# raintest: Rainbow Test In lmtest: Testing Linear Regression Models

 raintest R Documentation

## Rainbow Test

### Description

Rainbow test for linearity.

### Usage

```raintest(formula, fraction = 0.5, order.by = NULL, center = NULL,
data=list())
```

### Arguments

 `formula` a symbolic description for the model to be tested (or a fitted `"lm"` object). `fraction` numeric. The percentage of observations in the subset is determined by `fraction*n` if `n` is the number of observations in the model. `order.by` Either a vector `z` or a formula with a single explanatory variable like `~ z`. The observations in the model are ordered by the size of `z`. If set to `NULL` (the default) the observations are assumed to be ordered (e.g., a time series). If set to `"mahalanobis"` then the observations are ordered by their Mahalanobis distances from the mean regressor. `center` numeric. If `center` is smaller than 1 it is interpreted as percentages of data, i.e. the subset is chosen that `n*fraction` observations are around observation number `n*center`. If `center` is greater than 1 it is interpreted to be the index of the center of the subset. By default `center` is 0.5. If the Mahalanobis distance is chosen `center` is taken to be the mean regressor, but can be specified to be a `k`-dimensional vector if `k` is the number of regressors and should be in the range of the respective regressors. `data` an optional data frame containing the variables in the model. By default the variables are taken from the environment which `raintest` is called from.

### Details

The basic idea of the Rainbow test is that even if the true relationship is non-linear, a good linear fit can be achieved on a subsample in the "middle" of the data. The null hypothesis is rejected whenever the overall fit is significantly worse than the fit for the subsample. The test statistic under H_0 follows an F distribution with `parameter` degrees of freedom.

Examples can not only be found on this page, but also on the help pages of the data sets `bondyield`, `currencysubstitution`, `growthofmoney`, `moneydemand`, `unemployment`, `wages`.

### Value

A list with class `"htest"` containing the following components:

 `statistic` the value of the test statistic. `p.value` the p-value of the test. `parameter` degrees of freedom. `method` a character string indicating what type of test was performed. `data.name` a character string giving the name(s) of the data.

### References

J.M. Utts (1982), The Rainbow Test for Lack of Fit in Regression. Communications in Statistics – Theory and Methods 11, 2801–2815.

W. Krämer & H. Sonnberger (1986), The Linear Regression Model under Test. Heidelberg: Physica

`lm`

### Examples

```x <- c(1:30)
y <- x^2 + rnorm(30,0,2)
rain <- raintest(y ~ x)
rain
## critical value
qf(0.95, rain\$parameter, rain\$parameter)
```

lmtest documentation built on March 22, 2022, 1:06 a.m.