
PARTIAL RESIDUAL PLOTName:
Partial residual plots attempt to show the relationship between a given independent variable and the response variable given that other independent variables are also in the model. Partial residual plots are formed as:
where
\( \hat{\beta}_{i} \) = regression coefficient from the ith independent variable in the full model X_{i} = the ith independent variable Partial residual plots are widely discussed in the regression diagnostics literature (e.g., see the References section below). Although they can often be useful, be aware that they can also fail to indicate the proper relationship. In particular, if X_{i} is highly correlated with any of the other independent variables, the variance indicated by the partial residual plot can be much less than the actual variance. These issues are discussed in more detail in the references given below. Dataplot provides two forms for the partial residual plot. You can generate either a single partial residual plot or you can generate a matrix of partial residual plots (one plot for each independent variable in the model). For the matrix form of the command, a number of SET FACTOR PLOT options can be used to control the appearance of the plot (not all of the SET FACTOR PLOT options apply). These are discussed in the Notes section below. The CCPR plot is a variation of the PARTIAL RESIDUAL PLOT. Enter HELP CCPR PLOT for details.
<SUBSET/EXCEPT/FOR qualification> where <y> is the response variable; <x1> ... <xk> are the independent variables; <xi> is the independent variable for which the partial residual plot is being generated (note that <xi> must be one of the variables listed in <x1> ... <xk>; and where the <SUBSET/EXCEPT/FOR qualification> is optional. This is the syntax for generating a single partial residual plot.
<SUBSET/EXCEPT/FOR qualification> where <y> is the response variable; <x1> ... <xk> are the independent variables; and where the <SUBSET/EXCEPT/FOR qualification> is optional. This syntax is used to generate a matrix of partial residual plots.
MATRIX PARTIAL RESIDUAL PLOT Y X1 X2 X3 X4
PARTIAL RESIDUAL PLOT Y X1 X2 X3 X4 X2 SUBSET TAG > 2
Neter, Wasserman, and Kunter (1990), "Applied Linear Statistical Models", 3rd ed., Irwin. Draper and Smith (1998), "Applied Regression Analysis", 3rd. ed., John Wiley. Cook and Weisberg (1982), "Residuals and Influence in Regression", Chapman and Hall. Belsley, Kuh, and Welsch (1980), "Regression Diagnostics", John Wiley. Velleman and Welsch (1981), "Efficient Computing of Regression Diagnostiocs", The American Statistician, Vol. 35, No. 4, pp. 234242.
SKIP 25 READ HALD647.DAT Y X1 X2 X3 X4 . MULTIPLOT CORNER COORDINATES 5 5 95 95 MULTIPLOT SCALE FACTOR 2 LINE BLANK CHARACTER X X1LABEL DISPLACEMENT 12 Y1LABEL DISPLACEMENT 12 TIC OFFSET UNITS SCREEN TIC OFFSET 5 5 . MATRIX PARTIAL RESIDUAL PLOT Y X1 X2 X3 X4
 
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Date created: 8/19/2002 