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Simple Linear Regression - Assumption Violations
The three assumptions that should be strictly heeded in applying least squares linear regression are that
Y and X are truly linearly related
e
i
s must not depend upon one another
variability of the e
i
s must be constant
Various graphs can be used to
check these assumptions
. However, what happens when the data indicate a possible violation? If the graph of Y versus X is not linear, a
transformation
of Y and/or X may "straighten" things out. If a trend exists in the graph of studentized residuals versus X it may be that the data were collected improperly (i.e., not "randomly") or that an additional variable may be important in explaining the variation in Y (requiring
multiple regression
). When the graph of studentized residuals versus X shows the variability to change as X changes, a transformation or
weighted least squares
may provide a solution. It is an unfortunate fact that solving one violation may, however, create another.
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