of the technics of standard statistical analysis are based on the assumption that the relationship, if any, between variables is linear. Measures of linear relationship such as the Pearson r, cannot detect any nonlinear relationship between variables.
In analyses that are somehow related to predicted values of variables, the analysis of linearity is primarily conducted by evaluating the residual plots. More specifically, this is done by looking at the standardized residual plots with residuals for each observation appearing on the horizontal axis and their standardized values along the vertical axis.
A second more crude method of assessing linearity is accomplished by inspecting the bivariate scatterplots. If the variables being analyzed are, both normally distributed and linearly related, then the resulting scatterplot would be of elliptical shape.
Models which make use of the smoothing techniques such as locally weighted regression to identify and represent the possible non-linear relationships between the explanatory and th
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