This paper presents the application of a new semi-analytical method of linear regression for Poisson count data to COVID-19 events. The regression is based on the Bonamente and Spence (2022) maximum-likelihood solution for the best-fit parameters, and this paper introduces a simple analytical solution for the covariance matrix that completes the problem of linear regression with Poisson data. The analytical nature for both parameter estimates and their covariance matrix is made possible by a convenient factorization of the linear model proposed by J. Scargle (2013). The method makes use of the asymptotic properties of the Fisher information matrix, whose inverse provides the covariance matrix. The combination of simple analytical methods to obtain both the maximum-likelihood estimates of the parameters, and their covariance matrix, constitute a new and convenient method for the linear regression of Poisson-distributed count data, which are of common occurrence across a variety of fields. A comparison between this new linear regression method and two alternative methods often used for the regression of count data -- the ordinary least-square regression and the $\chi^2$ regression -- is provided with the application of these methods to the analysis of recent COVID-19 count data. The paper also discusses the relative advantages and disadvantages among these methods for the linear regression of Poisson count data.

翻译：本文介绍了一种新的半解析线性回归方法在泊松计数数据中的应用，并将其用于COVID-19事件的分析。该回归基于Bonamente和Spence（2022）提出的最佳拟合参数最大似然解，本文进一步引入了一种协方差矩阵的简单解析解，从而完善了泊松数据线性回归问题的求解。参数估计及其协方差矩阵的解析性质得益于J.Scargle（2013）提出的线性模型便利分解。该方法利用了Fisher信息矩阵的渐近性质，其逆矩阵提供了协方差矩阵。结合简单的解析方法获得参数的最大似然估计及其协方差矩阵，构成了一种新的、便捷的泊松分布计数数据线性回归方法，这类数据在多个领域普遍存在。通过将本方法与常用于计数数据回归的两种替代方法——普通最小二乘回归和χ²回归——应用于近期COVID-19计数数据的分析，进行了比较。本文还讨论了这些方法在泊松计数数据线性回归中的相对优缺点。