avplot (Partial Regression Plot)

1. Compute the residuals of regressing the response variable against the indpendent variables but omitting X_i

2. Compute the residuals from regressing X_i against the remaining indpendent variables.

3. Plot the residuals from (1) against the residuals from (2).

Velleman and Welsch (see References below) express this mathematically as:

Y_.[i] versus X_i.[i]

where

Y_.[i] = residuals from regressing Y (the response variable) against all the indpendent variables except X_i
X_i.[i] = residuals from regressing X_i against the remaining indpependent variables.

Velleman and Welsch list the following useful properties for this plot:

1. The least squares linear fit to this plot has the slope _i and intercept zero.

2. The residuals from the least squares linear fit to this plot are identical to the residuals from the least squares fit of the original model (Y against all the independent variables including X_i).

3. The influences of individual data values on the estimation of a coefficient are easy to see in this plot.

4. It is easy to see many kinds of failures of the model or violations of the underlying assumptions (nonlinearity, heteroscedasticity, unusual patterns).

===> 선형성 진단에도 쓸수 있다. (acprplot이 더 적합하지만)

http://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/partregr.htm

아래는 avplot 과 cprplot과 acprplot의 차이다.