  When multiple models are considered in regression problems, the model
averaging method can be used to weigh and integrate the models. In the present
study, we examined how the goodness-of-prediction of the estimator depends on
the dimensionality of explanatory variables when using a generalization of the
model averaging method in a linear model. We specifically considered the case
of high-dimensional explanatory variables, with multiple linear models deployed
for subsets of these variables. Consequently, we derived the optimal weights
that yield the best predictions. we also observe that the double-descent
phenomenon occurs in the model averaging estimator. Furthermore, we obtained
theoretical results by adapting methods such as the random forest to linear
regression models. Finally, we conducted a practical verification through
numerical experiments.
