# invResPlot

From car v2.0-20
by John Fox

##### Inverse Response Plots to Transform the Response

For a `lm`

model, draws an inverse.response plot with the response $Y$ on the
vertical axis and the fitted values $\hat{Y}$
on the horizontal axis. Uses `nls`

to
estimate $\lambda$ in the function
$\hat{Y}=b_0+b_1Y^{\lambda}$.
Adds the fitted curve to the plot.
`invResPlot`

is an alias for `inverseResponsePlot`

.

- Keywords
- hplot, regression

##### Usage

```
inverseResponsePlot(model, lambda=c(-1,0,1), robust=FALSE, xlab=NULL, ...)
## S3 method for class 'lm':
inverseResponsePlot(model, lambda=c(-1,0,1), robust=FALSE,
xlab=NULL, labels=names(residuals(model)), ...)
invResPlot(model, ...)
```

##### Arguments

- model
- A
`lm`

regression object - lambda
- A vector of values for lambda. A plot will be produced with curves corresponding to these lambdas and to the least squares estimate of lambda
- xlab
- The horizontal axis label. If
`NULL`

, it is constructed by the function. - labels
- Case labels if labeling is turned on; see
`invTranPlot`

and`showLabels`

for arguments. - robust
- If TRUE, then estimation uses Huber M-estimates with the median absolute deviation to estimate scale and k= 1.345. The default is FALSE.
- ...
- Other arguments passed to
`invTranPlot`

and then to`plot`

.

##### Value

- As a side effect, a plot is produced with the response on the horizontal axis and fitted values on the vertical axis. Several lines are added to be plot as the ols estimates of the regression of $\hat{Y}$ on $Y^{\lambda}$, interpreting $\lambda$ = 0 to be natural logarithms. Numeric output is a list with elements
lambda Estimate of transformation parameter for the response RSS The residual sum of squares at the minimum if robust=FALSE. If robust = TRUE, the value of Huber objective function is returned.

##### References

Fox, J. and Weisberg, S. (2011)
*An R Companion to Applied Regression*, Second Edition, Sage.
Pendergast, L, and Sheather, S. (in press). On sensitivity of response plot
estimation of a robust estimation approach. *Scandinavian Journal of
Statistics*.
Weisberg, S. (2014) *Applied Linear Regression*, Fourth Edition, Wiley, Chapter 7.

##### See Also

##### Examples

```
m2 <- lm(rate ~ log(len) + log(ADT) + slim + shld + log(sigs1), Highway1)
invResPlot(m2)
```

*Documentation reproduced from package car, version 2.0-20, License: GPL (>= 2)*

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