Women have always been underrepresented in movies and not until recently has the representation of women in movies improved. To investigate the improvement of female representation and its relationship with a movie's success, we propose a new measure, the female cast ratio, and compare it to the commonly used Bechdel test result. We employ generalized linear regression with $L_1$ penalty and a Random Forest model to identify the predictors that influence female representation, and evaluate the relationship between female representation and a movie's success in three aspects: revenue/budget ratio, rating, and popularity. Three important findings in our study have highlighted the difficulties women in the film industry face both upstream and downstream. First, female filmmakers, especially female screenplay writers, are instrumental for movies to have better female representation, but the percentage of female filmmakers has been very low. Second, movies that have the potential to tell insightful stories about women are often provided with lower budgets, and this usually causes the films to in turn receive more criticism. Finally, the demand for better female representation from moviegoers has also not been strong enough to compel the film industry to change, as movies that have poor female representation can still be very popular and successful in the box office.

中文翻译：

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随着时间的推移衡量电影中的女性代表性和影响

女性在电影中的代表性一直不足，直到最近女性在电影中的代表性才有所改善。为了研究女性代表性的提高及其与电影成功的关系，我们提出了一种新的衡量标准，即女性演员比例，并将其与常用的 Bechdel 测试结果进行比较。我们采用带有 $L_1$ 惩罚的广义线性回归和随机森林模型来识别影响女性代表性的预测因素，并从三个方面评估女性代表性与电影成功之间的关系：收入/预算比率、评级和受欢迎程度。我们研究中的三个重要发现突出了电影行业的女性在上游和下游面临的困难。首先，女性电影制作人，尤其是女性编剧，有助于电影获得更好的女性代表性，但女性电影制作人的比例非常低。其次，有潜力讲述关于女性的深刻故事的电影往往预算较低，这通常会导致电影反过来受到更多批评。最后，电影观众对更好的女性代表的需求也不足以迫使电影业做出改变，因为女性代表较差的电影在票房上仍然非常受欢迎和成功。