Suppose we have a training dataset $D$ for linear regression that is the union of two (disjoint) datasets $A$ and $B$, where $|A| \gg|B|$. For example, $A$ and $B$ might represent data from two different groups of individuals. Let $\left(x_a^{(i)}, y_a^{(i)}\right)$ denote the $i$-th example in $A$ and $\left(x_b^{(i)}, y_b^{(i)}\right)$ denote the $i$-th example in $B$. The reweighted training loss is defined as
$$
L(w)=\frac{1}{|A|} \sum_{i=1}^{|A|}\left(w x_a^{(i)}-y_a^{(i)}\right)^2+\frac{1}{|B|} \sum_{i=1}^{|B|}\left(w x_b^{(i)}-y_b^{(i)}\right)^2,
$$
where $w$ is the weight parameter for linear regression (in this problem, we will omit the bias term).
Explain why this loss function is more likely to promote more equal treatment of individuals in dataset $A$ and individuals in dataset $B$, compared with running normal linear regression on $D$.
