## Regression Diagnostics

## Usage

    influence.measures(lm.obj)
    summary.infl (object, digits = max(2, .Options$digits - 5), ...)
      print.infl (x, digits = max(3, .Options$digits - 4), ...)

    rstandard(lm.obj)
    rstudent(lm.obj)
    dfbetas(lm.obj)
    dffits(lm.obj)
    covratio(lm.obj)
    cooks.distance(lm.obj)
    hat(xmat)

## Arguments

`lm.obj` | the results returned by `lm`.
`xmat` | the `X' or design matrix.

## Description

This suite of functions can be used to compute some of the regression diagnostics discussed in Belsley, Kuh and Welsch (1980), and in Cook and Weisberg (1982).

The primary function is `influence.measures` which produces a class `"infl"` object tabular display showing the DFBETAS for each model variable, DFFITS, covariance ratios, Cook's distances and the diagonal elements of the hat matrix. Cases which are influential with respect to any of these measures are marked with an asterisk.

The functions `rstudent`, `dfbetas`, `dffits`, `covratio` and `cooks.distance` provide direct access to the corresponding diagnostic quantities.

## References

Belsley, D. A., E. Kuh and R. E. Welsch (1980). Regression Diagnostics. New York: Wiley.

Cook, R. D. and S. Weisberg (1982). Residuals and Influence in Regression. London: Chapman and Hall.

## See Also

`lm.influence`.

## Examples

    ## Analysis of the life-cycle savings data
    ## given in Belsley, Kuh and Welsch.
    data(savings)
    lm.SR <- lm(sr ~ pop15 + pop75 + dpi + ddpi, data = savings)
    summary(inflm.SR <- influence.measures(lm.SR))
    inflm.SR
    which(apply(inflm.SR$is.inf, 1, any)) # which observations `are' influential
    dim(dfb <- dfbetas(lm.SR))            # the 1st columns of influence.measures
    all(dfb == inflm.SR$infmat[, 1:5])
    rstudent(lm.SR)
    dffits(lm.SR)
    covratio(lm.SR)

    ## Huber's data [Atkinson 1985]
    xh <- c(-4:0, 10)
    yh <- c(2.48, .73, -.04, -1.44, -1.32, 0)
    summary(lmH <- lm(yh ~ xh))
    influence.measures(lmH)

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