Amemiya's prediction error.

## Details

Amemiya's Prediction Criterion penalizes R-squared more heavily than does adjusted R-squared for each addition degree of freedom used on the right-hand-side of the equation. The lower the better for this criterion.

$$((n + p) / (n - p))(1 - (R^2))$$

where *n* is the sample size, *p* is the number of predictors including the intercept and
*R^2* is the coefficient of determination.

## References

Amemiya, T. (1976). Selection of Regressors. Technical Report 225, Stanford University, Stanford, CA.

Judge, G. G., Griffiths, W. E., Hill, R. C., and Lee, T.-C. (1980). The Theory and Practice of Econometrics. New York: John Wiley & Sons.

## Examples

```
model <- lm(mpg ~ disp + hp + wt + qsec, data = mtcars)
ols_apc(model)
#> [1] 0.2259134
```