Build regression model from a set of candidate predictor variables by entering and removing predictors based on akaike information criteria, in a stepwise manner until there is no variable left to enter or remove any more.

## Usage

```
ols_step_both_aic(model, ...)
# S3 method for default
ols_step_both_aic(
model,
include = NULL,
exclude = NULL,
progress = FALSE,
details = FALSE,
...
)
# S3 method for ols_step_both_aic
plot(x, print_plot = TRUE, details = TRUE, digits = 3, ...)
```

## Arguments

- model
An object of class

`lm`

.- ...
Other arguments.

- include
Character or numeric vector; variables to be included in selection process.

- exclude
Character or numeric vector; variables to be excluded from selection process.

- progress
Logical; if

`TRUE`

, will display variable selection progress.- details
Logical; if

`TRUE`

, details of variable selection will be printed on screen.- x
An object of class

`ols_step_both_*`

.- print_plot
logical; if

`TRUE`

, prints the plot else returns a plot object.- digits
Number of decimal places to display.

## Value

List containing the following components:

- model
final model; an object of class

`lm`

- metrics
selection metrics

- others
list; info used for plotting and printing

## References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

## See also

Other both direction selection procedures:
`ols_step_both_adj_r2()`

,
`ols_step_both_r2()`

,
`ols_step_both_sbc()`

,
`ols_step_both_sbic()`

## Examples

```
if (FALSE) {
# stepwise regression
model <- lm(y ~ ., data = stepdata)
ols_step_both_aic(model)
# stepwise regression plot
model <- lm(y ~ ., data = stepdata)
k <- ols_step_both_aic(model)
plot(k)
# selection metrics
k$metrics
# final model
k$model
# include or exclude variables
# force variable to be included in selection process
model <- lm(y ~ ., data = stepdata)
ols_step_both_aic(model, include = c("x6"))
# use index of variable instead of name
ols_step_both_aic(model, include = c(6))
# force variable to be excluded from selection process
ols_step_both_aic(model, exclude = c("x2"))
# use index of variable instead of name
ols_step_both_aic(model, exclude = c(2))
# include & exclude variables in the selection process
ols_step_both_aic(model, include = c("x6"), exclude = c("x2"))
# use index of variable instead of name
ols_step_both_aic(model, include = c(6), exclude = c(2))
}
```