* always return that original instance.
   */
  public abstract LinearTransformation inverse();

  private static final class RegularLinearTransformation extends LinearTransformation {

    final double slope;
    final double yIntercept;

    @LazyInit @Nullable LinearTransformation inverse;

    RegularLinearTransformation(double slope, double yIntercept) {
      this.slope = slope;

    }
    double xSumOfSquaresOfDeltas = xStats.sumOfSquaresOfDeltas();
    if (xSumOfSquaresOfDeltas > 0.0) {
      if (yStats.sumOfSquaresOfDeltas() > 0.0) {
        return LinearTransformation.mapping(xStats.mean(), yStats.mean())
            .withSlope(sumOfProductsOfDeltas / xSumOfSquaresOfDeltas);
      } else {
        return LinearTransformation.horizontal(yStats.mean());
      }
    } else {

    }
    double xSumOfSquaresOfDeltas = xStats.sumOfSquaresOfDeltas();
    if (xSumOfSquaresOfDeltas > 0.0) {
      if (yStats.sumOfSquaresOfDeltas() > 0.0) {
        return LinearTransformation.mapping(xStats.mean(), yStats.mean())
            .withSlope(sumOfProductsOfDeltas / xSumOfSquaresOfDeltas);
      } else {
        return LinearTransformation.horizontal(yStats.mean());
      }
    } else {