  The coefficient of determination, the $R^2$, is often used to measure the
variance explained by an affine combination of multiple explanatory covariates.
An attribution of this explanatory contribution to each of the individual
covariates is often sought in order to draw inference regarding the importance
of each covariate with respect to the response phenomenon. A recent method for
ascertaining such an attribution is via the game theoretic Shapley value
decomposition of the coefficient of determination. Such a decomposition has the
desirable efficiency, monotonicity, and equal treatment properties. Under a
weak assumption that the joint distribution is pseudo-elliptical, we obtain the
asymptotic normality of the Shapley values. We then utilize this result in
order to construct confidence intervals and hypothesis tests regarding such
quantities. Monte Carlo studies regarding our results are provided. We found
that our asymptotic confidence intervals are computationally superior to
competing bootstrap methods and are able to improve upon the performance of
such intervals. In an expository application to Australian real estate price
modelling, we employ Shapley value confidence intervals to identify significant
differences between the explanatory contributions of covariates, between
models, which otherwise share approximately the same $R^2$ value. These
different models are based on real estate data from the same periods in 2019
and 2020, the latter covering the early stages of the arrival of the novel
coronavirus, COVID-19.
