What is a well-performing mutual fund?

Apparently I may have had misunderstanding about how to define a well-performing mutual fund, that today I learn from my lectures that there are two sides to study if a mutual fund is a well-performing one: one is selectivity, the other is if the fund is following the market. There is a simple regression model to exam the performance of a mutual fund:

Once α>0 and β>0, the mutual fund is considered as a well-performing mutual fund. The term, , represents the return of the fund; and the term, , represents the return of the market. The estimator, β, represents the risk of the fund; usually when the market is performing well, a mutual fund is likely to hold more assets with higher risk levels, and vice versa; it also represents how well the fund is able to adapt to the market environment. The estimator, α, represents the return of the fund when the market return is zero, and is able to represent the ability of the fund manager.

However, this rule may not apply to other types of funds. Mutual funds cover many different types of assets; however, some types of funds do not cover such wide range of assets, and they also aim to boost their returns by conducting risky investment strategies. The assessment would be different, because when focusing at growth or other types of investment strategies (PE, hedging, quant) rather than value, the ideologies are different from managing a mutual fund.

Buying mutual funds may use this rule; however, when conducting private investment or managing other types of investment, this rule may not be appropriate to use. In addition, some studies find that funds are not selective that α is statistically insignificant.