= Solution
{c}
Minimize the <residual sum of squares>
$$
Q(b_0,b_1,b_2)=\sum_i(Y_i-b_0-b_1x_{i1}-b_2x_{i2})^2.
$$
Setting its three <partial derivatives> to zero gives the <normal equations>
$$
\boxed{\sum_i(Y_i-\hat\beta_0-\hat\beta_1x_{i1}-\hat\beta_2x_{i2})=0,\quad
\sum_i x_{ij}(Y_i-\hat\beta_0-\hat\beta_1x_{i1}-\hat\beta_2x_{i2})=0\quad(j=1,2).}
$$
These equations characterize the <linear least squares> minimizers, since $Q$ is a convex quadratic. A unique coefficient vector additionally requires full <column rank> of the <design matrix>.
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