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 χ2 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.Comment: Accepted in Frontiers in Applied Mathematics and Statistic