The Imhof Approximations method uses a new distribution to estimate values in linear models, aiming to provide better approximations for certain estimators. By using a different distribution based on sample data moments, it can improve accuracy compared to traditional methods. The approach involves approximating the estimator using Taylor series and Edgeworth distributions, with potential errors from the approximation process. This method is particularly useful for cases with small sample sizes or high error variance. Overall, the Imhof Approximations technique offers a more precise way to estimate values in linear models.