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influence |
Residuals and influence for regression |

**DESCRIPTION**- Computes leverage, studentized and standardized residuals, dfbetas and Cook's distance for a linear model, generalized linear model or generalized additive model.
**USAGE**`inf <- influence(lm.obj)`

plot.t(inf)

plot.d(inf)**REQUIRED ARGUMENTS**`lm.obj`object of class lm or which inherits from lm. `plot.t`and`plot.d`take as argument the output of`influence`, which is a dataframe with named columns.**VALUE**`influence`returns a data frame with the following components: h - leverage values, z - studentized residuals, t - externally studentized residuals, d - Cook's distance. There is also one component for each term in the linear model giving the dfbetas.**SIDE EFFECTS**`plot.t`plots the externally studentized residuals, together with Bonferroni simultaneous 95% confidence bands.`plot.d`plots the Cook's distances.**DETAILS**- The leverages
*h*measure how unusual are the*x*-values for each observation, i.e., the potential of that point to be influential.The studentized residuals

*z*are approximately standard normal residuals, while the externally studentized residuals*t*are score test statistics for testing each point an outlier. Any point whose externally studentized residuals extends beyond the confidence bands is formally judged to be an outlier at the 5% level.Cook's distance measures the overall influence of each observation on the regression coefficients, including the intercept. The dfbetas measure the influence of each observation on each of the individuals regression coefficients, excluding the intercept. Specifically the dfbetas are the number of standard errors by which the coefficient changes when that observation is added to the regression. Cook's distance is roughly the average of the squares of the dfbetas.

The results for generalized linear models and generalized additive models are approximate.

**REFERENCES**- Hamilton, L. C. (1992).
*Regression with graphics*. Duxbury, Belmont, CA.

Weisberg, S. (1985).*Applied linear regression, 2nd Edition*. Wiley, New York. **EXAMPLES**`lm.yx <- lm(y~x)``inf <- influence(lm.yx)``plot.t(inf)``plot.d(inf)`

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Gordon Smyth.
Copyright © 1996-2016. *Last modified:
10 February 2004*